This chapter is from the book
This chapter is from the book
This chapter is from the book
R has a package named DescTools. It combines a large variety of functions: basic analyses that you might well want to carry out before undertaking a more advanced, perhaps more demanding analysis.
For example, one difficulty that can crop up when you want to compare the means of two or more groups is the Behrens-Fisher problem. The difficulty arises if you want to test the statistical significance of the difference between the group means.
When two groups have an unequal number of observations and also unequal variances, one of two outcomes is possible:
The larger group has the larger variance. The process of pooling the variances of the two groups gives the larger group a greater effect on the pooled variance. This artificially increases the denominator of the t-test, making it more conservative than the t-distribution would lead you to believe. The tables may tell you that your alpha level, the probability of rejecting a true null hypothesis, is 0.01 when—because of the relationship between the group sizes and the group variances—alpha is actually something like 0.005.
The larger group has the smaller variance. In this case, the larger group still exercises a greater effect on the pooled variance, just because it has more records. But in this case the effect is the reverse: to artificially reduce the denominator of the t-test, making the t-test more liberal than you would otherwise expect. Again, if the nominal alpha level is 0.01, the actual alpha level might be 0.05. You will reject a true null hypothesis more often than the tables say you will.
This is the sort of thing you’d like to know before you go to the trouble of running the t-test. Depending on the reason for the unequal group sizes, it may be legitimate to add or remove records so that both groups have the same number of observations. (With equal group sizes, unequal variances do not pose a problem to the statistical test.) Or you might decide to use Welch’s correction, which is a not entirely satisfactory solution to the Behrens-Fisher problem.
The point is that R’s DescTools package gives you the tools you need to make that sort of test, one that you would want to run early on in the analysis process. Before 2015, most of the tools in the package were available in R, but scattered across different packages. That made it a time-consuming task to get specific preliminary analyses done. Now you can get access to them by loading just the one DescTools package.