**A.**I know from the net that for a design with one binary variable and a second variable that is continuous but is

**NOT normally distributed**, I can use

**the point-biserial correlation (which is basically the**

*BOTH***parametric**Pearson correlation formula) as well as the Rank Biserial Correlation (which is equal to the

**nonparametric**Spearman or Kendall τ correlations).

**B.**I also have read about linear and monotonic correlations, which implies that even the Pearson coefficient (and of course, point-biserial) is OK for

**nonnormal**distributions.

**C.**And I understand that with one binary variable and a continuous one, it might even be better to use an independent-samples

**comparison**test (e.g., unpaired t or Mann-Whitney U) instead of a correlation coefficient.

**D.**I know that the Mann-Whitney test will yield the same p value as the Spearman coefficient, while the t-test will give the same p value as the Pearson coefficient (and point-biserial).

**E.**I know when the groups are not large enough AND when the error terms are not normally distributed, I should use the nonparametric Mann-Whitney instead of t-test.

**Two Questions:**

The above assumptions cause some inconsistencies and confusion in the following case:

I am analyzing this design with 2 groups of 20 patients each; the independent variable is

*Treatment*(the treatments A or B) and the dependent variable is the continuous

*Length*measured in each group.

**The latter is NOT normal**(the groups and

**the error terms are all NON-normal**).

The problem is that in this particular design, the nonparametric Spearman and

**Mann-Whitney**tests yield a statistically significant p value, while the parametric point-biserial [Pearson] and

**t-test**yield a quite non-significant p value > 0.1.

**Question 1.**Which one should I use? The nonparametric Spearman / Mann-Whitney? Or the parametric point-biserial [Pearson] / t-test? On the one hand, the assumption

**E**dictates that I must use the nonparametric Mann-Whitney. On the other hand, the assumptions

**A and B**allow me to use the parametric point-biserial [which is actually Pearson] correlation

**and by extension the t-test**. So what should I use?

**Question 2.**The assumption

**E**seems to be in total conflict with the assumptions

**A and B**: The results of Spearman / Mann-Whitney are identical, and so are the results of point-biserial [Pearson] / t-test. So if I am allowed to use the point-biserial [Pearson] in the absence of normality (assumptions

**A and B**),

**why not the t-test which gives the EXACT SAME result as point-biserial**?