Statistical Testing of More Than Two Data Sets Bartlett Test and ANOVA

6 Statistical Testing of More Than Two Data Sets Bartlett Test and ANOVA 

Comparisons of multiple data sets (m,j 2) require examination of three questions, two of which are obvious extensions of those pertinent to the simple t-test applied to m,j = 2 data sets. 

Question 7. Do all data sets have the same standard deviation (or variance), indistinguishable within a stated confidence level For the m = 2 case (Section 8.2.5) this question was answered by the F-test, but for 2 the Bartlett test is used (see below). If at least one data set variance is thus found to be significantly different from the rest, it is advisable to investigate the reasons for the discrepancy before continuing the statistical testing and/or to omit that particular dataset. On the other hand, if the variances are found to be indistinguishable they can be pooled as described below. 

In the following discussion of this three-step process, numerical examples are generally not provided as they occupy too much space indeed these tests are usually conducted using a computer algorithm (Meier 2000). A more complete discussion, together with an example of a fuUy worked-out procedure, are presented elsewhere (Meier 2000, Section 4.4). Here we sketch out the basic procedures without referring at all to the mathematical theory that justifies the various 

To answer Question 1, the Bartlett test (Bartlett 1937) is applied to the null hypothesis [H(j s j = s 2 = = with [Hj same as H(j BUT at least one of the equalities is replaced by an inequality]. As before, within each data set j, dof = (Wj — 1), and summations over) are over the range] = 1 to The following computational steps are performed  

---