In the first part of this chapter you have looked at statistical theory concerned with the issue of how you can generalize from statistical samples to statistical populations. In some research this may be all you want to do. You may be interested in identifying the levels of job commitment in an organization, or the ethnic mix of the people there. To do so you can take a random sample of, say, 50 people, and measure their job-commitment levels, or take 30 people at random and note their ethnicity. You can then use this information to estimate the mean job-commitment level, or the proportion of people from different ethnic groups, in the organization as a whole.
In the case of surveys such as this, all you may wish to do is to provide information about the central tendency and dispersion of the continuous data in your sample (for example, the mean, confidence interval of the mean, and the standard deviation of well-being levels), or the frequencies of categories of categorical data (for example, the proportion of men and of women). These may be the only reasons for conducting the survey.
However, in analytical research you will wish to go beyond merely describing the data in your samples, and beyond using your sample statistics to estimate population parameters.
For example, you may, in addition, want to:
■ examine relationships between different variables;
■ try to predict scores on one variable from the scores on one or more others;
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■ see if the central tendency of a variable is greater for one group of people than another.
Broadly speaking, this is achieved by focusing on two sorts of relationships: associations and differences.
Associations
Associations occur between variables. While the nature of these associations can, in prin-ciple, be very complex, in practice most widely used statistical techniques assume that these relationships are relatively simple. We will focus on the possible associations between two continuous variables. Such associations can be positive, or negative, or there can be no asso-ciation at all. Examples of each of these three types of relationship are shown in Tables 2.4, 2.5 and 2.6. In each table the well-being and job commitment of five employees is shown.
Both of these variables are measured on scales ranging from 1 to 5. So the first person in Table 2.4 scored 5 for being and 5 for job commitment, the second scored 4 for well-being and 3 for job commitment and so on.
You would say that there is a positive association between well-being and job commit-ment in the data presented in Table 2.4 because, quite clearly, having a relatively high well-being score is associated with receiving a relatively high job-commitment score. And,
Table 2.4 A positive association between well-being and job commitment
Case Well- Job
being commitment
1 5 5
2 4 3
3 3 4
4 2 2
5 1 1
Table 2.5 A negative association between well-being and job commitment
Case Well- Job
being commitment
1 5 1
2 4 2
3 3 3
4 2 4
5 1 5
Table 2.6 No association between well-being and job commitment
Case Well- Job
being commitment
1 5 5
2 4 1
3 3 2
4 2 3
5 1 4
of course, the converse is also true, low well-being is associated with low commitment. In Table 2.5 there is a negative or inverse relationship between well-being and job commit-ment. Here, the higher the well-being score, the lower the job-commitment score tends to be. Finally, in Table 2.6 there is no association at all between well-being and job commit-ment. We cannot say that higher well-being is associated with higher job commitment, nor can we say that higher well-being is associated with lower job commitment: the variables are not associated at all.
Differences
Having considered associations, you can now move on to the issue of differences. In the case of categorical data, researchers are generally interested in differences between propor-tions. In Table 2.7 the contingency table presented in Chapter 1 (Table 1.6) is reproduced.
It shows the numbers and proportions of males working in four regions and the numbers (and proportions) of females working in those four regions. You might be interested in examining whether the proportion of men working in each of the four regions is different from the proportion of women working in each of the regions.
In the case of continuous variables, you will usually be interested in differences in central tendency. Tables 2.8 and 2.9 give the scores for the well-being of men and women, again measured on a 5-point scale. In Table 2.8 the mean well-being score for men, 4.2, is higher than the mean well-being score for women, 2.8. Therefore, there is a difference in the central tendency of the well-being scores of the men and women. However, in Table 2.9 the mean score is 4.0 both for men and for women, and there is no difference in central tendency in this case.
It is worth noting that while with continuous variables you will usually be interested in dif-ferences in central tendencies of various variables, it is also possible to examine whether differ-ences exist in their dispersion (for example, are the well-being scores of men more dispersed than those of women?).
You can examine associations between both categorical and continuous variables, and you can also examine differences between both categorical variables (in relation to propor-tions) and continuous ones (in relation to central tendency, and sometimes dispersion). The analysis of associations and differences lies at the heart of many inferential statistical methods and, as you will see later, statistical packages like SPSS contain a variety of powerful and 1111
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Table 2.7 Breakdown of the region in which people work and their gender: frequencies and percentages (reproduced from Table 1.6)
Male Female
Number Percentage Number Percentage
North 26 28.0 130 57.8
South 14 15.1 13 5.8
East 31 33.3 12 5.3
West 22 23.7 70 31.1
sophisticated statistical techniques to examine associations and differences in great detail, and under a variety of circumstances. However, before moving on to discuss these tech-niques, we will first of all examine some of the core theoretical ideas on which they are based. Armed with an understanding of these ideas, you will be in a much better position to understand what the techniques are doing, and how the results they produce should be interpreted.