# Bonferroni correction for two different tests on the same dataset

I am having trouble figuring out the correction factor to choose for a Bonferroni correction. Let me explain.

I have two datasets, control ($x$) and data from left ($y_1$, affected limb) and right limb ($y_2$, non-affected limb) of a pathology group. As $y_1$ and $y_2$ were from the same subject (paired data), I have performed a Wilcoxon signed-rank test to compare if these data were statistically different.

However, when I compared the data between $x$ and $y_1$ or, between $x$ and $y_2$, I used a Wilcoxon Rank-Sum Test.

As there are multiple tests, should I use correction factor of 3 ($p<=\frac{0.05}{3}$)?

Or ($p<=\frac{0.05}{2}$) for group ($x$ and $y_1$) and ($x$ and $y_2$) only and no correction for group ($y_1$ and $y_2$)?

I would really appreciate your kind reply. Thank you.

• It seems natural to have control data for left and right arms separately, x1 and x2. – ttnphns Mar 18 '14 at 8:41
• Thanks very much for editing, Glen_b. Thanks for your reply, @ttnphns Yes I do have both $x_1$ and $x_2$ data. As these paired data were symmetric, it is a common practice where control's data were averaged and compared with affected and non-affected data from pathological group. Again, the data were measured once only. Data were organised as affected vs non-affected group as these subjects were mixed of left limb total knee arthroplasty and right limb arthroplasty. If I separate, I have to make two groups of pathology subject right? – Md. Ferdous Wahid Mar 19 '14 at 0:58

In general it shouldn't matter how the p-values were calculated (ie which particular test statistic they came from). A $p < .05$ type decision still has a $5\%$ chance of a false positive, so if you did three hypothesis tests you should correct for three hypothesis tests.