Analysis of variance
Making sense of ANOVA results
Two-way ANOVA tests
In Chapter 17, we looked at the t test, which provides us with a parametric method for exploring the differences between two sets of scores. The t test, as we saw in that chapter, works by comparing the means and the standard deviations of the two groups. If the means seem similar, and the standard deviations overlap, then the test concludes that the two sets of scores are likely to have come from the same population. But if they seem very different, the test statistic tells us that they are likely to have come from different populations.
The only problem with the t test – or the main one, anyway – is that it can only deal with two sets of scores at a time. Quite often in modern research, we find that we are actually dealing with several sets of scores, and not just two. Sometimes, this is because we are looking at several different categories of one variable, like having three or four age groups in the study, rather than just two. Sometimes it is because we want to look at the effect of more than one variable at a time. For example, there are many more mature students doing degrees nowadays, and so if we were looking at study skills, we might want to take both age and IQ as variables to be investigated, rather than just looking at one of them on its own.
It's possible, of course, to look at these results by doing lots of different t tests. But that has a number of disadvantages. One of them is that it is clumsy, and gets even more so the more variables we include. But a more important one is that doing several tests affects the probabilities. If a test comes out as significant at the level of p < .05, that means that the result we have obtained is likely to come about because of chance one time in twenty. What this implies is that if we did twenty tests, then we would be very likely to get these findings by