Reference no: EM132247939

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.

For math achievement test scores, F(2, 70) = 7.88, p = .001 indicating a statistically significant difference between the different education levels.

D8.2 Interpreting One-Way ANOVA with Post Hoc test

For Problems 11.2 and 11.3, the author ran different post hoc comparisons to identify the source of variances between means. The author found a statistically significant difference between the three levels of father's education for:

grades in high school, F(2, 70) = 4.09, p = .021,

math achievement, F(2, 70) = 7.88, p = .001.

Using the SPSS software, the author generated a multiple comparison table based on the Tukey test (Figure 11.2a), Tukey subsets table (Figure 11.2b), one-way ANOVA table (Figure 11.2c) and multiple comparisons table based on the Games-Howell test (Figure 11.2d).

Figure 11.2b indicates that the mean grade in high school is 5.34 for students whose fathers whose education level did not exceed high school graduation, 5.56 for students whose fathers attended some college, and 6.53 for students whose fathers obtained a bachelor's degree or higher level of education (Morgan et al., 2013).

The Tukey HSD tests in Figure 11.2b illustrated a significant difference in grades between that the high school education level and BS degree level groups with a large effect size (p < .05, d = .85). Using the Games-Howell post hoc test, the author also observed a statistically significant difference between the means of math achievement for the low education and medium education group with (p < .017, d = .80).

The mean math education for low education group also displayed a significant difference from that of the high education group of (p = .008, d = 1.0).

This information allowed the author to conclude that there is not a statistically significant between the grades of students whose fathers did not exceed a high school education and those with some college. However, there was a statistically significant difference in the math achievement scores between these same groups.

Figure 11.2a

Figure 11.2b

Figure 11.2c

Figure 11.2d

For Problem 11.3, the author used a nonparametric statistic to test the differences among the three categories of father's education for the math achievement and competence scale dependent variables.

This was necessary because the homogeneity of variance assumption was violated for math achievement as explained in the authors' analysis of Problem 11.1. Using the SPSS software, a Kruskal-Wallis test was performed resulting in a ranks table (Figure 11.3a) and test statistics table (Figure 11.3b).

Figure 11.3a

Figure 11.3b

The ranks table (Figure 11.3a) shows the mean ranks of math achievement test scores and competence scale for each category or level of father's education. The Kruskal Wallis test results χ² (2, N = 73) = 13.38, p = .001 (Figure 11.3b) suggest that the three father's education groups differed significantly on levels of math achievement.

Figure 11.3a shows that fathers with some college (43.78, n = 16) displayed significantly higher math achievement scores than fathers of students who did not progress beyond high school (28.43, n = 38).

Also, the mean rank for math achievement of students whose fathers had a bachelor's degree or higher level of education (48.42, n = 19) was much higher than the mean rank for fathers who were high school graduates or less (28.43, n = 38). This information collectively supports the conclusion that the education levels of the fathers of students have a statistically significant impact on their math achievement scores.

References

Morgan, G., Leech, N., Gloeckner, G., Barrett, K. (2013). IBM SPSS for Introductory Statistics. New York: Routledge.