How to Design a Research Study Using a One-Way ANOVA

The single factor ANOVA is a parametric technique which tests whether the several group means are statistically different from each other (Laureate Education, 2016). Considering the HS Long Study data provided, one of the potential studies that can be analyzed using this technique is to examine whether the student’s score for mathematics utility varies with their gender. Tentatively, the research question with this study would be, “How does the student’s mathematics utility vary with their gender?” In this case, the gender is the independent variable (IV) measured in a nominal scale while the mathematics utility is the dependent variable (DV) measured in an interval scale. Stated as the hypothesis is:

H0: The math utility mean scores were equal across the two genders

H1: The math utility mean scores were different across the two genders

The study tested assessed whether gender had any impact on the students’ perceived mathematics utility. The findings reveal that the mean scores for the two groups were statistically difference, F (1,18800) = 18.284, p < 0.05. Since the observed probability was less than 5% significance level, the H0 was rejected (Aron and Coups, 2008).

Table 1

One-Way Anova Test Output 

The above analysis tells that the difference between the group means is exceeding what is expected (that the mean difference is zero) due to random variation and the effect of gender on the perceptions on the utility achieved from learning mathematics - gender influenced the student’s rating on their mathematics utility (Gamst et al. 2008). However, the post hoc analysis and effect size could not be calculated since the groups were less than three. Though it is clear that the mean utility for males exceeded that of the females, Males, 95% CI [-0.0065, 0.0346] and Females, 95% CI [-0.0679, -0.0284]. It implies that, adopting gender-oriented learning approaches may improve on the utilities for both these two genders.

References

Aron, A., & Coups, E. J. (2008). Statistics for the behavioral and social sciences: A brief course . Upper Saddle River, NJ: Pearson Prentice Hall.

Laureate Education (Producer). (2016). One-way ANOVA demonstration [Video file]. Baltimore, MD: Author.

Gamst, G., Meyers, L. S., & Guarino, A. J. (2008). Analysis of variance designs: A conceptual and computational approach with SPSS and SAS . Cambridge University Press.