Test
Scenario
Interpretation
Used when dealing with large sample sizes or when the population standard deviation is known.
A small p-value (smaller than 0.05) indicates strong evidence against the null hypothesis, leading to its rejection.
Appropriate for small sample sizes or when the population standard deviation is unknown.
Similar to the Z-test
Used for tests of independence or goodness-of-fit.
A small p-value indicates that there is a significant association between the categorical variables, leading to the rejection of the null hypothesis.
Commonly used in Analysis of Variance (ANOVA) to compare variances between groups.
A small p-value suggests that at least one group mean is different from the others, leading to the rejection of the null hypothesis.
Measures the strength and direction of a linear relationship between two continuous variables.
A small p-value indicates that there is a significant linear relationship between the variables, leading to rejection of the null hypothesis that there is no correlation.
In general, a small p-value indicates that the observed data is unlikely to have occurred by random chance alone, which leads to the rejection of the null hypothesis. However, it’s crucial to choose the appropriate test based on the nature of the data and the research question, as well as to interpret the p-value in the context of the specific test being used.
The table given below shows the importance of p-value and shows the various kinds of errors that occur during hypothesis testing.
|
|
|
| Correct decision based | Type I error |
| Type II error | Incorrect decision based |
Type I error: Incorrect rejection of the null hypothesis. It is denoted by α (significance level). Type II error: Incorrect acceptance of the null hypothesis. It is denoted by β (power level)
A researcher wants to investigate whether there is a significant difference in mean height between males and females in a population of university students.
Suppose we have the following data:
Starting with interpreting the process of calculating p-value
H0: There is no significant difference in mean height between males and females.
H1: There is a significant difference in mean height between males and females.
The appropriate test statistic for this scenario is the two-sample t-test, which compares the means of two independent groups.
The t-statistic is a measure of the difference between the means of two groups relative to the variability within each group. It is calculated as the difference between the sample means divided by the standard error of the difference. It is also known as the t-value or t-score.
So, the calculated two-sample t-test statistic (t) is approximately 5.13.
The t-distribution is used for the two-sample t-test . The degrees of freedom for the t-distribution are determined by the sample sizes of the two groups.
The t-distribution is a probability distribution with tails that are thicker than those of the normal distribution.
The degrees of freedom (63) represent the variability available in the data to estimate the population parameters. In the context of the two-sample t-test, higher degrees of freedom provide a more precise estimate of the population variance, influencing the shape and characteristics of the t-distribution.
T-Statistic
The t-distribution is symmetric and bell-shaped, similar to the normal distribution. As the degrees of freedom increase, the t-distribution approaches the shape of the standard normal distribution. Practically, it affects the critical values used to determine statistical significance and confidence intervals.
Step 5 : Calculate Critical Value.
To find the critical t-value with a t-statistic of 5.13 and 63 degrees of freedom, we can either consult a t-table or use statistical software.
We can use scipy.stats module in Python to find the critical t-value using below code.
Comparing with T-Statistic:
The larger t-statistic suggests that the observed difference between the sample means is unlikely to have occurred by random chance alone. Therefore, we reject the null hypothesis.
In case the significance level is not specified, consider the below general inferences while interpreting your results.
Graphically, the p-value is located at the tails of any confidence interval. [As shown in fig 1]
Fig 1: Graphical Representation
The p-value in hypothesis testing is influenced by several factors:
Understanding these factors is crucial for interpreting p-values accurately and making informed decisions in hypothesis testing.
The p-value is a crucial concept in statistical hypothesis testing, serving as a guide for making decisions about the significance of the observed relationship or effect between variables.
Let’s consider a scenario where a tutor believes that the average exam score of their students is equal to the national average (85). The tutor collects a sample of exam scores from their students and performs a one-sample t-test to compare it to the population mean (85).
Since, 0.7059>0.05 , we would conclude to fail to reject the null hypothesis. This means that, based on the sample data, there isn’t enough evidence to claim a significant difference in the exam scores of the tutor’s students compared to the national average. The tutor would accept the null hypothesis, suggesting that the average exam score of their students is statistically consistent with the national average.
The p-value is a crucial concept in statistical hypothesis testing, providing a quantitative measure of the strength of evidence against the null hypothesis. It guides decision-making by comparing the p-value to a chosen significance level, typically 0.05. A small p-value indicates strong evidence against the null hypothesis, suggesting a statistically significant relationship or effect. However, the p-value is influenced by various factors and should be interpreted alongside other considerations, such as effect size and context.
Why is p-value greater than 1.
A p-value is a probability, and probabilities must be between 0 and 1. Therefore, a p-value greater than 1 is not possible.
It means that the observed test statistic is unlikely to occur by chance if the null hypothesis is true. It represents a 1% chance of observing the test statistic or a more extreme one under the null hypothesis.
A good p-value is typically less than or equal to 0.05, indicating that the null hypothesis is likely false and the observed relationship or effect is statistically significant.
It is a measure of the statistical significance of a parameter in the model. It represents the probability of obtaining the observed value of the parameter or a more extreme one, assuming the null hypothesis is true.
A low p-value means that the observed test statistic is unlikely to occur by chance if the null hypothesis is true. It suggests that the observed relationship or effect is statistically significant and not due to random sampling variation.
Compare p-values: Lower p-value indicates stronger evidence against null hypothesis, favoring results with smaller p-values in hypothesis testing.
Similar reads.
In relation to machine learning , linear regression is defined as a predictive modeling technique that allows us to build a model which can help predict continuous response variables as a function of a linear combination of explanatory or predictor variables. While training linear regression models, we need to rely on hypothesis testing in relation to determining the relationship between the response and predictor variables. In the case of the linear regression model, two types of hypothesis testing are done. They are T-tests and F-tests . In other words, there are two types of statistics that are used to assess whether linear regression models exist representing response and predictor variables. They are t-statistics and f-statistics. As data scientists , it is of utmost importance to determine if linear regression is the correct choice of model for our particular problem and this can be done by performing hypothesis testing related to linear regression response and predictor variables. Many times, it is found that these concepts are not very clear with a lot many data scientists. In this blog post, we will discuss linear regression and hypothesis testing related to t-statistics and f-statistics . We will also provide an example to help illustrate how these concepts work.
Table of Contents
A linear regression model can be defined as the function approximation that represents a continuous response variable as a function of one or more predictor variables. While building a linear regression model, the goal is to identify a linear equation that best predicts or models the relationship between the response or dependent variable and one or more predictor or independent variables.
There are two different kinds of linear regression models. They are as follows:
While training linear regression models, the requirement is to determine the coefficients which can result in the best-fitted linear regression line. The learning algorithm used to find the most appropriate coefficients is known as least squares regression . In the least-squares regression method, the coefficients are calculated using the least-squares error function. The main objective of this method is to minimize or reduce the sum of squared residuals between actual and predicted response values. The sum of squared residuals is also called the residual sum of squares (RSS). The outcome of executing the least-squares regression method is coefficients that minimize the linear regression cost function .
The residual e of the ith observation is represented as the following where [latex]Y_i[/latex] is the ith observation and [latex]\hat{Y_i}[/latex] is the prediction for ith observation or the value of response variable for ith observation.
[latex]e_i = Y_i – \hat{Y_i}[/latex]
The residual sum of squares can be represented as the following:
[latex]RSS = e_1^2 + e_2^2 + e_3^2 + … + e_n^2[/latex]
The least-squares method represents the algorithm that minimizes the above term, RSS.
Once the coefficients are determined, can it be claimed that these coefficients are the most appropriate ones for linear regression? The answer is no. After all, the coefficients are only the estimates and thus, there will be standard errors associated with each of the coefficients. Recall that the standard error is used to calculate the confidence interval in which the mean value of the population parameter would exist. In other words, it represents the error of estimating a population parameter based on the sample data. The value of the standard error is calculated as the standard deviation of the sample divided by the square root of the sample size. The formula below represents the standard error of a mean.
[latex]SE(\mu) = \frac{\sigma}{\sqrt(N)}[/latex]
Thus, without analyzing aspects such as the standard error associated with the coefficients, it cannot be claimed that the linear regression coefficients are the most suitable ones without performing hypothesis testing. This is where hypothesis testing is needed . Before we get into why we need hypothesis testing with the linear regression model, let’s briefly learn about what is hypothesis testing?
Before getting into understanding the hypothesis testing concepts in relation to the linear regression model, let’s train a multi-variate or multiple linear regression model and print the summary output of the model which will be referred to, in the next section.
The data used for creating a multi-linear regression model is BostonHousing which can be loaded in RStudioby installing mlbench package. The code is shown below:
install.packages(“mlbench”) library(mlbench) data(“BostonHousing”)
Once the data is loaded, the code shown below can be used to create the linear regression model.
attach(BostonHousing) BostonHousing.lm <- lm(log(medv) ~ crim + chas + rad + lstat) summary(BostonHousing.lm)
Executing the above command will result in the creation of a linear regression model with the response variable as medv and predictor variables as crim, chas, rad, and lstat. The following represents the details related to the response and predictor variables:
The following will be the output of the summary command that prints the details relating to the model including hypothesis testing details for coefficients (t-statistics) and the model as a whole (f-statistics)
Hypothesis tests are the statistical procedure that is used to test a claim or assumption about the underlying distribution of a population based on the sample data. Here are key steps of doing hypothesis tests with linear regression models:
The reasons why we need to do hypothesis tests in case of a linear regression model are following:
While training linear regression models, hypothesis testing is done to determine whether the relationship between the response and each of the predictor variables is statistically significant or otherwise. The coefficients related to each of the predictor variables is determined. Then, individual hypothesis tests are done to determine whether the relationship between response and that particular predictor variable is statistically significant based on the sample data used for training the model. If at least one of the null hypotheses is rejected, it represents the fact that there exists no relationship between response and that particular predictor variable. T-statistics is used for performing the hypothesis testing because the standard deviation of the sampling distribution is unknown. The value of t-statistics is compared with the critical value from the t-distribution table in order to make a decision about whether to accept or reject the null hypothesis regarding the relationship between the response and predictor variables. If the value falls in the critical region, then the null hypothesis is rejected which means that there is no relationship between response and that predictor variable. In addition to T-tests, F-test is performed to test the null hypothesis that the linear regression model does not exist and that the value of all the coefficients is zero (0). Learn more about the linear regression and t-test in this blog – Linear regression t-test: formula, example .
One response.
Very informative
Your email address will not be published. Required fields are marked *
I found it very helpful. However the differences are not too understandable for me
Very Nice Explaination. Thankyiu very much,
in your case E respresent Member or Oraganization which include on e or more peers?
Such a informative post. Keep it up
Thank you....for your support. you given a good solution for me.
