Very often in psychology, you will have two columns of numbers and will want to know whether their means differ significantly. To do this you begin by setting up a null hypothesis which says that the means do not differ significantly, and any difference you might see is due to chance.

When you have established this null hypothesis you set up an opposite experimental hypothesis which states that the means do not differ due to chance but rather differ as a result of your manipulation.

You then work out the probability of the null hypothesis being correct. If it is judged to be sufficiently improbable (i.e., a low p value) then you reject it and say that the difference in the means is due to your manipulation and not to chance.

Your two columns of numbers might be from two different groups in an independent-measures experiment (e.g., men versus women, young people versus older people) or they may come from the same people giving scores on two different occasions in a repeated-measures experiment (e.g., before and after caffeine).

How do I know which test to use?

You first need to look at your data and see if they fulfil the following criteria:

1. Interval or ratio data
2. Normally distributed
3. Homogeneity of variance, i.e., are the scores in each of the two groups more-or-less evenly spread about the mean? (although sometimes SPSS actually lets you get away with this one!)

Field (2000) also lists a fourth criterion, which is that that the data should be independent. That is, the behaviour of one participant should not be able to affect the data from another participant.

If you have fulfilled these criteria (that is, if your data are parametric) then you can use a t-test. This will be an independent-measures t-test if your experiment uses an independent-measures design and a repeated-measures t-test if your experiment uses a repeated-measures design.

Information on how to report the results of your t-test can be found on the reporting results page.

If you fail to fulfil the above criteria then you are forced to use a less-powerful non-parametric test. The non-parametric versions of the t-test are as follows:

Independent-measures design: Mann-Whitney U test
Repeated-measures design: Wilcoxon matched-pairs signed-ranks test (to give it its full, glorious title)

All the tests are accessed in SPSS from the Analyse menu. t-tests are then found from the compare means submenu and the others are found from the nonparametric tests submenu. Remember, the repeated-measures t-test is called 'paired-samples t-test' in SPSS. The Mann-Whitney is accessed through nonparametric tests > 2 independent samples and the Wilcoxon test is accessed through the nonparametric tests > 2 related samples option.

For the between-subjects tests you'll need to use a grouping variable to tell SPSS which group each score belongs to. The simplest way is to put a 1 or a 2 in the next column, next to each score, to indicate this, and put those data into the 'grouping variable' field in the dialogue box. Then click 'define groups' and tell SPSS to expect a 1 or a 2.