# Why report test statistics in a publication?

Some style guides instruct authors to report not only the results of a hypothesis test, but also the value of the test statistic from which it was calculated. For example, APA Style suggests t(DOF)=t statistic, p=p value for reporting the results of a t-test, as shown in the following examples, taken from here¹.

One sample: “Younger teens woke up earlier (M = 7:30, SD = .45) than teens in general, t(33) = 2.10, p = 0.31″

Dependent/Independent samples: “Younger teens indicated a significant preference for video games (M = 7.45, SD = 2.51) than books (M = 4.22, SD = 2.23), t(15) = 4.00, p < .001.”

The $$p$$-value is obviously useful², as it tells you if the results are unlikely under the null hypothesis. Descriptive statistics are important for understanding the characteristics of the data/subject pool, as well as the size of any purported effect.

The $$t$$-statistic (or similar for $$\chi^2$$ tests) seems more like an intermediate step, needed to get one from the other. Likewise the degree(s) of freedom are often closely related to the number of data points, but the actual value of $$N$$ seems easier to interpret.

How does including the test statistic help me interpret these results? Is it merely convention, an aid to meta-analysis, or can astute reader learn something from these numbers?

I'm particularly interested in the case of "simple" tests; I can imagine that $$F(x,y)$$ tells you something about the design of an ANOVA that might not be clear from a written description.

1. These examples don't actually seem very good to me; the mean of the within-subject differences would be more informative, for example.

2. In a NHST framework, of course. Assume we're happy working in it for the purposes of this question.

• Controversial topic: Maybe an overdue attempt to squelch mindless use/abuse of P-values standing alone as 'evidence'--especially rampant in social sciences for some years. Recent position papers by ASA and others have pointed out inappropriate gaming of P-values leading to inappropriate, probably false or demonstrably irreproducible 'discoveries'. // One extreme example: You do complex study. Find several dozen P-values for various 'effects'. Report only the 5% of 'significant' ones--anticipated by chance alone. Don't mention that the rest of the study showed nothing. Apr 21 '20 at 19:06
• I'm...not totally sure about that. I definitely agree those are issues but I'm not seeing how the t-statistic helps address them. I think this style also predates the those position papers (though concerns about NSHT have been around for a while). Apr 22 '20 at 16:01
• In my experience one is happier following style manuals than trying to understand them. They are often arbitrary policies set without much scientific input or as a compromise after conflicting input. You can work through scientific societies to try for changes. // As to this particular issue, I see no problem in reporting sample sizes, t-values, and whether one or 2-sided test, in addition to P-value. I've heard few pubs have banned mention of P-values, which I think is going too far. (But if enough other info is revealed, reader can deduce P-values.) Apr 22 '20 at 17:21
• @BruceET Sorry I may be hijacking the thread here. You say Report only the 5% of 'significant' ones--anticipated by chance alone. I understand why this is a problem. What I do not understand is why it is blamed on NHST, p-values or frequentist statistics in general. If you report only the extreme posterior distributions without mentioning all the others, wouldn't the problem of reproducibility be the same? Apr 23 '20 at 14:31
• If you test multiple hypotheses in the same data, you have to use a method of avoiding false discovery. If you are submitting a paper, follow the style manual. This site discourages chatting in comments. Done here. Apr 23 '20 at 15:59