Salvatore S. Mangiafico
Search Rcompanion.org
Traditionally when students first learn about the analysis of experiments, there is a strong focus on hypothesis testing and making decisions based on p -values. Hypothesis testing is important for determining if there are statistically significant effects. However, readers of this book should not place undo emphasis on p -values. Instead, they should realize that p -values are affected by sample size, and that a low p -value does not necessarily suggest a large effect or a practically meaningful effect. Summary statistics, plots, effect size statistics, and practical considerations should be used. The goal is to determine: a) statistical significance, b) effect size, c) practical importance. These are all different concepts, and they will be explored below.
Most of what we’ve covered in this book so far is about producing descriptive statistics: calculating means and medians, plotting data in various ways, and producing confidence intervals. The bulk of the rest of this book will cover statistical inference: using statistical tests to draw some conclusion about the data. We’ve already done this a little bit in earlier chapters by using confidence intervals to conclude if means are different or not among groups.
As Dr. Nic mentions in her article in the “References and further reading” section, this is the part where people sometimes get stumped. It is natural for most of us to use summary statistics or plots, but jumping to statistical inference needs a little change in perspective. The idea of using some statistical test to answer a question isn’t a difficult concept, but some of the following discussion gets a little theoretical. The video from the Statistics Learning Center in the “References and further reading” section does a good job of explaining the basis of statistical inference.
One important thing to gain from this chapter is an understanding of how to use the p -value, alpha , and decision rule to test the null hypothesis. But once you are comfortable with that, you will want to return to this chapter to have a better understanding of the theory behind this process.
Another important thing is to understand the limitations of relying on p -values, and why it is important to assess the size of effects and weigh practical considerations.
The packages used in this chapter include:
The following commands will install these packages if they are not already installed:
if(!require(lsr)){install.packages("lsr")}
The null and alternative hypotheses.
The statistical tests in this book rely on testing a null hypothesis, which has a specific formulation for each test. The null hypothesis always describes the case where e.g. two groups are not different or there is no correlation between two variables, etc.
The alternative hypothesis is the contrary of the null hypothesis, and so describes the cases where there is a difference among groups or a correlation between two variables, etc.
Notice that the definitions of null hypothesis and alternative hypothesis have nothing to do with what you want to find or don't want to find, or what is interesting or not interesting, or what you expect to find or what you don’t expect to find. If you were comparing the height of men and women, the null hypothesis would be that the height of men and the height of women were not different. Yet, you might find it surprising if you found this hypothesis to be true for some population you were studying. Likewise, if you were studying the income of men and women, the null hypothesis would be that the income of men and women are not different, in the population you are studying. In this case you might be hoping the null hypothesis is true, though you might be unsurprised if the alternative hypothesis were true. In any case, the null hypothesis will take the form that there is no difference between groups, there is no correlation between two variables, or there is no effect of this variable in our model.
Most of the tests in this book rely on using a statistic called the p -value to evaluate if we should reject, or fail to reject, the null hypothesis.
Given the assumption that the null hypothesis is true , the p -value is defined as the probability of obtaining a result equal to or more extreme than what was actually observed in the data.
We’ll unpack this definition in a little bit.
The p -value for the given data will be determined by conducting the statistical test.
This p -value is then compared to a pre-determined value alpha . Most commonly, an alpha value of 0.05 is used, but there is nothing magic about this value.
If the p -value for the test is less than alpha , we reject the null hypothesis.
If the p -value is greater than or equal to alpha , we fail to reject the null hypothesis.
For an example of using the p -value for hypothesis testing, imagine you have a coin you will toss 100 times. The null hypothesis is that the coin is fair—that is, that it is equally likely that the coin will land on heads as land on tails. The alternative hypothesis is that the coin is not fair. Let’s say for this experiment you throw the coin 100 times and it lands on heads 95 times out of those hundred. The p -value in this case would be the probability of getting 95, 96, 97, 98, 99, or 100 heads, or 0, 1, 2, 3, 4, or 5 heads, assuming that the null hypothesis is true .
This is what we call a two-sided test, since we are testing both extremes suggested by our data: getting 95 or greater heads or getting 95 or greater tails. In most cases we will use two sided tests.
You can imagine that the p -value for this data will be quite small. If the null hypothesis is true, and the coin is fair, there would be a low probability of getting 95 or more heads or 95 or more tails.
Using a binomial test, the p -value is < 0.0001.
(Actually, R reports it as < 2.2e-16, which is shorthand for the number in scientific notation, 2.2 x 10 -16 , which is 0.00000000000000022, with 15 zeros after the decimal point.)
Assuming an alpha of 0.05, since the p -value is less than alpha , we reject the null hypothesis. That is, we conclude that the coin is not fair.
binom.test(5, 100, 0.5)
Exact binomial test number of successes = 5, number of trials = 100, p-value < 2.2e-16 alternative hypothesis: true probability of success is not equal to 0.5
As another example, imagine we are considering two classrooms, and we have counts of students who passed a certain exam. We want to know if one classroom had statistically more passes or failures than the other.
In our example each classroom will have 10 students. The data is arranged into a contingency table.
Classroom Passed Failed A 8 2 B 3 7
We will use Fisher’s exact test to test if there is an association between Classroom and the counts of passed and failed students. The null hypothesis is that there is no association between Classroom and Passed/Failed , based on the relative counts in each cell of the contingency table.
Input =(" Classroom Passed Failed A 8 2 B 3 7 ") Matrix = as.matrix(read.table(textConnection(Input), header=TRUE, row.names=1)) Matrix
Passed Failed A 8 2 B 3 7
fisher.test(Matrix)
Fisher's Exact Test for Count Data p-value = 0.06978
The reported p -value is 0.070. If we use an alpha of 0.05, then the p -value is greater than alpha , so we fail to reject the null hypothesis. That is, we did not have sufficient evidence to say that there is an association between Classroom and Passed/Failed .
More extreme data in this case would be if the counts in the upper left or lower right (or both!) were greater.
Classroom Passed Failed A 9 1 B 3 7 Classroom Passed Failed A 10 0 B 3 7 and so on, with Classroom B...
In most cases we would want to consider as "extreme" not only the results when Classroom A has a high frequency of passing students, but also results when Classroom B has a high frequency of passing students. This is called a two-sided or two-tailed test. If we were only concerned with one classroom having a high frequency of passing students, relatively, we would instead perform a one-sided test. The default for the fisher.test function is two-sided, and usually you will want to use two-sided tests.
Classroom Passed Failed A 2 8 B 7 3 Classroom Passed Failed A 1 9 B 7 3 Classroom Passed Failed A 0 10 B 7 3 and so on, with Classroom B...
In both cases, "extreme" means there is a stronger association between Classroom and Passed/Failed .
Wait, does this make any sense.
Recall that the definition of the p -value is:
The astute reader might be asking herself, “If I’m trying to determine if the null hypothesis is true or not, why would I start with the assumption that the null hypothesis is true? And why am I using a probability of getting certain data given that a hypothesis is true? Don’t I want to instead determine the probability of the hypothesis given my data?”
The answer is yes , we would like a method to determine the likelihood of our hypothesis being true given our data, but we use the Null Hypothesis Significance Test approach since it is relatively straightforward, and has wide acceptance historically and across disciplines.
In practice we do use the results of the statistical tests to reach conclusions about the null hypothesis.
Technically, the p -value says nothing about the alternative hypothesis. But logically, if the null hypothesis is rejected, then its logical complement, the alternative hypothesis, is supported. Practically, this is how we handle significant p -values, though this practical approach generates disapproval in some theoretical circles.
Note the language used when testing the null hypothesis. Based on the results of our statistical tests, we either reject the null hypothesis, or fail to reject the null hypothesis.
This is somewhat similar to the approach of a jury in a trial. The jury either finds sufficient evidence to declare someone guilty, or fails to find sufficient evidence to declare someone guilty.
Failing to convict someone isn’t necessarily the same as declaring someone innocent. Likewise, if we fail to reject the null hypothesis, we shouldn’t assume that the null hypothesis is true. It may be that we didn’t have sufficient samples to get a result that would have allowed us to reject the null hypothesis, or maybe there are some other factors affecting the results that we didn’t account for. This is similar to an “innocent until proven guilty” stance.
For the most part, the statistical tests we use are based on probability, and our data could always be the result of chance. Considering the coin flipping example above, if we did flip a coin 100 times and came up with 95 heads, we would be compelled to conclude that the coin was not fair. But 95 heads could happen with a fair coin strictly by chance.
We can, therefore, make two kinds of errors in testing the null hypothesis:
• A Type I error occurs when the null hypothesis really is true, but based on our decision rule we reject the null hypothesis. In this case, our result is a false positive ; we think there is an effect (unfair coin, association between variables, difference among groups) when really there isn’t. The probability of making this kind error is alpha , the same alpha we used in our decision rule.
• A Type II error occurs when the null hypothesis is really false, but based on our decision rule we fail to reject the null hypothesis. In this case, our result is a false negative ; we have failed to find an effect that really does exist. The probability of making this kind of error is called beta .
The following table summarizes these errors.
Reality ___________________________________ Decision of Test Null is true Null is false Reject null hypothesis Type I error Correctly (prob. = alpha) reject null (prob. = 1 – beta) Retain null hypothesis Correctly Type II error retain null (prob. = beta) (prob. = 1 – alpha)
The statistical power of a test is a measure of the ability of the test to detect a real effect. It is related to the effect size, the sample size, and our chosen alpha level.
The effect size is a measure of how unfair a coin is, how strong the association is between two variables, or how large the difference is among groups. As the effect size increases or as the number of observations we collect increases, or as the alpha level increases, the power of the test increases.
Statistical power in the table above is indicated by 1 – beta , and power is the probability of correctly rejecting the null hypothesis.
An example should make these relationship clear. Imagine we are sampling a large group of 7 th grade students for their height. That is, the group is the population, and we are sampling a sub-set of these students. In reality, for students in the population, the girls are taller than the boys, but the difference is small (that is, the effect size is small), and there is a lot of variability in students’ heights. You can imagine that in order to detect the difference between girls and boys that we would have to measure many students. If we fail to sample enough students, we might make a Type II error. That is, we might fail to detect the actual difference in heights between sexes.
If we had a different experiment with a larger effect size—for example the weight difference between mature hamsters and mature hedgehogs—we might need fewer samples to detect the difference.
Note also, that our chosen alpha plays a role in the power of our test, too. All things being equal, across many tests, if we decrease our alph a, that is, insist on a lower rate of Type I errors, we are more likely to commit a Type II error, and so have a lower power. This is analogous to a case of a meticulous jury that has a very high standard of proof to convict someone. In this case, the likelihood of a false conviction is low, but the likelihood of a letting a guilty person go free is relatively high.
The level of alpha is traditionally set at 0.05 in some disciplines, though there is sometimes reason to choose a different value.
One situation in which the alpha level is increased is in preliminary studies in which it is better to include potentially significant effects even if there is not strong evidence for keeping them. In this case, the researcher is accepting an inflated chance of Type I errors in order to decrease the chance of Type II errors.
