## Interpreting Independent Samples t Test

** 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 *p*values 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 * M*male = 5.50, female 5.83 with a mean difference of -.33; and visualization test

*male 6.4265, female 4.2622 with a 2.163 mean difference. The 95 % confidence interval lower and upper ranges for*

**M***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.