It is simply the positive square root of the variance. In the examples shown in figure 2.2, the standard deviation in the first group of numbers is 1.41, while in the second group it is 2.83. The variance and the standard deviation usually have no very obvious interpretation. Analyzing variance, however, is extremely important and will be the basis of much of what follows in this chapter. In other words, its purpose is to tell us the degree to which groups are different from one another in terms of some variable.
Total variance is calculated exactly as shown earlier in the chapter.
Within-group variance is calculated in the same way, except that, for each case, the group mean is substituted for the overall mean in the variance formula. Figure 2.3 shows numbers for three groups. Eta 2 thus equals .89, indicating that 89 per cent of total variance reflects differences between the three groups, with within-group variance accounting for the remaining 11 per cent. A scatterplot is used to provide a graphic display of the relationship between two variables. Each case in a set of data can be placed on the graph by plotting the intersection of its coordinates on the two axes.