Chapter 6, Table 1: Performing a Trend Analysis Through SPSS Syntax

The data in Table 6.1 consist of recall scores for 24 children who have been randomly assigned to one of four experimental conditions where there are 6 children in each condition. The experimental conditions of interest are 1, 2, 3, and 4 minutes where the number of minutes is the amount of time the child is allotted to study a list of words before attempting to recall the words. The dependent variable (i.e., the recall scores) are the number of words the child is able to recall after a brief interference task.

The first hypothesis of interest is whether the number of words recalled is linearly related to the number of minutes spent studying. We first test this hypothesis by determining if the linear trend (/POLYNOMIAL = 1) is statistically significant. Pages 252 and 253 are associated with this test.

At this point, click Run and then All to obtain the results.

If one is interested in estimating the slope associated with the linear trend, then one should specify a /CONTRAST statement (as was done in Chapter 4) with the contrast coefficients corresponding to a linear trend instead of a /POLYNOMIAL statement. Of course, one must then remember to divide by the sum of the squared contrast coefficients in order to obtain the correct estimate of the slope.

Next, we are interested in determining if there is any nonlinearity present in the relationship between the number of words recalled and the amount of time spent studying. In fact, the analysis just presented supplies the statistical test of this hypothesis in the “Deviation” row under “Linear Term” in the output. Page 257 demonstrates the results associated with this statistical test.

Finally, we are interest in determining if the quadratic or cubic components of the relationship between the number of words recalled and the amount of time spent studying are statistically significant. In order to obtain the results for these tests, simply specify the degree of the polynomial as cubic instead of linear (/POLYNOMIAL = 3). It is important to note that the results for the linear, deviation from linear, quadratic, and cubic trends replicated by the procedures shown here are illustrated in Table 6.3.