# Writing statistical analysis for Thesis (two tailed vs. one tailed)

So I'm writing the statistical analysis part of my thesis. Should I mention if the tests were two-tailed or one-tailed? The tests I have used are:

intra-class-correlation coefficient
Spearman's correlation
two-way repeated measure ANOVA
Friedman test
Wilcoxon signed-rank test


Can those tests be either one or two-tailed? Should I mention which it was for all of them? (I only specified that I used a two-tailed Wilcoxon)

• Welcome to our site. This might be a question you can answer yourself. Do you think your audience might like to know what you did? And if you think not, you might consider whether it was worth doing or worth reporting at all.
– whuber
Aug 24, 2018 at 21:30
• I suppose the details depend on the field and the statistical sophistication of important readers. The Wilcoxon test can be one or two-sided. Whether in symbols (stating the null and alternative hypotheses formally) or in the descriptive language you need to make it clear why you did the test (e.g., to find if 'different' or 'greater'), what you found, and why the results matter. [If you did a one-sided test that was just barely significant, so that a two-sided test would not have been, then somehow the language needs to defend why one-sided.] By contrast ANOVA is technically one sided,... Aug 25, 2018 at 4:52
• ... rejecting for large F, but the purpose is to decide whether or not there is info to confirm some group means are significantly different from others. Then (if there are signif diffs) for the ad hoc tests you need to say something about direction(s) or patterns of signif differences, indicate you took 'family' error rate into account, and what results imply for your research. // Other sections of your thesis will have already stated purposes and will summarize findings. So with clever, consistent choices of language, the discussions of statistical findings can terselyfocus on stat issues. Aug 25, 2018 at 5:06

Short answer, the citations of probabilities, and the language used to describe them, should reflect what was done. For example, for ANOVA, the regression probability reflects how likely that regression fit is to occur by chance alone, thus although one-tailed, one would not usually refer to that fact.

When the probability of a test statistic occurring by chance alone is from a difference, that likelihood includes the areas of the density function of that statistic both more extremely lesser than and greater than the observed value. For a one-tailed test, one is concerned with areas only either more extremely greater than or lesser than the observed value, but not both and is thus 1/2 of the null hypothesis probability of both extremes for symmetric distributions like the W-statistic of the nonparametric Wilcoxon signed-rank test. For those distributions that are asymmetric and two-tailed, e.g., this, the doubling rule would not hold.

For intraclass correlation there is a rating scale but no hypothesis testing per se.

For Spearman's rank correlation significance testing, the test is essentially one-tailed, and ditto for ANOVA F-statistic testing two-way repeated measures. However, the confidence intervals for parameter values are two-tailed, so it depends what one is talking about within the ANOVA procedure. Friedman's test is nonparametric one-way ANOVA, so its interpretation is similar to other ANOVA.

• In response to the edits I have removed the downvote. But the conclusion "thus 1/2" not only appears without justification, it isn't always correct, either. The principal exceptions occur when the test statistic is asymmetric or it is discrete--which is the case of the tests mentioned in the question. Moreover, your post doesn't actually answer the question that was asked.
– whuber
Aug 26, 2018 at 19:30