Imagine an experiment in which you wanted to see if various environmental treatments would improve student learning. In a preliminary study, you might have many treatments, with few observations each, and you want to retain any potentially successful treatments for future study. For example, you might try playing classical music, improved lighting, complimenting students, and so on, and see if there is any effect on student learning. You might relax your alpha value to 0.10 or 0.15 in the preliminary study to see what treatments to include in future studies.
On the other hand, in situations where a Type I, false positive, error might be costly in terms of money or people’s health, a lower alpha can be used, perhaps, 0.01 or 0.001. You can imagine a case in which there is an established treatment for cancer, and a new treatment is being tested. Because the new treatment is likely to be expensive and to hold people’s lives in the balance, a researcher would want to be very sure that the new treatment is more effective than the established treatment. In reality, the researchers would not just lower the alpha level, but also look at the effect size, submit the research for peer review, replicate the study, be sure there were no problems with the design of the study or the data collection, and weigh the practical implications.
In theory, as a researcher, you would determine the alpha level you feel is appropriate. That is, the probability of making a Type I error when the null hypothesis is in fact true.
In reality, though, 0.05 is almost always used in most fields for readers of this book. Choosing a different alpha value will rarely go without question. It is best to keep with the 0.05 level unless you have good justification for another value, or are in a discipline where other values are routinely used.
One good practice is to report actual p -values from analyses. It is fine to also simply say, e.g. “The dependent variable was significantly correlated with variable A ( p < 0.05).” But I prefer when possible to say, “The dependent variable was significantly correlated with variable A ( p = 0.026).
It is probably best to avoid using terms like “marginally significant” or “borderline significant” for p -values less than 0.10 but greater than 0.05, though you might encounter similar phrases. It is better to simply report the p -values of tests or effects in straight-forward manner. If you had cause to include certain model effects or results from other tests, they can be reported as e.g., “Variables correlated with the dependent variable with p < 0.15 were A , B , and C .”
Considering some of the examples presented, it may have occurred to the reader to ask if the null hypothesis is ever really true. For example, in some population of 7 th graders, if we could measure everyone in the population to a high degree of precision, then there must be some difference in height between girls and boys. This is an important limitation of null hypothesis significance testing. Often, if we have many observations, even small effects will be reported as significant. This is one reason why it is important to not rely too heavily on p -values, but to also look at the size of the effect and practical considerations. In this example, if we sampled many students and the difference in heights was 0.5 cm, even if significant, we might decide that this effect is too small to be of practical importance, especially relative to an average height of 150 cm. (Here, the difference would be 0.3% of the average height).
Practical importance and statistical significance.
It is important to remember to not let p -values be the only guide for drawing conclusions. It is equally important to look at the size of the effects you are measuring, as well as take into account other practical considerations like the costs of choosing a certain path of action.
For example, imagine we want to compare the SAT scores of two SAT preparation classes with a t -test.
Class.A = c(1500, 1505, 1505, 1510, 1510, 1510, 1515, 1515, 1520, 1520) Class.B = c(1510, 1515, 1515, 1520, 1520, 1520, 1525, 1525, 1530, 1530) t.test(Class.A, Class.B)
Welch Two Sample t-test t = -3.3968, df = 18, p-value = 0.003214 mean of x mean of y 1511 1521
The p -value is reported as 0.003, so we would consider there to be a significant difference between the two classes ( p < 0.05).
But we have to ask ourselves the practical question, is a difference of 10 points on the SAT large enough for us to care about? What if enrolling in one class costs significantly more than the other class? Is it worth the extra money for a difference of 10 points on average?
It should be remembered that p -values do not indicate the size of the effect being studied. It shouldn’t be assumed that a small p -value indicates a large difference between groups, or vice-versa.
For example, in the SAT example above, the p -value is fairly small, but the size of the effect (difference between classes) in this case is relatively small (10 points, especially small relative to the range of scores students receive on the SAT).
In converse, there could be a relatively large size of the effects, but if there is a lot of variability in the data or the sample size is not large enough, the p -value could be relatively large.
In this example, the SAT scores differ by 100 points between classes, but because the variability is greater than in the previous example, the p -value is not significant.
Class.C = c(1000, 1100, 1200, 1250, 1300, 1300, 1400, 1400, 1450, 1500) Class.D = c(1100, 1200, 1300, 1350, 1400, 1400, 1500, 1500, 1550, 1600) t.test(Class.C, Class.D)
Welch Two Sample t-test t = -1.4174, df = 18, p-value = 0.1735 mean of x mean of y 1290 1390
boxplot(cbind(Class.C, Class.D))
It should also be remembered that p -values are affected by sample size. For a given effect size and variability in the data, as the sample size increases, the p -value is likely to decrease. For large data sets, small effects can result in significant p -values.
As an example, let’s take the data from Class.C and Class.D and double the number of observations for each without changing the distribution of the values in each, and rename them Class.E and Class.F .
Class.E = c(1000, 1100, 1200, 1250, 1300, 1300, 1400, 1400, 1450, 1500, 1000, 1100, 1200, 1250, 1300, 1300, 1400, 1400, 1450, 1500) Class.F = c(1100, 1200, 1300, 1350, 1400, 1400, 1500, 1500, 1550, 1600, 1100, 1200, 1300, 1350, 1400, 1400, 1500, 1500, 1550, 1600) t.test(Class.E, Class.F)
Welch Two Sample t-test t = -2.0594, df = 38, p-value = 0.04636 mean of x mean of y 1290 1390
boxplot(cbind(Class.E, Class.F))
Notice that the p -value is lower for the t -test for Class.E and Class.F than it was for Class.C and Class.D . Also notice that the means reported in the output are the same, and the box plots would look the same.
One way to account for the effect of sample size on our statistical tests is to consider effect size statistics. These statistics reflect the size of the effect in a standardized way, and are unaffected by sample size.
An appropriate effect size statistic for a t -test is Cohen’s d . It takes the difference in means between the two groups and divides by the pooled standard deviation of the groups. Cohen’s d equals zero if the means are the same, and increases to infinity as the difference in means increases relative to the standard deviation.
In the following, note that Cohen’s d is not affected by the sample size difference in the Class.C / Class.D and the Class.E / Class.F examples.
library(lsr) cohensD(Class.C, Class.D, method = "raw")
cohensD(Class.E, Class.F, method = "raw")
Effect size statistics are standardized so that they are not affected by the units of measurements of the data. This makes them interpretable across different situations, or if the reader is not familiar with the units of measurement in the original data. A Cohen’s d of 1 suggests that the two means differ by one pooled standard deviation. A Cohen’s d of 0.5 suggests that the two means differ by one-half the pooled standard deviation.
For example, if we create new variables— Class.G and Class.H —that are the SAT scores from the previous example expressed as a proportion of a 1600 score, Cohen’s d will be the same as in the previous example.
Class.G = Class.E / 1600 Class.H = Class.F / 1600 Class.G Class.H cohensD(Class.G, Class.H, method="raw")
Statistics is not like a trial.
When analyzing data, the analyst should not approach the task as would a lawyer for the prosecution. That is, the analyst should not be searching for significant effects and tests, but should instead be like an independent investigator using lines of evidence to find out what is most likely to true given the data, graphical analysis, and statistical analysis available.
The problem of multiple p -values
One concept that will be in important in the following discussion is that when there are multiple tests producing multiple p -values, that there is an inflation of the Type I error rate. That is, there is a higher chance of making false-positive errors.
This simply follows mathematically from the definition of alpha . If we allow a probability of 0.05, or 5% chance, of making a Type I error for any one test, as we do more and more tests, the chances that at least one of them having a false positive becomes greater and greater.
One way we deal with the problem of multiple p -values in statistical analyses is to adjust p -values when we do a series of tests together (for example, if we are comparing the means of multiple groups).
There are various p -value adjustments available in R. In some cases, we will use FDR, which stands for false discovery rate , and in R is an alias for the Benjamini and Hochberg method. There are also cases in which we’ll use Tukey range adjustment to correct for the family-wise error rate.
Unfortunately, students in analysis of experiments courses often learn to use Bonferroni adjustment for p -values. This method is simple to do with hand calculations, but is excessively conservative in most situations, and, in my opinion, antiquated.
There are other p -value adjustment methods, and the choice of which one to use is dictated either by which are common in your field of study, or by doing enough reading to understand which are statistically most appropriate for your application.
The statistical tests covered in this book assume that tests are preplanned for their p -values to be accurate. That is, in theory, you set out an experiment, collect the data as planned, and then say “I’m going to analyze it with kind of model and do these post-hoc tests afterwards”, and report these results, and that’s all you would do.
Some authors emphasize this idea of preplanned tests. In contrast is an exploratory data analysis approach that relies upon examining the data with plots and using simple tests like correlation tests to suggest what statistical analysis makes sense.
If an experiment is set out in a specific design, then usually it is appropriate to use the analysis suggested by this design.
It is important when approaching data from an exploratory approach, to avoid committing p -value hacking. Imagine the case in which the researcher collects many different measurements across a range of subjects. The researcher might be tempted to simply try different tests and models to relate one variable to another, for all the variables. He might continue to do this until he found a test with a significant p -value.
But this would be a form of p -value hacking.
Because an alpha value of 0.05 allows us to make a false-positive error five percent of the time, finding one p -value below 0.05 after several successive tests may simply be due to chance.
Some forms of p -value hacking are more egregious. For example, if one were to collect some data, run a test, and then continue to collect data and run tests iteratively until a significant p -value is found.
A related issue in science is that there is a bias to publish, or to report, only significant results. This can also lead to an inflation of the false-positive rate. As a hypothetical example, imagine if there are currently 20 similar studies being conducted testing a similar effect—let’s say the effect of glucosamine supplements on joint pain. If 19 of those studies found no effect and so were discarded, but one study found an effect using an alpha of 0.05, and was published, is this really any support that glucosamine supplements decrease joint pain?
"statistically significant".
In the context of this book, the term "significant" means "statistically significant".
Whenever the decision rule finds that p < alpha , the difference in groups, the association, or the correlation under consideration is then considered "statistically significant" or "significant".
No effect size or practical considerations enter into determining whether an effect is “significant” or not. The only exception is that test assumptions and requirements for appropriate data must also be met in order for the p -value to be valid.
What you need to consider :
• The null hypothesis
• p , alpha , and the decision rule,
• Your result. That is, whether the difference in groups, the association, or the correlation is significant or not.
• The p -value
• The conclusion, e.g. "There was a significant difference in the mean heights of boys and girls in the class." It is best to preface this with the "reject" or "fail to reject" language concerning your decision about the null hypothesis.
In the context of this book, I use the term "size of the effect" to suggest the use of summary statistics to indicate how large an effect is. This may be, for example the difference in two medians. I try reserve the term “effect size” to refer to the use of effect size statistics. This distinction isn’t necessarily common.
