Paired Comparisons


I don’t understand why there are two formulas for paired comparisons test. Can you help me?

d - udz / sd ; d / sd .


When testing hypotheses concerning the differences between means (paired comparison), one must make an assumption about the (unknown) population variances. If one assumes the population variances to be equal for both groups, then both samples are used to obtained a pooled estimate of the single population variance. If assumed unequal, both population variances are estimated from the individual samples.

These two assumptions affect the computation of the degrees of freedom and denominator of the t-statistic. This is covered in paragraph 3.2 of Reading 11 of the CFAI curriculum.