Relationship between GPA and Race
The research study intended to be investigated in our case, based on the data provided, there are statistically significant differences between the means of the high school GPA among the three races. The races being tested include; black, White, and Hispanic. The one-way analysis Variance is the statistical analysis used to test the hypothesis, which is:
Alternative hypothesis
- There is a relationship between GPA and Race.
Null hypothesis
- There is no relationship between GPA and race.
I believe the One-way ANOVA method is appropriate in this case because the one-way analysis of variance (ANOVA) is often used in determining if there is a statistically significant difference in the means of two or more independent variables or groups. It is used when there is a minimum of three variables, which are the three races: Black, White, and Hispanic in this case.
Findings
| Descriptives | ||||||||
| High School GPA (recoded from “grade”) | ||||||||
| N | Mean | Std. Deviation | Std. Error | 95% Confidence Interval for Mean | Minimum | Maximum | ||
| Lower Bound | Upper Bound | |||||||
| BLACK:(1) | 166 | 3.0572 | .63440 | .04924 | 2.9600 | 3.1544 | 1.00 | 4.00 |
| WHITE:(2) | 758 | 3.2323 | .63649 | .02312 | 3.1869 | 3.2777 | 1.00 | 4.00 |
| HISPANIC:(3) | 179 | 3.0905 | .66169 | .04946 | 2.9929 | 3.1881 | 1.00 | 4.00 |
| Total | 1103 | 3.1830 | .64399 | .01939 | 3.1449 | 3.2210 | 1.00 | 4.00 |
Looking above in the highlighted section, the sample data produces a difference in the mean scores of the GPA among the three races. In particular, the data analysis shows that the Whites’ GPA is higher than that of the other three races. The key question to be investigated if the differences reach significance.
| Test of Homogeneity of Variances | |||||
| Levene Statistic | df1 | df2 | Sig. | ||
| High School GPA (recoded from “grade”) | Based on Mean | .209 | 2 | 1100 | .812 |
| Based on Median | .104 | 2 | 1100 | .901 | |
| Based on Median and with adjusted df | .104 | 2 | 1079.492 | .901 | |
| Based on trimmed mean | .164 | 2 | 1100 | .848 | |
In the highlighted section above, the Levene statistic’s significance value based on a comparison of medians is 0.901. This means that the homogeneity of variance requirement has not been met since 0.901 is greater than 0.05 hence not a significant result. In this case, the ANOVA test can be considered to be robust.
F statistic result:
| ANOVA | |||||
| High School GPA (recoded from “grade”) | |||||
| Sum of Squares | df | Mean Square | F | Sig. | |
| Between Groups | 6.001 | 2 | 3.001 | 7.318 | .001 |
| Within Groups | 451.018 | 1100 | .410 | ||
| Total | 457.020 | 1102 | |||
Our F value is 7.318 with a p-value of 0.001whis is less than alpha 0.05, which means that there is a statistically significant difference among the three races’ GPA. However, to know which of the various pairs of means the difference is significant, we look at the post hoc Tukey HSD test result.
| Multiple Comparisons | ||||||
| Dependent Variable: High School GPA (recoded from “grade”) | ||||||
| Tukey HSD | ||||||
| (I) Respondent’s race (trichotomized B/W/H) | (J) Respondent’s race (trichotomized B/W/H) | Mean Difference (I-J) | Std. Error | Sig. | 95% Confidence Interval | |
| Lower Bound | Upper Bound | |||||
| BLACK:(1) | WHITE:(2) | -.17509* | .05487 | .004 | -.3039 | -.0463 |
| HISPANIC:(3) | -.03327 | .06900 | .880 | -.1952 | .1287 | |
| WHITE:(2) | BLACK:(1) | .17509* | .05487 | .004 | .0463 | .3039 |
| HISPANIC:(3) | .14182* | .05321 | .021 | .0169 | .2667 | |
| HISPANIC:(3) | BLACK:(1) | .03327 | .06900 | .880 | -.1287 | .1952 |
| WHITE:(2) | -.14182* | .05321 | .021 | -.2667 | -.0169 | |
| *. The mean difference is significant at the 0.05 level. | ||||||
From the Tukey HSD (Honest Significant Difference) above, the highlighted values show the mean differences between the GPA and RACE groups that are significant. For BLACK-WHITE and WHITE-BLACK, the p-value is 0.004, which is less than 0.05; hence it is significant. For the WHITE-HISPANIC and HISPANIC-WHITE, the p-value is 0.021, which is less than 0.05 hence significant.
Conclusion
There was a statistically significant difference between groups, as demonstrated by one-way ANOVA (F (6,451) = 7.381, p = 0.001). Hence we reject the null hypothesis that there is no relationship between GPA and race and accept the alternative hypothesis. This means that there is a significant relationship between GPA and Race.
Reference:
Gayles, J. (2012). Race, Late Bloomers, and First-Year GPA: Predicting beyond the Freshman Year. Educational Research Quarterly, 36(1), 13-29.