# How important is it to include a hypothesis for a report?

I am writing a research report for my final university project. For my analysis I have used logistic regression.

I have provided research questions which have been answered.
So, how important would it be to include a hypothesis'? Is it ok to leave these out?

Many thanks

As @adam.r says, any hypothesis you actually tested should be specified if its results are of interest or interpreted substantively. However, logistic regression doesn't strictly test hypotheses. One certainly can (and often will by default) perform tests of model fit and significance of coefficients, but these aren't necessarily important to report if you don't consider them important for your research. For example, it's probably relatively rare to see anyone explicitly state the null hypothesis about the intercept.

The hypothesis that a given predictor does not significantly improve the model's fit over the null model is often a useful hypothesis, but you might even be better off dropping the NHST framework and focusing on effect size and confidence interval (CI) estimation. If you report the regression coefficient for a given predictor and its CI, a test of the null hypothesis may be effectively redundant. A potential exception/counterargument would arise in any insignificant result, though: if you're not forcing a fail to/reject decision on your null hypothesis, but looking instead to judge the amount of evidence against the null on a continuous scale, your $p$ value may be more precisely useful than whichever bound of the CI crosses the null value. I.e., if you want to know exactly how likely results at least as extreme as yours are to occur in a replication of your study if the null is literally true, then you want a $p$ value, not the less different-from-zero bound of a 95% CI.

Then again, you could also find the CI for the level of confidence corresponding to your $p$ value and thereby get a sense for an equally plausible null on the other side of your CI without losing the info of the $p$ value. That the confidence level for a CI for which one bound is equal to the null (presumably the default, zero) tells you what you need to know to get a $p$ value may not be obvious to your audience though, so even if you go with this approach, you might want to report the $p$ value as well. It generally doesn't take a lot of extra space if you're already reporting more important statistics, and it doesn't do much harm. You can always bury it between other, more useful statistics if you don't want to emphasize it (I mentioned this idea initially in my answer to "Accommodating entrenched views of p-values").

If you ever have time to read up on confidence intervals, you might want to check out the reference I list here. Some others I mention in my answer to "Why are 0.05 < p < 0.95 results called false positives?" and the responses there in general might also be helpfully informative. There are some big issues underneath the surface of this question.

Reference
Cumming, G. (2012). Understanding the new statistics: Effect sizes, confidence intervals, and meta-analysis. New York: Routledge.

• "The hypothesis that a given predictor does not significantly improve the model's fit over the null model is often a useful hypothesis"? Apr 24 '14 at 21:09
• Should I have said null hypothesis? I meant useful for the sake of falsification, as a way of justifying further study of the predictor for the sake of theory development...but I hope I didn't come across as overly enthusiastic about NHST in general at least! Apr 24 '14 at 21:12
• It's just that I didn't understand what you meant: statistical hypotheses refer to true values of the population parameters, not to how well models fit a particular sample. Perhaps it's nothing more than that the wording conflates the hypothesis tested with the motive for testing it. Apr 25 '14 at 8:45
• Wouldn't my wording be suitable for an F-test of a model with the predictor vs. a model without it? Maybe I've implied conflation of that test with the H$_0$ of a t-test for the predictor, but I've been under the impression that those tests are equivalent when they only concern the addition/removal of a single predictor. It would be good to know if I'm wrong about that. Apr 25 '14 at 18:39
• For some reason (perhaps the context given by your comments) it doesn't confuse me any more, so I now feel I'm being pedantic. Nevertheless the null hypothesis, whether for an F-test or for the equivalent t-test (you're right), is just that the true value of coefficient for that predictor is zero - e.g. $H_0: \beta_3=0$. Even if you're using the test to decide whether or not to include a parameter in a final model, that hypothesis doesn't change. Apr 29 '14 at 12:46

If you used any hypothesis test, you need to specify the hypothesis. Do you have a p-value anywhere?

• I agree if your point is that hypotheses should be specified for any test that the analyst intends to base important inferences on, but I don't think it's necessary to report a $p$ value just because one's software happens to produce it (not that this is necessarily what you meant to imply). Also, frankly, I wouldn't necessarily trust the instructor as the final arbiter of statistical propriety ;) The OP certainly has other recourses available, such as our good ol' community right here...not that we can ensure a good grade! Apr 24 '14 at 20:47