Usually you will consider an effect in relation to the magnitude of measurements. That is, you might look at the difference in medians as a percent of the median of one group or of the global median. Or, you might look at the difference in medians in relation to the range of answers. For example, a one-point difference on a 5-point Likert item. Counts might be expressed as proportions of totals or subsets.
What you should report on assignments :
• The size of the effect. That is, the difference in medians or means, the difference in counts, or the proportions of counts among groups.
• Where appropriate, the size of the effect expressed as a percentage or proportion.
• If there is an effect size statistic—such as r , epsilon -squared, phi , Cramér's V , or Cohen's d —: report this and its interpretation (small, medium, large), and incorporate this into your conclusion.
If there is a significant result, the question of practical importance asks if the difference or association is large enough to matter in the real world.
If there is no significant result, the question of practical importance asks if the a difference or association is large enough to warrant another look, for example by running another test with a larger sample size or that controls variability in observations better.
• Your conclusion as to whether this effect is large enough to be important in the real world.
• The context, explanation, or support to justify your conclusion.
• In some cases you might include considerations that aren't included in the data presented. Examples might include the cost of one treatment over another, including time investment, or whether there is a large risk in selecting one treatment over another (e.g., if people's lives are on the line).
Significant.
xkcd.com/882/
xkcd.com/892/
xkcd.com/1478/
Types of experimental designs, experimental designs.
A true experimental design assigns treatments in a systematic manner. The experimenter must be able to manipulate the experimental treatments and assign them to subjects. Since treatments are randomly assigned to subjects, a causal inference can be made for significant results. That is, we can say that the variation in the dependent variable is caused by the variation in the independent variable.
For interval/ratio data, traditional experimental designs can be analyzed with specific parametric models, assuming other model assumptions are met. These traditional experimental designs include:
• Completely random design
• Randomized complete block design
• Factorial
• Split-plot
• Latin square
Often a researcher cannot assign treatments to individual experimental units, but can assign treatments to groups. For example, if students are in a specific grade or class, it would not be practical to randomly assign students to grades or classes. But different classes could receive different treatments (such as different curricula). Causality can be inferred cautiously if treatments are randomly assigned and there is some understanding of the factors that affect the outcome.
In observational studies, the independent variables are not manipulated, and no treatments are assigned. Surveys are often like this, as are studies of natural systems without experimental manipulation. Statistical analysis can reveal the relationships among variables, but causality cannot be inferred. This is because there may be other unstudied variables that affect the measured variables in the study.
Good sampling practices are critical for producing good data. In general, samples need to be collected in a random fashion so that bias is avoided.
In survey data, bias is often introduced by a self-selection bias. For example, internet or telephone surveys include only those who respond to these requests. Might there be some relevant difference in the variables of interest between those who respond to such requests and the general population being surveyed? Or bias could be introduced by the researcher selecting some subset of potential subjects, for example only surveying a 4-H program with particularly cooperative students and ignoring other clubs. This is sometimes called “convenience sampling”.
In election forecasting, good pollsters need to account for selection bias and other biases in the survey process. For example, if a survey is done by landline telephone, those being surveyed are more likely to be older than the general population of voters, and so likely to have a bias in their voting patterns.
It is sometimes necessary to change experimental conditions during the course of an experiment. Equipment might fail, or unusual weather may prevent making meaningful measurements.
But in general, it is much better to plan ahead and be consistent with measurements.
People sometimes have the tendency to change measurement frequency or experimental treatments during the course of a study. This inevitably causes headaches in trying to analyze data, and makes writing up the results messy. Try to avoid this.
If you are testing an experimental treatment, include a check treatment that almost certainly will have an effect and a control treatment that almost certainly won’t. A control treatment will receive no treatment and a check treatment will receive a treatment known to be successful. In an educational setting, perhaps a control group receives no instruction on the topic but on another topic, and the check group will receive standard instruction.
Including checks and controls helps with the analysis in a practical sense, since they serve as standard treatments against which to compare the experimental treatments. In the case where the experimental treatments have similar effects, controls and checks allow you say, for example, “Means for the all experimental treatments were similar, but were higher than the mean for control, and lower than the mean for check treatment.”
It often happens that measuring equipment fails or that a certain measurement doesn’t produce the expected results. It is therefore helpful to include measurements of several variables that can capture the potential effects. Perhaps test scores of students won’t show an effect, but a self-assessment question on how much students learned will.
Including additional independent variables that might affect the dependent variable is often helpful in an analysis. In an educational setting, you might assess student age, grade, school, town, background level in the subject, or how well they are feeling that day.
The effects of covariates on the dependent variable may be of interest in itself. But also, including co-variates in an analysis can better model the data, sometimes making treatment effects more clear or making a model better meet model assumptions.
The nhst controversy.
Particularly in the fields of psychology and education, there has been much criticism of the null hypothesis significance test approach. From my reading, the main complaints against NHST tend to be:
• Students and researchers don’t really understand the meaning of p -values.
• p -values don’t include important information like confidence intervals or parameter estimates.
• p -values have properties that may be misleading, for example that they do not represent effect size, and that they change with sample size.
• We often treat an alpha of 0.05 as a magical cutoff value.
Personally, I don’t find these to be very convincing arguments against the NHST approach.
The first complaint is in some sense pedantic: Like so many things, students and researchers learn the definition of p -values at some point and then eventually forget. This doesn’t seem to impact the usefulness of the approach.
The second point has weight only if researchers use only p -values to draw conclusions from statistical tests. As this book points out, one should always consider the size of the effects and practical considerations of the effects, as well present finding in table or graphical form, including confidence intervals or measures of dispersion. There is no reason why parameter estimates, goodness-of-fit statistics, and confidence intervals can’t be included when a NHST approach is followed.
The properties in the third point also don’t count much as criticism if one is using p -values correctly. One should understand that it is possible to have a small effect size and a small p -value, and vice-versa. This is not a problem, because p -values and effect sizes are two different concepts. We shouldn’t expect them to be the same. The fact that p -values change with sample size is also in no way problematic to me. It makes sense that when there is a small effect size or a lot of variability in the data that we need many samples to conclude the effect is likely to be real.
(One case where I think the considerations in the preceding point are commonly problematic is when people use statistical tests to check for the normality or homogeneity of data or model residuals. As sample size increases, these tests are better able to detect small deviations from normality or homoscedasticity. Too many people use them and think their model is inappropriate because the test can detect a small effect size, that is, a small deviation from normality or homoscedasticity).
The fourth point is a good one. It doesn’t make much sense to come to one conclusion if our p -value is 0.049 and the opposite conclusion if our p -value is 0.051. But I think this can be ameliorated by reporting the actual p -values from analyses, and relying less on p -values to evaluate results.
Overall it seems to me that these complaints condemn poor practices that the authors observe: not reporting the size of effects in some manner; not including confidence intervals or measures of dispersion; basing conclusions solely on p -values; and not including important results like parameter estimates and goodness-of-fit statistics.
Estimates and confidence intervals.
One approach to determining statistical significance is to use estimates and confidence intervals. Estimates could be statistics like means, medians, proportions, or other calculated statistics. This approach can be very straightforward, easy for readers to understand, and easy to present clearly.
The most popular competitor to the NHST approach is Bayesian inference. Bayesian inference has the advantage of calculating the probability of the hypothesis given the data , which is what we thought we should be doing in the “Wait, does this make any sense?” section above. Essentially it takes prior knowledge about the distribution of the parameters of interest for a population and adds the information from the measured data to reassess some hypothesis related to the parameters of interest. If the reader will excuse the vagueness of this description, it makes intuitive sense. We start with what we suspect to be the case, and then use new data to assess our hypothesis.
One disadvantage of the Bayesian approach is that it is not obvious in most cases what could be used for legitimate prior information. A second disadvantage is that conducting Bayesian analysis is not as straightforward as the tests presented in this book.
[Video] “Understanding statistical inference” from Statistics Learning Center (Dr. Nic). 2015. www.youtube.com/watch?v=tFRXsngz4UQ .
[Video] “Hypothesis tests, p-value” from Statistics Learning Center (Dr. Nic). 2011. www.youtube.com/watch?v=0zZYBALbZgg .
[Video] “Understanding the p-value” from Statistics Learning Center (Dr. Nic). 2011.
www.youtube.com/watch?v=eyknGvncKLw .
[Video] “Important statistical concepts: significance, strength, association, causation” from Statistics Learning Center (Dr. Nic). 2012. www.youtube.com/watch?v=FG7xnWmZlPE .
“Understanding statistical inference” from Dr. Nic. 2015. Learn and Teach Statistics & Operations Research. creativemaths.net/blog/understanding-statistical-inference/ .
“Basic concepts of hypothesis testing” in McDonald, J.H. 2014. Handbook of Biological Statistics . www.biostathandbook.com/hypothesistesting.html .
“Hypothesis testing” , section 4.3, in Diez, D.M., C.D. Barr , and M. Çetinkaya-Rundel. 2012. OpenIntro Statistics , 2nd ed. www.openintro.org/ .
“Hypothesis Testing with One Sample”, sections 9.1–9.2 in Openstax. 2013. Introductory Statistics . openstax.org/textbooks/introductory-statistics .
"Proving causation" from Dr. Nic. 2013. Learn and Teach Statistics & Operations Research. creativemaths.net/blog/proving-causation/ .
[Video] “Variation and Sampling Error” from Statistics Learning Center (Dr. Nic). 2014. www.youtube.com/watch?v=y3A0lUkpAko .
[Video] “Sampling: Simple Random, Convenience, systematic, cluster, stratified” from Statistics Learning Center (Dr. Nic). 2012. www.youtube.com/watch?v=be9e-Q-jC-0 .
“Confounding variables” in McDonald, J.H. 2014. Handbook of Biological Statistics . www.biostathandbook.com/confounding.html .
“Overview of data collection principles” , section 1.3, in Diez, D.M., C.D. Barr , and M. Çetinkaya-Rundel. 2012. OpenIntro Statistics , 2nd ed. www.openintro.org/ .
“Observational studies and sampling strategies” , section 1.4, in Diez, D.M., C.D. Barr , and M. Çetinkaya-Rundel. 2012. OpenIntro Statistics , 2nd ed. www.openintro.org/ .
“Experiments” , section 1.5, in Diez, D.M., C.D. Barr , and M. Çetinkaya-Rundel. 2012. OpenIntro Statistics , 2nd ed. www.openintro.org/ .
1. Which of the following pair is the null hypothesis?
A) The number of heads from the coin is not different from the number of tails.
B) The number of heads from the coin is different from the number of tails.
2. Which of the following pair is the null hypothesis?
A) The height of boys is different than the height of girls.
B) The height of boys is not different than the height of girls.
3. Which of the following pair is the null hypothesis?
A) There is an association between classroom and sex. That is, there is a difference in counts of girls and boys between the classes.
B) There is no association between classroom and sex. That is, there is no difference in counts of girls and boys between the classes.
