Frequently experimenters wish to make more complex comparisons than simply comparisons between pairs of means. In a hypothetical experiment described earlier, the researcher wished to compare the average pain relief experienced by the aspirin and Tylenol groups with relief experienced by the placebo group. The null hypothesis was:

In other words, the null hypothesis was that the average amount of relief experienced by subjects taking either of the two drugs was the same as the relief experienced by subjects taking a placebo. This null hypothesis can be specified in terms of a linear combination of means:

H

It makes a tremendous difference whether or not a comparison among means is planned prior to viewing the data. If the comparison is planned in advance, it can be tested using the procedures spelled out in another section.