Related t test
Independent t test
The previous two chapters were concerned with descriptive statistics – statistics which simply describe the data which have been obtained, without making any particular inferences about them. In the final three chapters, we will be looking at inferential statistics. Inferential statistics allow us to go beyond the data that we have actually obtained, to infer things about the population that the data have come from. They let us make judgements about whether the distinctive patterns or characteristics in our scores are important, or whether they are just likely to be an artefact, which has happened because of sampling errors or problems with methodology.
As we saw in Chapter 14, these judgements are assessments of probability. We can't be absolutely certain about our conclusions, because there is always room for chance or for sampling errors. We can't rule these out altogether: it is always possible that we may have drawn our sample of research participants from a particularly unusual section of the population, so that they are not representative of their population at all. So there is always some level of uncertainty in our conclusions. When we carry out inferential tests, we become able to put a figure to that uncertainty – to state just what the odds are that our results have happened as a result of sampling error. We can't rule out uncertainty altogether. But we can be pretty exact about how uncertain we are!
In this chapter we will be looking at the kind of statistics we use when we have two or more sets of scores, and we want to know whether they are significantly different. This situation happens surprisingly often in psychological research. It can happen because we have