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 D7.1 Interpreting Independent Samples t Test

In Output 10.2, we investigated the difference between two unrelated or independent groups (in this problem males and females) on whether there is a difference regarding their average math achievement scores. Grades in high school, and visualization test scores.  An assumption of the independent samples t test was conducted using the Levene’s test to see whether the variances of the two groups are equal (Morgan, Leech, Gloeckner, & Barrett. 2013).  Based on the Levene’s Test equal variances assumed, there is a significant difference for the three independent variables.  Math achievement test scores p = .009, t = 2.697, df =73; grades in high school p = .369, t = -.903, df = 73; and visualization test scores p = .016, t = 2.466, and df = 73.  Therefore, because math achievement test scores and visualization test scores pvalues are less than .05 the F test concludes that there is statistically significance.  On the other hand, grades in high school p value is not statistically significant because p value is greater than .05 (Morgan et al., 2013).

The t test group statistics table for Output 10.2 show the N as 34 males and 41 females.  The mean (M) for the two variables grades in high school and visualization test are as follows, grades in high school Mmale = 5.50, female 5.83 with a mean difference of -.33; and visualization test M male 6.4265, female 4.2622 with a 2.163 mean difference.  The 95 % confidence interval lower and upper ranges for grades in high school is -1.056 – .397 and visualization test is .41486 – 3.91369.  According to Morgan et al (2013), the effect size d for grades in high school is approximately .6, which is a typical size for effects in behavioral sciences (p. 177).  This implies that based on 34 males and 41 females, the males have higher visualization test scores, but females have slightly higher grades in high school compared to the males (Morgan et al., 2013). 

D7.2 Interpreting Paired Samples t Test

In Output 10.4, the paired samples correlation for mother’s education and father’s education was conducted to determine if students’ fathers and mothers have more education and if there is a correlation in the education levels.  The paired samples statistics test table show the father’s education means (M = 4.73) and mother’s education mean (M = 4.14).  The Paired Samples Correlations for these two variables is .681 or .68 (Morgan et al., 2013).  The results of the paired or correlated samples t test indicated that the students’ fathers had an average significantly more education than their mothers, t (72) = 2.40, p = .019, d = .28.  The difference, although statistically significant is small according to the Cohen (1998) guidelines (Morgan et al., 2013, p. 182).

If the r was 0.90 and the t was 0.00 it would suggest a strong correlation between father’s and mother’s education which would indicate that there are no unequal variances based on the t test assumptions.  In contrast, if the r was 0.00 and the t test was 5.0 there would be an assumption that the variables does not correlate and the t test would adjust the unequal variances of the two variables (Morgan et al., 2013).

Reference

Morgan, G. A., Leech, N., Gloeckner, G., & Barrett, K. (2013). IBM SPSS for introductory statistics: Use and interpretation (5th ed.). New York: Brunner-Routledge.