## Interpreting One‐Way ANOVA

D8.1 Interpreting One‐Way ANOVA

Procedures

In this exercise, the author used the one-way ANOVA parametric statistic to compare three levels of father’s education in terms of high school grades, visualization test scores and math achievement test scores. By using the SPSS software to compare means, the author produced the descriptive statistics table (Figure 11.1a), a test of homogeneity of variances (Figure 11.1.b) and ANOVA table (Figure 11.1.c) used in the analysis below.

Figure 11.1a

Figure 11.1b

Figure 11.1c

Analysis

The descriptive statistics table (Figure 11.1a) contains information about the valid no scores, means, standard deviation and confidence intervals for each value of the three dependent variables. Figure 11.1b provides the outcomes for Levene’s Test of Homogeneity of Variances for each of the three dependent variables and the associated father’s education levels. The following can be interpreted from the results in this table:

• For grades in high school, p = .220 is not statistically significant, thus illustrating that the assumption of equal variances was not violated (Morgan, Leech, Gloeckner, and Barrett, 2013).
• For visualization test, p = .153 is not statistically significant, thus illustrating that the assumption of equal variances was not violated (Morgan et al., 2013).
• For math achievement test scores, p = .049 is statistically significant, indicating that the assumption of equal variances was violated and that equal variances should not be assumed (Morgan et al., 2013). Since the ANOVA table shows a statistically significant value of F = 7.881, p = .001, therefore, a post hoc test could be used to evaluate this variable.

The ANOVA Table (Figure 11.1c) shows the following differences between groups:

• For grades in high school, F(2, 70) = 4.09, p = .021 indicating a statistically significant difference between the different education levels.
• For visualization test, F(2, 70) = .763, p = .47 indicating that different father’s education levels did not make a statistically significant difference in visualization test scores.