4. We flip a coin 10 times and it lands on heads 7 times. We want to know if the coin is fair.
a. What is the null hypothesis?
b. Looking at the code below, and assuming an alpha of 0.05,
What do you decide (use the reject or fail to reject language)?
c. In practical terms, what do you conclude?
binom.test(7, 10, 0.5)
Exact binomial test number of successes = 7, number of trials = 10, p-value = 0.3438
5. We measure the height of 9 boys and 9 girls in a class, in centimeters. We want to know if one group is taller than the other.
c. In practical terms, what do you conclude? Address the practical importance of the results.
Girls = c(152, 150, 140, 160, 145, 155, 150, 152, 147) Boys = c(144, 142, 132, 152, 137, 147, 142, 144, 139) t.test(Girls, Boys)
Welch Two Sample t-test t = 2.9382, df = 16, p-value = 0.009645 mean of x mean of y 150.1111 142.1111
mean(Boys) sd(Boys) quantile(Boys)
mean(Girls) sd(Girls) quantile(Girls) boxplot(cbind(Girls, Boys))
6. We count the number of boys and girls in two classrooms. We are interested to know if there is an association between the classrooms and the number of girls and boys. That is, does the proportion of boys and girls differ statistically across the two classrooms?
Classroom Girls Boys A 13 7 B 5 15
Input =(" Classroom Girls Boys A 13 7 B 5 15 ") Matrix = as.matrix(read.table(textConnection(Input), header=TRUE, row.names=1)) fisher.test(Matrix)
Fisher's Exact Test for Count Data p-value = 0.02484
Matrix rowSums(Matrix) colSums(Matrix) prop.table(Matrix, margin=1) ### Proportions for each row barplot(t(Matrix), beside = TRUE, legend = TRUE, ylim = c(0, 25), xlab = "Class", ylab = "Count")
7. Why should you not rely solely on p -values to make a decision in the real world? (You should have at least two reasons.)
8. Create your own example to show the importance of considering the size of the effect . Describe the scenario: what the research question is, and what kind of data were collected. You may make up data and provide real results, or report hypothetical results.
9. Create your own example to show the importance of weighing other practical considerations . Describe the scenario: what the research question is, what kind of data were collected, what statistical results were reached, and what other practical considerations were brought to bear.
10. What is 5e-4 in common decimal notation?
©2016 by Salvatore S. Mangiafico. Rutgers Cooperative Extension, New Brunswick, NJ.
Non-commercial reproduction of this content, with attribution, is permitted. For-profit reproduction without permission is prohibited.
If you use the code or information in this site in a published work, please cite it as a source. Also, if you are an instructor and use this book in your course, please let me know. My contact information is on the About the Author of this Book page.
Mangiafico, S.S. 2016. Summary and Analysis of Extension Program Evaluation in R, version 1.20.07, revised 2024. rcompanion.org/handbook/ . (Pdf version: rcompanion.org/documents/RHandbookProgramEvaluation.pdf .)
Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Q&A for work
Connect and share knowledge within a single location that is structured and easy to search.
Regarding the p-value of multiple linear regression analysis, the introduction from Minitab's website is shown below.
The p-value for each term tests the null hypothesis that the coefficient is equal to zero (no effect). A low p-value (< 0.05) indicates that you can reject the null hypothesis. In other words, a predictor that has a low p-value is likely to be a meaningful addition to your model because changes in the predictor's value are related to changes in the response variable.
For example, I have a resultant MLR model as $ y=0.46753{{X}_{1}}-0.2668{{X}_{2}}+1.6193{{X}_{3}}+4.5424{{X}_{4}}+14.48 $. and the out put is shown below. Then a $y$ can be calculated using this equation.
Based on the introduction above, the null hypothesis is that the coefficient equals 0. My understanding is that the coefficient, for example the coefficient of $X_{4}$, will be set as 0 and another y will be calculated as $y_{2}=0.46753{{X}_{1}}-0.2668{{X}_{2}}+1.6193{{X}_{3}}+0{{X}_{4}}+14.48$. Then a paired t-test is conducted for $y$ and $y_{2}$, but the p-value of this t-test is 6.9e-12 which does not equal to 0.1292 (p-value of coefficient of $X_{4}$.
Can anyone help on the correct understanding? Many thanks!
This is incorrect for a couple reasons:
The model "without" X4 will not necessarily have the same coefficient estimates for the other values. Fit the reduced model and see for yourself.
The statistical test for the coefficient does not concern the "mean" values of Y obtained from 2 predictions. The predicted $Y$ will always have the same grand mean, thus have a p-value from the t-test equal to 0.5. The same holds for the residuals. Your t-test had the wrong value per the point above.
The statistical test which is conducted for the statistical significance of the coefficient is a one sample t-test. This is confusing since we do not have a "sample" of multiple coefficients for X4, but we have an estimate of the distributional properties of such a sample using the central limit theorem. The mean and standard error describe the location and shape of such a limiting distribution. If you take the column "Est" and divide by "SE" and compare to a standard normal distribution, this gives you the p-values in the 4th column.
A fourth point: a criticism of minitab's help page. Such a help file could not, in a paragraph, summarize years of statistical training, so I need not contend with the whole thing. But, to say that a "predictor" is "an important contribution" is vague and probably incorrect. The rationale for choosing which variables to include in a multivariate model is subtle and relies on scientific reasoning and not statistical inference.
Your initial interpretation of p-values appears correct, which is that only the intercept has a coefficient that's significantly different from 0. You'll notice that the estimate of the coefficient for x4 is still quite high, but there's enough error that it's not significantly different from 0.
Your paired t test of y1 and y2 suggests that the models are different from one another. That's to be expected, in one model you included a large but imprecise coefficient that's contributing quite a bit to your model. There's no reason to think that the p-value of these models being different from one another should be the same as the p-value of the coefficient of x4 being different from 0.
Sign up or log in, post as a guest.
Required, but never shown
By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy .
Find centralized, trusted content and collaborate around the technologies you use most.
Q&A for work
Connect and share knowledge within a single location that is structured and easy to search.
Get early access and see previews of new features.
I used linearHypothesis function in order to test whether two regression coefficients are significantly different. Do you have any idea how to interpret these results?
Here is my output:
Short Answer
Your F statistic is 104.34 and its p-value 2.2e-16. The corresponding p-value suggests that we can reject the null hypothesis that both coefficients cancel each other at any level of significance commonly used in practice.
Were your p-value greater than 0.05, it is accustomed that you would not reject the null hypothesis.
Long Answer
The linearHypothesis function tests whether the difference between the coefficients is significant. In your example, whether the two betas cancel each other out β1 − β2 = 0.
Linear hypothesis tests are performed using F-statistics. They compare your estimated model against a restrictive model which requires your hypothesis (restriction) to be true.
An alternative linear hypothesis testing would be to test whether β1 or β2 are nonzero, so we jointly test the hypothesis β1=0 and β2 = 0 rather than testing each one at a time. Here the null is rejected when one is rejected. Rejection here means that at least one of your hypotheses can be rejected. In other words provide both linear restrictions to be tested as strings
Here are few examples of the multitude of ways you can test hypothese:
You can test a linear combination of coeffecients
joint probability
Aside from the t statistics, which test for the predictive power of each variable in the presence of all the others, another test which can be used is the F-test. (this is the F-test that you would get at the bottom of a linear model)
This tests the null hypothesis that all of the β’s are equal to zero against the alternative that allows them to take any values. If we reject this null hypothesis (which we do because the p-value is small), then this is the same as saying there is enough evidence to conclude that at least one of the covariates has predictive power in our linear model, i.e. that using a regression is predictively ‘better’ than just guessing the average.
So basically, you are testing whether all coefficients are different from zero or some other arbitrary linear hypothesis, as opposed to a t-test where you are testing individual coefficients.
The answer given above is detailed enough except that for this test we are more interested in the two variables hence the linear hypothesis does not investigate the null hypothesis that all of the β’s are equal to zero against the alternative that allows them to take any values but just for two variables of interest which makes this test equivalent to a t-test.
Reminder: Answers generated by artificial intelligence tools are not allowed on Stack Overflow. Learn more
Post as a guest.
Required, but never shown
By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy .
BMC Health Services Research volume 24 , Article number: 977 ( 2024 ) Cite this article
37 Accesses
Metrics details
The global variable of missed nursing care and practice environment are widely recognized as two crucial contextual factors that significantly impact the quality of nursing care. This study assessed the current status of missed nursing care and the characteristics of the nursing practice environment in Iran. Additionally, this study aimed to explore the relationship between these two variables.
We conducted an across-sectional study from May 2021 to January 2022 in which we investigated 255 nurses. We utilized the Missed Nursing Care Survey, the Nursing Work Index-Practice Environment Scale, and a demographic questionnaire to gather the necessary information. We used the Shapiro‒Wilk test, Pearson correlation coefficient test, and multiple linear regression test in SPSS version 20 for the data analyses.
According to the present study, 41% of nurses regularly or often overlooked certain aspects of care, resulting in an average score of 32.34 ± 7.43 for missed nursing care. It is worth noting that attending patient care conferences, providing patient bathing and skin care, and assisting with toileting needs were all significant factors contributing to the score. The overall practice environment was unfavorable, with a mean score of 2.25 ± 0.51. Interestingly, ‘nursing foundations for quality of care’ was identified as the sole predictor of missed nursing care, with a β value of -0.22 and a p -value of 0.036.
This study identified attending patient care interdisciplinary team meetings and delivering basic care promptly as the most prevalent instances of missed nursing care. Unfortunately, the surveyed hospitals exhibited an undesirable practice environment, which correlated with a higher incidence of missed nursing care. These findings highlight the crucial impact of nurses’ practice environment on care delivery. Addressing the challenges in the practice environment is essential for reducing instances of missed care, improving patient outcomes, and enhancing overall healthcare quality.
Peer Review reports
Missed Nursing Care (MNC) is the failure to provide any necessary aspect of patient care, partially or entirely, or delay in delivering it [ 1 ]. MNCs can have severe side effects on patients, including safety threats [ 2 ] and even mortality [ 3 ]. It also significantly decreases the quality of nursing care [ 4 ]. MNC can also have adverse and destructive effects on nurses, including decreased job satisfaction, increased absenteeism, and the intention to leave their jobs [ 5 ]. As a result, MNCs have become a key focus of nursing researchers in recent years and are widely recognized as a significant global problem [ 6 ].
A literature review revealed that MNCs are multidimensional and vary significantly in frequency and elements across different research communities [ 7 ]. In Iran, information regarding MNCs is limited. According to our search, only one reliable study [ 8 ] has been conducted on this topic in the last five years. Chegini et al. conducted a study that showed that the percentage of participants who missed care was 72.1%. The most common tasks of missed nursing care included patient discharge planning and teaching, emotional support for patients and their families, interdisciplinary care conferences, and patient education regarding their illness, tests, and diagnostic procedures. Although the study by Chegini et al. has provided valuable information, the generalizability of its results is limited due to its small sample size. The study included nurses from only medical-surgical wards and used the census sampling method.
