CRITERIA FOR SELECTING BIVARIATE TESTS OF DIFFERENCES

significant. Thus, for example, when analyzing data we may wish to know the answers to some of the following kinds of questions: Is the proportion of black to white workers the same among men as it is among women? Do women workers earn less than their male counterparts? Does job satisfaction change from one month to the next? Do the scores in one treatment group differ from those in another?

In looking at differences between two variables, the variable which we use to form our comparison groups usually has a small number of values or levels, say between two and six. We shall call this the comparison-group variable to distinguish it from the other one which we shall refer to as the criterion variable. The comparison variable is sometimes known as the independent variable, and the criterion variable as the dependent one. An example of a comparison-group variable would be gender if we wanted to compare men with women. This typically has two levels (i.e. men and women) which go to make up two comparison groups. Race or ethnic origin, on the other hand, may take on two or more levels (e.g. Caucasian, Negroid, Asian, and Mongolian), thereby creating two or more comparison groups. Other examples of comparison-group variables include different experimental treatments (for example drugs versus psychotherapy in treating depression), different points in time (for example two consecutive months), and the categorization of participants into various levels on some variable (such as high, intermediate, and low job satisfaction). The other variable is the one that we shall use to make our comparison (for example income or job satisfaction).

CRITERIA FOR SELECTING BIVARIATE TESTS OF DIFFERENCES

There are a relatively large number of statistical tests to determine whether a difference between two or more groups is significant. In deciding which is the most appropriate statistical test to use to analyze your data, it is necessary to bear the following considerations in mind.

116 Bivariate analysis: exploring differences Categorical data

If the data are of a categorical or nominal nature, where the values refer to the number or frequency of cases that fall within particular categories, such as the number of black female workers, it is only possible to use what is referred to as a non-parametric test (see below for an explanation). Thus, for example, in trying to determine whether there are significantly more white than black female employees, it would be necessary to use a non-parametric test.

Ordinal and interval/ratio data

If the data are of a non-categorical nature, such as the rating of how skilled workers are or how much they earn, then it is necessary to decide whether it is more appropriate to use a parametric or non-parametric test. Since this issue is a complex and controversial one, it will be discussed later in some detail.

Means or variances?

Most investigators who use parametric tests are primarily interested in checking for differences between means. Differences in variances are also normally carried out but only to determine the appropriateness of using such a test to check for differences in the means. Variance is an expression showing the spread or dispersion of data around the mean and is the square of the standard deviation. If the variances are found to differ markedly, then it may be more appropriate to use a non-parametric test. However, differences in variance (i.e. variability) may be of interest in their own right, and so these tests have been listed separately. Thus, for example, it may be reasonable to suppose that the variability of job satisfaction of women will be greater than that of men, but that there will be no difference in their mean scores. In this case, it would also be necessary to pay attention to the differences between the variances to determine if this is so.

Related or unrelated comparison groups?

Which test you use also depends on whether the values that you want to compare come from different cases or from the same or similar ones. If, for example, you are comparing different groups of people such as men and women or people who have been assigned to different experimental treatments, then you are dealing with unrelated samples of participants. It is worth noting that this kind of situation or design is also referred to in some of the following other ways: independent or uncorrelated groups or samples; and between-subjects design. If, on the other hand, you are comparing the way that the same people have responded on separate occasions or under different conditions, then you are dealing with related samples of observations. This is also true of groups of

people who are or have been matched or paired on one or more important characteristics such as, for example, husbands and wives, which may also make them more similar in terms of the criterion variable under study. Once again, there are a number of other terms used to describe related scores such as the following: dependent or correlated groups or samples; repeated measures; and within-subjects design.

Two or more comparison groups?

Different tests are generally used to compare two rather than three or more comparison groups.

The tests to be used given these criteria are listed in Table 7.1. Readers may wish to use this table as a guide to the selection of tests appropriate to their needs. Page numbers are inserted in the table cells to facilitate finding the appropriate tests.