Studentized Range Distribution (1 of 3)

The studentized range distribution is used for testing all differences among pairs of means. It is similar to the t distribution, differing only in that it takes into account the number of means under consideration. The more means under consideration, the larger the critical value of ts (studentized t). This makes sense since the more means there are, the greater the likelihood that at least some differences between pairs of means will be large due to chance alone. First, consider the case in which there are only two means. The formula for t used to compare two sample means is:

where is Md = M1 - M2, µ1- µ2 is the value specified by the null hypothesis (almost always zero), and

where MSE is the means square error and nh is the harmonic mean of the two sample sizes. If the null hypothesis is that µ1 - µ2 = 0, then the formula for t can be written as shown on the next page: next