MNC is influenced by various individual and organizational factors [ 9 ]. In a systematic review, Chiappinotto et al. identified significant factors contributing to MNC, such as low nurse-to-patient ratios, high workloads, and poor work environments. Moreover, stress, job dissatisfaction, and inadequate education among nurses were recognized as crucial elements. Furthermore, patient clinical instability was found to further worsen MNC [ 10 ]. However, some researchers argue that organizational and environmental factors are more influential in causing MNC than individual factors [ 11 ].
Another influential organizational variable on nursing performance is the practice environment (PE) [ 12 ]. PE in nursing is inclusive of material and human resources, a cooperative environment, and other elements related to the environment that directly or indirectly affect how care is provided [ 13 ]. PE is involved in nurses’ burnout [ 14 ], job satisfaction, stay in nursing [ 15 ], and overall quality of nursing care [ 16 ]. Like in MNCs, evidence suggests that PE varies across different hospitals and wards within a hospital [ 17 ]. For instance, a study conducted by Choi & Boyle in the U.S. demonstrated that pediatric wards had more favorable PEs than did medical-surgical wards. However, previous studies have shown that MNCs differ across poor, moderate, and suitable PEs. Weak PE has been found to increase MNCs [ 18 ], while optimal PE reduces MNCs [ 17 ]. Due to the global significance of MNCs and PEs for quality of care and the variability of these two variables due to different sociocultural factors, it is essential to understand the weaknesses of MNCs and PEs in every community thoroughly. Therefore, this study aimed to determine the status of MNCs, the characteristics of PEs, and the relationships between these two variables among nurses working in two teaching hospitals.
The present study was cross-sectional from May 30, 2021, to January 19, 2022. The study was conducted according to the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) guidelines. The study included nurses employed in the medical-surgical, emergency, and intensive care units of two major teaching hospitals in Zanjan Province. This province is situated in the northwestern region of Iran and has a population of approximately 1,016,000 people. To be eligible for participation in the study, the nurses needed to meet the following specific inclusion criteria:
A minimum of three months of work experience in the desired ward.
Holding a bachelor’s degree or higher.
Consent to participate in the study was obtained.
We utilized Formula 1 for a finite population to determine the sample size. The values used in this formula were N (total population) = 553, power (the probability of correctly rejecting the null hypothesis) = 0.80, standard deviation (SD) = 13.97, d (margin of error or precision) = 1.2, and Z (standardized value for the corresponding level of confidence) = 1.96. The formula indicated that a minimum sample size of 246 was required based on these variables. During the research, we found that a recent study comparable to our work was conducted by Park et al. [ 18 ]. For our research, we utilized the standard deviation of the variables in Formula 1. Their study recorded the mean and standard deviation of the MNC and PE as 84.06 ± 13.79 and 2.92 ± 0.25, respectively. We included the higher standard deviation (related to MNCs) to ensure a larger sample size. We prepared 270 questionnaires and distributed them among the selected nurses. We also considered the possibility of spoiled questionnaires and distributed extra questionnaires accordingly. Fifteen questionnaires were excluded from the study due to incomplete data, leaving a total of 255 questionnaires that were used for data analysis out of the 270 that were distributed.
We utilized a systematic random method to select the nurses for the study. In the first step, a list of nurses working in the desired wards was taken, and the sampling frame was prepared. In the second step, each nurse was assigned a number from a table of random numbers. This process generated a new sampling frame. In the third step, we calculated the distance between the study samples, denoted as ‘K’, using the formula K = N/n.’ We computed K by dividing the total population (N) of 553 by the sample size (n) of 270, approximately 2. To select the participants, we utilized a systematic random method. A new sampling frame was generated in the first step, as described earlier. The first nurse was selected randomly from this new sampling frame, and the subsequent samples were taken at a distance of two people from the previous nurse.
To collect the data, we used three different questionnaires: (a) a demographic profile form, (b) the Missed Nursing Care (MISSCARE) Survey, and (c) the Nursing Work Index-Practice Environment Scale (NWI-PES). The demographic profile included various variables, including sex, age, marital status, educational degree, work experience, position, shift work, employment type, and ward type.
In this study, we utilized the MISSCARE survey (MISSED) to assess MNC. We chose the MISSED based on its extensive utilization and strong psychometric properties, as evidenced in the literature. As noted by Chiappinotto et al. [ 10 ], 34 out of the 58 studies reviewed utilized a version of the MISSCARE survey, highlighting its reliability and validity in assessing MNC. The MISSCARE Survey consists of two parts: Part ‘A’ and Part ‘B’. Part ‘A’ included the most missed care components, while Part ‘B’ included the reasons for missing nursing care. We utilized part ‘A’ of the questionnaire, which constituted 24 items of the MISSCARE Survey. Each of the 24 items comprises five answer options: 1) rarely or never missed, 2) occasionally missed, 3) frequently missed, 4) always missed, and 5) nonapplicable. Kalisch & Williams included the option of ‘nonapplicable’ to account for nurses who operate in situations where certain care activities may not be performed [ 19 ]. The total score range of this survey is 24–96, where higher scores indicate a greater probability of missed care. In line with the findings of a previous study [ 17 ], we considered the combination of “frequently missed” and “always missed” options as missed care to demonstrate the frequency of missed nursing care. The MISSCARE Survey has undergone psychometric analysis, and its applicability has been approved for the nursing community in Iran [ 20 ]. The internal consistency of the tool was measured based on Cronbach’s alpha coefficient (α = 0.88) in this study.
The psychometric analysis of the NWI-PES has been conducted, and its usage has been approved [ 21 ]. Developed by Lake in 2002 and authorized by the National Quality Forum (NQF), this scale comprises thirty-one items and operates on a four-point Likert scale, with scores ranging from four to one. The response options were strongly agree = 4, somewhat agree = 3, somewhat disagree = 2, and strongly disagree = 1. According to [ 22 ], the possible score range of the whole scale and its subscales is one to four. The NWI-PES comprises five subscales:
The nurses’ participation in hospital affairs was evaluated with nine items.
‘Staffing and resource adequacy’, which includes four items.
The three items used were “Collegial nurse‒physician relations”.
‘Nursing foundations for quality of care’ with ten items.
The five items asked about nurses’ ability, leadership, and support.
A scale midpoint greater than 2.5 is considered an acceptable PE [ 22 ]. The NWI-PES demonstrated high internal consistency, with a Cronbach’s alpha of 0.93. The Cronbach’s alpha for each of the subscales of the NWI-PES was computed. The results were as follows: ‘nurse participation in hospital affairs,’ α = 0.88; ‘nursing foundations for quality-of-care,’ α = 0.72;‘staffing and resource adequacy,’ α = 0.87; ‘collegial nurse‒physician relations,’ α = 0.90; and ‘nurse manager ability, leadership, and support of nurses,’ α = 0.84.
We computed the means and standard deviations of the MNC and PE scores and utilized the Shapiro‒Wilk test to determine the normality of the data distribution. The results revealed that the data followed a normal distribution. We employed the Pearson correlation coefficient to determine the correlation between PEs and MNCs. Furthermore, we conducted a multiple linear regression test to examine whether changes in the MNC score, as the dependent variable, were associated with changes in the PE subscale scores. Before conducting the multiple linear regression analysis, we confirmed that the assumptions were met and evaluated. We confirmed the assumption of independent errors by using the Durbin–Watson test. Homoscedasticity and linearity assumptions were assessed through P-P plots. The hypothesis of multicollinearity was examined by determining the variance inflation factor (VIF) and tolerance [ 23 ]. The VIF ranged from 1.006 (TOL = 0.99) for ‘collegial nurse‒physician relations’ to 1.04 (TOL = 0.96) for ‘nursing foundations for quality-of-care.’ Independent t tests and ANOVA were used to evaluate the associations between demographic variables and MNCs. The statistical analysis of the data was conducted using SPSS software version 24, and a P value lower than 0.05 was used to indicate statistical significance.
The majority of the participants were females (84.3%), were married (68.2%), and were employed on a 5-year contract (46.7%). The majority of the participants were females (84.3%), were married (68.2%), and were employed on a 5-year contract (46.7%).
In addition, almost all of the participants (95.7%) had a Bachelor of Science in Nursing (BSN) degree, and a significant proportion (45.8%) worked in medical-surgical wards. Most of the respondents (91.4%) were staff nurses, and 89.8% of them worked in rotational shift work. The.
The participants’ average age and work experience were 33.94 ± 7.40 and 9.25 ± 7.14, respectively (Table 1 ).
The overall mean score for MNCs, with a score ranging from 24 to 96, was 32.34 ± 7.43. Of the total nurses, 41% reported that they always or frequently missed at least one aspect of nursing care. Based on the findings, the items with the highest mean score in descending order were attending an interdisciplinary patient care conference, patient bathing or skin care, assisting with toileting needs within 5 min of request, mouth care, and feeding the patient when the food was still warm (Table 2 ).
The mean MNC score was significantly greater for male nurses than for female nurses (X̄1 = 36.25, X̄2 = 31.56; t = -3.738, p < 0.001). Other demographic and occupational variables of the nurses, such as age, marital status, degree, work experience, position, rotational shift work, type of employment, and working place, had no significant association with MNCs ( p > 0.05).
The overall mean score for PE was 2.25 ± 0.51. Among the different subscales of the PE scale, the highest mean score was observed for ‘collegial nurse‒physician relations’ (M = 2.45, SD = 0.72). Furthermore, the mean scores for “nursing foundations for quality of care”, “nurse manager ability, leadership, and support of nurses”, and “nurse participation in hospital affairs” were 2.43 ± 0.58, 2.23 ± 0.65, and 2.16 ± 0.58, respectively. The lowest mean score was observed for ‘staffing and resource adequacy’ (M = 1.81, SD = 0.64).
The study’s results indicate a significant and negative correlation between the mean score of PEs and the overall mean score of MNCs ( r = -0.18, p = 0.002). There was a strong link between the overall mean score of MNCs and two of the five NWI-PES subscales: “nursing foundations for quality of care” ( r = -0.21, p < 0.001) and “nurse manager ability, leadership, and support of nurses” ( r = -0.16, p = 0.006).
According to Table 3 , linear regression analysis showed that only “nursing foundations for quality of care” (β = -0.22, p = 0.036) of the five NWI-PES subscales could predict MNC.
