alternative hypothesis

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Null vs Alternative hypothesis in practice

From the beginning of the most introductory statistics course, the declaration of a null and alternative hypothesis is the "first step" of any good experiment and subsequent analysis. Now that I have been venturing into more complex courses and topics, I see this exercise still being performed. I have always perceived the proposal of the null v. alternative as a teachable example of how to think of a study or experiment rather than a necessity (once you have an understanding of hypothesis testing and experimental design).

Do statisticians consistently propose a null and alternative in practice for all tests they perform? Is this common practice in the field or within a company? Or rather is it a "mental" heuristic when approaching statistical testing?

From my time doing experiments in biological research, we have always had a hypothesis to guide and motivate an experiment, but there was never the clear definition of a null and alternative. Is this an example of lack of scientific rigor?

Sorry for the naiveté of question as I am not a statistician.

• hypothesis-testing

• 1 $\begingroup$ Although it's unclear what you mean by "propose these hypotheses," perhaps it's relevant to know there is a theoretical statistical literature that provides clear, rigorous definitions of null and alternative hypotheses. In that literature, the null must imply a definite distribution of a test statistic. In all but the simplest cases (consisting of a "simple null" and "simple alternative"), that uniquely determines the null. Any lack of rigor, then, must originate within the intro stats courses to which you refer, not in the discipline itself. $\endgroup$ –  whuber ♦ Commented Jun 7, 2023 at 19:24
• $\begingroup$ In light of that, perhaps one of these posts about null hypotheses answers your questions. The thread at stats.stackexchange.com/questions/31 comes particularly to mind, because many of the answers there refer to null hypotheses and attempt to characterize them. Please check it out. $\endgroup$ –  whuber ♦ Commented Jun 7, 2023 at 19:25
• 2 $\begingroup$ It’s so common to test a null hypothesis of no effect against an alternative of some effect that it’s kind of a slang to leave that implicit. (Whether or not this is good for the field or science in general is a different matter.) $\endgroup$ –  Dave Commented Jun 7, 2023 at 19:34
• 1 $\begingroup$ While the null and alternative hypothesis has a strong theoretical basis - its use is in fact quite extensive in the real world. In A.H. Studenmund's Using Econometrics: A Practical Guide - the author explains how the FDA tests new products before bringing them to market. For instance, if side effects were observed more frequently then would be expected by chance, then the product would be withheld. Under such a scenario, there would be a difference between the two groups (what would typically be observed and what is actually observed), and the null would be rejected in this scenario. $\endgroup$ –  Michael Grogan Commented Jun 7, 2023 at 19:39
• 4 $\begingroup$ "From my time doing experiments in biological research, we have always had a hypothesis to guide and motivate an experiment, [...]". It is worth remembering a scientific / research hypothesis is different from a statistical hypothesis. The individual concepts are probably rigorously studied, though there is probably a weaker link in between (e.g., coming up with a statistical hypothesis based on the research hypothesis) in practice, leading to concepts like Type III error . $\endgroup$ –  B.Liu Commented Jun 7, 2023 at 20:18

3 Answers 3

Your question starts out as if the statistical null and alternative hypotheses are what you are interested in, but the penultimate sentence makes me think that you might be more interested in the difference between scientific and statistical hypotheses.

Statistical hypotheses can only be those that are expressible within a statistical model. They typically concern values of parameters within the statistical model. Scientific hypotheses almost invariably concern the real world, and they often do not directly translate into the much more limited universe of the chosen statistical model. Few introductory stats books spend any real time considering what constitutes a statistical model (it can be very complicated) and the trivial examples used have scientific hypotheses so simple that the distinction between model and real-world hypotheses is blurry.

I have written an extensive account of hypothesis and significance testing that includes several sections dealing with the distinction between scientific and statistical hypotheses, as well as the dangers that might come from assuming a match between the statistical model and the real-world scientific concerns: A Reckless Guide to P-values

So, to answer your explicit questions:

• No, statisticians do not always use null and alternative hypotheses. Many statistical methods do not require them.

• It is common practice in some disciplines (and maybe some schools of statistics) to specify the null and alternative hypothesis when a hypothesis test is being used. However, you should note that a hypotheses test requires an explicit alternative for the planning stage (e.g. for sample size determination) but once the data are in hand that alternative is no longer relevant. Many times the post-data alternative can be no more than 'not the null'.

• I'm not sure of the mental heuristic thing, but it does seem possible to me that the beginner courses omit so much detail in the service of simplicity that the word 'hypothesis' loses its already vague meaning.

the declaration of a null and alternative hypothesis is the "first step" of any good experiment and subsequent analysis.

Well, you did put quotes around first step, but I'd say the first step in an experiment is figuring out what you want to figure out.

As to "subsequent analysis", it might even be that the subsequent analysis does not involve testing a hypothesis! Maybe you just want to estimate a parameter. Personally, I think tests are overused.

Often, you know in advance that the null is false and you just want to see what is actually going on.

A null hypothesis is not meaningful in every case where statistics are used. It is useful for questions of the type "Do this effect a measurable change on something?"

But if I want to see "how far can I consistently throw a frisbee", there is no null hypothesis. There is still statistics; do a lot of throws, average distances, until I can say with 95% confidence that I can indeed throw the frisbee this far.

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