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I just realised that even though I know how to perform an independent samples t-test or a Mann whitney test, I am not sure how their results should be reported in a paper. I was given this study to read in preparation for a Research Methodology class but it does not report the "easy" tests, so I wonder.

Edit in response to the comment:

I mean reporting according to strict scientific guidelines. I suppose there is a rule, similarly to when eg we report normally distributed variables we mention the mean and the SD.

Edit number two :)

I am sorry I didn't realise I wasn't specific. My orientation is medical research so I am primarily interested in knowing what is the best way to present data in papers that result from medical studies. The class I am taking right now is more general though (the article was from a study from the Law school) so it did not occur to me that this was a detail I should have mentioned in the first place.

So lets assume I checked if x_bubblenephrine is different between say, a group of people who have Y-itis and a group who of people who do not. Say that I got p>0,005. Is there a "correct way" per se to report this? Or I can get away with "there was no difference between the two groups (p>0,05)"?

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    $\begingroup$ Is this paper you're reporting them in something you just freely create or is there a requirement to report according to specific guidelines? $\endgroup$ – John Sep 21 '13 at 0:11
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    $\begingroup$ "according to strict scientific guidelines" -- where are these strict guidelines? I suspect you probably mean something more like 'according to convention'... and convention is very much dependent on what area you work in. $\endgroup$ – Glen_b -Reinstate Monica Sep 21 '13 at 1:54
  • $\begingroup$ there are different guidelines in different disciplines, so please specify where you want to use these tests. APA guidelines would be an example for psychology and some social sciences. They would require you to specify the test statistic, degrees of freedom/sample size, p-value (two digits) and depending on the outlet some measure of effect size. Then again, with t-tests means and SDs are expected to be mentioned and medians for the mann-whitney U-test. The best thing to do is to study pubications in the journal you are targeting or in journals from the area you work in. $\endgroup$ – jank Sep 21 '13 at 2:35
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    $\begingroup$ (post edit2) -- what is accepted as 'the correct way to write this' very much depends on your audience. For the t-test, I'd at least want an estimate and interval for the mean difference to go with the p-value. With the WMW, if you're interested in it as a test of location difference, I'd hope to see some measure of that effect (for a WMW, the corresponding location-difference measure is the median of pairwise differences but it would be okay to report any meaningful location difference) plus an interval for the effect. If you see the WMW as a more general test, then it may not matter so much. $\endgroup$ – Glen_b -Reinstate Monica Sep 21 '13 at 2:38
  • $\begingroup$ ... But those are my preferences, not what would be seen as 'the correct way' by some general but unspecified audience. $\endgroup$ – Glen_b -Reinstate Monica Sep 21 '13 at 2:40
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Stats can be reported in many modes (e.g., class hw, conference presentation, journal article) and research fields. The general rules vary depending on where and how you are reporting them.

Often times, when people want to see stats reported in a certain way, they will tell you. For example, when researchers submit a manuscript to a journal, that specific journal should have its own guidelines on how to format the paper.

Other than that, you just have to study and understand stats until you kind of get an idea of what is and isn't important in the context that you are in. Like the other comments, it depends a lot on the audience.

I can't list out everything, but a few examples that I believe in:

More numbers should be reported on a paper than a presentation.

Report actual p-values whenever possible, not just p>.05 or p<.05 (but if p<.001 then just say p<.001)

standardized effect sizes (like r or r^2) is more useful when your study involves latent variables (i.e., variables without clear units, like happiness score on a questionnaire).

Confidence intervals are more useful when you are dealing with manifest variables (i.e., variables with meaningful units, like height in inches)

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there is consistency among guidelines regarding reporting of results, in particular the t-test and mann whitney U test. You have for example the CONSORT statement and ICHE9:

ICHE9: "Estimates of treatment effects should be accompanied by confidence intervals, whenever possible" (ICHE9)

CONSORT, checklist item: "results for each group, and the estimated effect size and its precision (such as 95% confidence interval)" (BMJ CONSORT)

thus the p-value should be accompanied by an estimate of the effect and its confidence interval. For the two sample t-test this is simply an estimate of the difference between means. But nonparametric tests tend to emphasise p-values, so what to use as an effect size estimate for the mann whitney U test? In this case you may report the probability index and its 95% confidence interval. The probability index is easily derived from the U statistic itself: probability index as an effect size measure

Regarding the p-value, you should not report it as >0.05. Instead give the p-value exactly eg 0.0621. You still see this in medical journals ie p-values displayed in tables as "NS" indicating not statistically significant. But this is generally considered unacceptable. Douglas Altman and others have written in eg The BMJ about the best way to present statistical results.

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