The main objective of this study was to determine the status of MNCs, the characteristics of PEs, and the relationships between these two variables among Iranian nurses working in two teaching hospitals. The findings showed that 41% of nurses reported frequently or always missing at least one aspect of nursing care. A systematic review also reported that 55–98% of nurses missed at least one course of nursing care [ 24 ]. However, the overall mean score of MNCs in our study was 32.3. A literature review revealed that our study’s mean MNC score was lower than that reported in the United States, Turkey, and Australia, except for Iceland [ 25 ]. By comparing our study results with those from other countries [ 26 ], it can be concluded that low MNCs were reported in our study. Like in many previous studies, in this study, we used the self-reporting method. The reason for the lower mean score of MNCs in our study compared to that in other studies might be due to two biases: “acquiescence response style” (tendency to respond positively) and “social desirability bias” (tendency to present oneself socially to be acceptable, but it does not fully reflect the reality of the individual). Due to the two biases mentioned earlier, the ‘truth-telling’ in our survey might have been compromised. This is because we used the self-reporting method to collect data, and the nature of MNCs is one of the essential aspects of ethics in nursing. The study findings indicated that patients who participated in interdisciplinary conferences had the highest mean score. However, not attending training classes can decrease knowledge and make nursing care less updated, ultimately reducing the quality of care provided to patients [ 27 ]. This finding is consistent with that of another study conducted in Brazil [ 7 ]. Based on our field experiences and observations, several factors, including the following, seem to play a significant role in missing nursing care:
Time limitation due to a nursing shortage.
Inappropriate timing of training classes or conferences and conflicts in daily schedules.
There is a lack of support and encouragement from managers, especially hospital managers.
Inappropriate and nonequipped venues for classes.
Improper teaching methods and giving lectures instead of using new teaching methods.
There is a lack of proper alert reminders for nurses regarding the date, time, and place of meetings.
Our study revealed that the lowest scores for missed care were related to items such as ‘bedside glucose monitoring as ordered”, ‘peripheral IV/central line site care and assessments according to hospital policy’, and ‘vital signs assessments as ordered.’ The lower scores associated with this care could be attributed to the use of an accurate system for recording patients in patient files and additional unique records above patients’ beds in the current research environment, which helps staff remember and check this care more often. However, these care tasks are crucial parts of a patient’s vital nursing care and should be performed during each work shift to monitor the patient’s hemodynamic status. This information about each patient was provided to the assigned nurse during the shift handover. A lack of ‘blood sugar control’ was also indicated in the studies of Smith et al. [ 17 ] in the U.S.
Our study revealed a low PE score among the participating nurses. Given that nurses have greater responsibility for caring and have essential tasks such as performing technical procedures, making decisions, and leading patient care, such tasks are affected by poor practices. Consequently, patient and family satisfaction decreases, and adverse patient outcomes, such as mortality and infection, may increase. Azevedo Filho et al. also demonstrated a poor nursing practice environment in Brazil [ 13 ], consistent with our study results. In another study [ 17 ], the average PE score was significantly greater than that in our study and that of Azevedo Filho et al. [ 13 ]. The high score in the Smith et al. research population could be because the surveyed hospitals were magnet hospitals. In magnet hospitals, there is more focus on creating a healthier and more desirable work environment. Our study revealed a significant inverse correlation between PE characteristics and MNCs. In other words, missed nursing care increases significantly in patients with unfavorable PEs. However, this relationship was not strong. Several researchers have emphasized the importance of providing qualified nursing services and improving the nursing work environment [ 17 ].
Among the different dimensions of PE, “nursing foundations for quality of care” and “nurse manager ability, leadership, and support of nurses” had significant relationships with MNCs. These findings suggest that targeted interventions aimed at improving each dimension of PE can help reduce the incidence of MNCs. Additionally, the ability of nursing managers and leaders should be accompanied by reduced missed care because nursing managers are responsible for managing the working conditions of nurses, determining their duties, coordinating existing resources, and developing basic nursing settings for the quality of patient care [ 28 ].
Our study on the relationship between nurses’ occupational and demographic variables and MNCs contradicts the findings of Blackman et al. [ 29 ], who indicated that men’s mean score for missed care is significantly greater than women’s. A study conducted in Iran also showed that female nurses’ quality of nursing care is greater than that of male nurses [ 30 ]. Women tend to care for patients more carefully, and less missed care is provided by women. Except for gender, the results of our study suggested no correlation between MNCs and other occupational and demographic variables of nurses.
The study offers insights into missed nursing care and its relationship with the practice environment. However, several limitations should be considered. The study’s cross-sectional design creates potential biases, which may limit our ability to establish causation. Additionally, the reliance on self-reports introduces the likelihood of response bias. Furthermore, the study focused on specific hospitals in Zanjan Province, which may restrict the generalizability of the findings to a broader context. Confounding factors, which are inherent to observational studies, might influence the observed relationships. Despite the abovementioned limitations, the study provides valuable contributions to comprehending the complex dynamics between the practice environment and missed nursing care.
According to our study, nurses consistently neglect a significant portion of nursing care, with patient-related team meetings and training sessions being the most overlooked. This is a noteworthy finding. The findings highlight a possible lack of awareness or inadequacy in planning critical sessions, which demands increased attention. Notably, basic nursing care is the second most commonly overlooked aspect of care. The unfavorable practice environment identified in the hospitals under study highlights the urgent need for improvement by planners and senior managers. Notably, our findings demonstrated a significant statistical relationship between the practice environment and unattended nursing care. This indicates that improving the practice environment could help reduce the number of missed care cases. Notably, managerial competencies, particularly leadership, are vital in preventing overlooked nursing care. These results provide essential insights for the field, highlighting the importance of targeted improvements in practice environments to improve patient care outcomes. Our research provides a foundation for future research and interventions to optimize nursing care delivery.
No datasets were generated or analysed during the current study.
Analysis of Variance
Missed Nursing Care
National Quality Forum
Practice Environment
Variance Inflation Factor
Kalisch BJ, Landstrom GL, Hinshaw AS. Missed nursing care: a concept analysis. J Adv Nurs. 2009;65(7):1509–17. https://doi.org/10.1111/j.1365-2648.2009.05027.x
Article PubMed Google Scholar
Cho SH, Lee JY, You SJ, Song KJ, Hong KJ. Nurse staffing, nurses prioritization, missed care, quality of nursing care, and nurse outcomes. Int J Nurs Pract. 2020;26(1):e12803. https://doi.org/10.1111/ijn.12803
Ball JE, Bruyneel L, Aiken LH, Sermeus W, Sloane DM, Rafferty AM, et al. Postoperative mortality, missed care and nurse staffing in nine countries: a cross-sectional study. Int J Nurs Stud. 2018;78:10–5. https://doi.org/10.1016/j.ijnurstu.2017.08.004
Lake ET, Riman KA, Sloane DM. Improved work environments and staffing lead to less missed nursing care: a panel study. J Nurs Manag. 2020;28(8):2157–65. https://doi.org/10.1111/jonm.12970
Article PubMed PubMed Central Google Scholar
Chaboyer W, Harbeck E, Lee BO, Grealish L. Missed nursing care: an overview of reviews. KJMS. 2021;37(2):82–91. https://doi.org/10.1002/kjm2.12308
Nahasaram ST, Ramoo V, Lee WL. Missed nursing care in the Malaysian context: a cross-sectional study from nurses’ perspective. J Nurs Manag. 2021;29(6):1848–56. https://doi.org/10.1111/jonm.13281
Lima JCd, Silva AEBC, Caliri MHL. Omission of nursing care in hospitalization units. Rev Lat -Am Enferm. 2020;28. https://doi.org/10.1590/1518-8345.3138.3233
Chegini Z, Jafari-Koshki T, Kheiri M, Behforoz A, Aliyari S, Mitra U, et al. Missed nursing care and related factors in Iranian hospitals: a cross‐sectional survey. J Nurs Manag. 2020;28(8):2205–15. https://doi.org/10.1111/jonm.13055
Duffy JR, Culp S, Padrutt T. Description and factors associated with missed nursing care in an acute care community hospital. JONA. 2018;48(7/8):361–7. https://doi.org/10.1097/NNA.0000000000000630
Article Google Scholar
Chiappinotto S, Papastavrou E, Efstathiou G, Andreou P, Stemmer R, Ströhm C, et al. Antecedents of unfinished nursing care: a systematic review of the literature. BMC Nurs. 2022;21(1):137. https://doi.org/10.1186/s12912-022-00890-6
Ausserhofer D, Zander B, Busse R, Schubert M, De Geest S, Rafferty AM, et al. Prevalence, patterns and predictors of nursing care left undone in European hospitals: results from the multicountry cross-sectional RN4CAST study. BMJ Qual Saf. 2014;23(2):126–35. https://doi.org/10.1136/bmjqs-2013-002318
Amaliyah E, Tukimin S. The relationship between working environment and quality of nursing care: an integrative literature review. Br J Health Care Manag. 2021;27(7):194–200. https://doi.org/10.12968/bjhc.2020.0043
Azevedo FMd, Rodrigues MCS, Cimiotti JP. Nursing practice environment in intensive care units. ACTA Paul Enferm. 2018;31:217–23. https://doi.org/10.1590/1982-0194201800031
Knupp AM, Patterson ES, Ford JL, Zurmehly J, Patrick T. Associations among nurse fatigue, individual nurse factors, and aspects of the nursing practice environment. J Nurs Adm. 2018;48(12):642–8. https://doi.org/10.1097/nna.0000000000000693
Al Sabei SD, Labrague LJ, Miner Ross A, Karkada S, Albashayreh A, Al Masroori F, et al. Nursing work environment, turnover intention, job burnout, and quality of care: the moderating role of job satisfaction. J Nurs Scholarsh. 2020;52(1):95–104. https://doi.org/10.1111/jnu.12528
Lake ET, de Cordova PB, Barton S, Singh S, Agosto PD, Ely B, et al. Missed nursing care in pediatrics. Hosp Pediatr. 2017;7(7):378–84. https://doi.org/10.1542/hpeds.2016-0141
Smith JG, Morin KH, Wallace LE, Lake ET. Association of the nurse work environment, collective efficacy, and missed care. West J Nurs Res. 2018;40(6):779–98. https://doi.org/10.1177/0193945917734159
Park SH, Hanchett M, Ma C. Practice environment characteristics associated with missed nursing care. J Nurs Scholarsh. 2018;50(6):722–30. https://doi.org/10.1111/jnu.12434
Kalisch BJ, Williams RA. Development and psychometric testing of a tool to measure missed nursing care. J Nurs Adm. 2009;39(5):211–9. https://doi.org/10.1097/NNA.0b013e3181a23cf5
Khajooee R, Bagherian B, Dehghan M, Azizzadeh Forouzi M. Missed nursing care and its related factors from the points of view of nurses affiliated to Kerman University of Medical Sciences in 2017. Hayat. 2019;25(1):11–24.
Google Scholar
Elmi S, Hassankhani H, Abdollahzadeh F, Abadi MAJ, Scott J, Nahamin M. Validity and reliability of the Persian practice environment scale of nursing work index. IJNMR. 2017;22(2):106. https://doi.org/10.4103/1735-9066.205953
Lake ET. Development of the practice environment scale of the nursing work index. Res Nurs Health. 2002;25(3):176–88. https://doi.org/10.1002/nur.10032
Gustafsson N, Leino-Kilpi H, Prga I, Suhonen R, Stolt M. Missed care from the patient’s perspective–a scoping review. Patient Prefer Adherence. 2020;25:383–400. https://doi.org/10.2147/PPA.S238024
Jones TL, Hamilton P, Murry N. Unfinished nursing care, missed care, and implicitly rationed care: state of the science review. Int J Nurs Stud. 2015;52(6):1121–37. https://doi.org/10.1016/j.ijnurstu.2015.02.012
Bragadóttir H, Burmeister EA, Terzioglu F, Kalisch BJ. The association of missed nursing care and determinants of satisfaction with current position for direct-care nurses—an international study. J Nurs Manag. 2020;28(8):1851–60. https://doi.org/10.1111/jonm.13051
Bruzios K, Harwood E. Issues of response styles. Wiley Encyclopedia Personality Individual Differences: Meas Assess. 2020:169–73. https://doi.org/10.1002/9781118970843.ch99
Price S, Reichert C. The importance of continuing professional development to career satisfaction and patient care: meeting the needs of novice to mid-to late-career nurses throughout their career span. Adm Sci. 2017;7(2):17. https://doi.org/10.3390/admsci7020017
Stalpers D, Van Der Linden D, Kaljouw MJ, Schuurmans MJ. Nurse-perceived quality of care in intensive care units and associations with work environment characteristics: a multicenter survey study. J Adv Nurs. 2017;73(6):1482–90. https://doi.org/10.1111/jan.13242
Blackman I, Papastavrou E, Palese A, Vryonides S, Henderson J, Willis E. Predicting variations to missed nursing care: a three-nation comparison. J Nurs Manag. 2018;26(1):33–41. https://doi.org/10.1111/jonm.12514
Khaki S, Esmaeilpourzanjani S, Mashouf S. Nursing cares quality in nurses. S J Nursing, Midwifery and Paramedical Faculty. 2018;3:1–14. https://doi.org/10.29252/sjnmp.3.4.1
Download references
We want to thank all the nurses who participated in this study. Their invaluable contributions were crucial in making this research possible. We would also like to thank the hospitals in Zanjan Province for their cooperation and support during the data collection. Furthermore, we would like to acknowledge the Zanjan University of Medical Sciences’ Biomedical Research Ethics Committee for approving and overseeing the ethical aspects of this research. We are grateful for their collaboration and commitment to advancing healthcare research, which made this study possible.
This work was supported by the Research and Technology Deputy of Zanjan University of Medical Sciences, Zanjan, Iran (grant number: A-11-86-17).
Authors and affiliations.
Department of Medical-Surgical Nursing, School of Nursing and Midwifery, Zanjan University of Medical Sciences, Zanjan, Iran
Somayeh Babaei
Department of Psychiatric Nursing, School of Nursing and Midwifery, Zanjan University of Medical Sciences, Mahdavi St., Zanjan, 4515789589, Iran
Kourosh Amini
Department of Critical Care Nursing, School of Nursing and Midwifery, Zanjan University of Medical Sciences, Zanjan, Iran
Farhad Ramezani-Badr
You can also search for this author in PubMed Google Scholar
Study design: KA. Data collection: SB. Data analysis: KA, FR. Study supervision: KA. Manuscript writing: KA, SB, FR. Critical revisions for important intellectual content: KA, FR.
Correspondence to Kourosh Amini .
Ethics approval and consent to participate.
The research proposal with the code IR.ZUMS.REC.1399.053 was approved by the Zanjan University of Medical Sciences’ Biomedical Research Ethics Committee (ZUMS.REC). We obtained written informed consent from all participants and preserved the confidential identity of each participant throughout the study. Before using the two MISSCARE Survey and Practice Environment Scale questionnaires, permission was obtained from the developers of the participants (Professor Kalisch and Professor Lake, respectively) through email.
Not applicable.
The authors declare no competing interests.
Publisher’s note.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ .
Reprints and permissions
Cite this article.
Babaei, S., Amini, K. & Ramezani-Badr, F. Unveiling missed nursing care: a comprehensive examination of neglected responsibilities and practice environment challenges. BMC Health Serv Res 24 , 977 (2024). https://doi.org/10.1186/s12913-024-11386-1
Download citation
Received : 31 January 2024
Accepted : 01 August 2024
Published : 23 August 2024
DOI : https://doi.org/10.1186/s12913-024-11386-1
Anyone you share the following link with will be able to read this content:
Sorry, a shareable link is not currently available for this article.
Provided by the Springer Nature SharedIt content-sharing initiative
ISSN: 1472-6963
IMAGES
COMMENTS
The hypotheses are: Find the critical value using dfE = n − p − 1 = 13 for a two-tailed test α = 0.05 inverse t-distribution to get the critical values ±2.160. Draw the sampling distribution and label the critical values, as shown in Figure 12-14. Figure 12-14: Graph of t-distribution with labeled critical values.
The p value gets smaller as the test statistic calculated from your data gets further away from the range of test statistics predicted by the null hypothesis. The p value is a proportion: if your p value is 0.05, that means that 5% of the time you would see a test statistic at least as extreme as the one you found if the null hypothesis was true.
The linear regression p value for each independent variable tests the null hypothesis that the variable has no correlation with the dependent variable. ... perhaps it exists in the population but the small sample size and/or weak relationship made it so the hypothesis test cannot detect it (i.e., the hypothesis test had insufficient statistical ...
The P -value is, therefore, the area under a tn - 1 = t14 curve to the left of -2.5 and to the right of 2.5. It can be shown using statistical software that the P -value is 0.0127 + 0.0127, or 0.0254. The graph depicts this visually. Note that the P -value for a two-tailed test is always two times the P -value for either of the one-tailed tests.
In this example, the regression coefficient for the intercept is equal to 48.56. This means that for a student who studied for zero hours, the average expected exam score is 48.56. The p-value is 0.002, which tells us that the intercept term is statistically different than zero. In practice, we don't usually care about the p-value for the ...
Here is the technical definition of P values: P values are the probability of observing a sample statistic that is at least as extreme as your sample statistic when you assume that the null hypothesis is true. Let's go back to our hypothetical medication study. Suppose the hypothesis test generates a P value of 0.03.
To find the p value for your sample, do the following: Identify the correct test statistic. Calculate the test statistic using the relevant properties of your sample. Specify the characteristics of the test statistic's sampling distribution. Place your test statistic in the sampling distribution to find the p value.
A p-value is the probability of observing a sample statistic that is at least as extreme as your sample statistic, given that the null hypothesis is true. For example, suppose a factory claims that they produce tires that have a mean weight of 200 pounds. An auditor hypothesizes that the true mean weight of tires produced at this factory is ...
P Value Definition. A p value is used in hypothesis testing to help you support or reject the null hypothesis. The p value is the evidence against a null hypothesis. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis. P values are expressed as decimals although it may be easier to understand what they ...
9.5: The p value of a test. In one sense, our hypothesis test is complete; we've constructed a test statistic, figured out its sampling distribution if the null hypothesis is true, and then constructed the critical region for the test. Nevertheless, I've actually omitted the most important number of all: the p value.
It is the cutoff probability for p-value to establish statistical significance for a given hypothesis test. For an observed effect to be considered as statistically significant, the p-value of the test should be lower than the pre-decided alpha value. Typically for most statistical tests (but not always), alpha is set as 0.05.
A p-value, or probability value, is a number describing how likely it is that your data would have occurred by random chance (i.e., that the null hypothesis is true). The level of statistical significance is often expressed as a p-value between 0 and 1. The smaller the p -value, the less likely the results occurred by random chance, and the ...
The P value is used all over statistics, from t-tests to regression analysis.Everyone knows that you use P values to determine statistical significance in a hypothesis test.In fact, P values often determine what studies get published and what projects get funding.
The p -value is used in the context of null hypothesis testing in order to quantify the statistical significance of a result, the result being the observed value of the chosen statistic . [ note 2] The lower the p -value is, the lower the probability of getting that result if the null hypothesis were true. A result is said to be statistically ...
Formally, the p-value is the probability that the test statistic will produce values at least as extreme as the value it produced for your sample.It is crucial to remember that this probability is calculated under the assumption that the null hypothesis H 0 is true!. More intuitively, p-value answers the question: Assuming that I live in a world where the null hypothesis holds, how probable is ...
Using P values and Significance Levels Together. If your P value is less than or equal to your alpha level, reject the null hypothesis. The P value results are consistent with our graphical representation. The P value of 0.03112 is significant at the alpha level of 0.05 but not 0.01.
Hypothesis test for testing that a subset — more than one, ... (0.54491/(32-4)) = 16.43 with p-value 0.000. To test whether a subset — more than one, but not all — of the slope parameters are 0, there are two equivalent ways to calculate the F-statistic: Use the general linear F-test formula by fitting the full model to find SSE(F) ...
Output: t-statistic: -0.3895364838967159 p-value: 0.7059365203154573 Fail to reject the null hypothesis. The difference is not statistically significant. Since, 0.7059>0.05, we would conclude to fail to reject the null hypothesis.This means that, based on the sample data, there isn't enough evidence to claim a significant difference in the exam scores of the tutor's students compared to ...
This essentially means that the value of all the coefficients is equal to zero. So, if the linear regression model is Y = a0 + a1x1 + a2x2 + a3x3, then the null hypothesis states that a1 = a2 = a3 = 0. Determine the test statistics: The next step is to determine the test statistics and calculate the value.
First lets use statsmodel to find out what the p-values should be. import pandas as pd. import numpy as np. from sklearn import datasets, linear_model. from sklearn.linear_model import LinearRegression. import statsmodels.api as sm. from scipy import stats. diabetes = datasets.load_diabetes() X = diabetes.data.
Using a binomial test, the p -value is < 0.0001. (Actually, R reports it as < 2.2e-16, which is shorthand for the number in scientific notation, 2.2 x 10 -16, which is 0.00000000000000022, with 15 zeros after the decimal point.) Assuming an alpha of 0.05, since the p -value is less than alpha, we reject the null hypothesis.
18. Regarding the p-value of multiple linear regression analysis, the introduction from Minitab's website is shown below. The p-value for each term tests the null hypothesis that the coefficient is equal to zero (no effect). A low p-value (< 0.05) indicates that you can reject the null hypothesis. In other words, a predictor that has a low p ...
An alternative linear hypothesis testing would be to test whether β1 or β2 are nonzero, so we jointly test the hypothesis β1=0 and β2 = 0 rather than testing each one at a time. Here the null is rejected when one is rejected. Rejection here means that at least one of your hypotheses can be rejected. In other words provide both linear ...
We used the Shapiro‒Wilk test, Pearson correlation coefficient test, and multiple linear regression test in SPSS version 20 for the data analyses. Results According to the present study, 41% of nurses regularly or often overlooked certain aspects of care, resulting in an average score of 32.34 ± 7.43 for missed nursing care.