One-Way Analysis of Variance

One-Way Analysis of Variance

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One-Way Analysis of Variance

Analysis of variances focuses on assessing whether there is a statistically significant mean difference between independent groups. One way analysis of variance focuses on determining the mean difference in a given categorical variable based on a continuous dependent variable (Mena et al., 2017). There is only a one-factor variable that is assessed when focusing on a one-way analysis of variance. The high school longitudinal study student data was used in this discussion. The variables included are student gender and T2 Scale of student’s mathematics identity. The dependent variable is the T2 Scale of student’s mathematics identity, while the factor variable is student gender.

Assumptions

Conducting a One-way analysis of variance requires the integration of specific assumptions that must be satisfied to ensure that it is accurately used in statistical analysis. The dependent variable should be measured on an interval or ratio scale. The dependent variable is the T2 Scale of student’s mathematics identity measured on a ratio scale. The independent variable should be made of two or more categories. The independent variable is student gender, which is made of two categories, male and female. Another assumption is that there must be independence of observations (Statistics, 2019).  The observations that have been identified in this case are independent.

The dependent variable should be normally distributed.

The histogram shows that the data is normally distributed, which satisfies this assumption to conduct a one-way analysis of variance.

Another assumption is that there should be no significant outlier in the dependent variable dataset.

The boxplot shows that there are no significant outliers within the dataset hence satisfies the assumption to conduct a one-way analysis of variance.

Analysis

One way analysis of variance was conducted to determine whether there was a mean difference between male and female students based on the T2 Scale of student’s mathematics identity. The results found a statistically significant difference in student gender based on T2 Scale of student’s mathematics identity F(1,20022) = 171.218, p = 0.000, p<0.05). The factor variable included only two categories hence unable to conduct a post hoc test.

Social implications

The findings from the study have shown that there is a difference between male and female students based on the T2 Scale of student’s mathematics identity. Thus student’s mathematical utility differs among students based on gender, which is not supposed to be the case. Teachers need to identify these differences and ensure that there is an equal understanding of mathematics utility between male and female students.

References

Mena, B., José, M., Alarcón, R., Arnau Gras, J., Bono Cabré, R., & Bendayan, R. (2017). Non-normal data: Is ANOVA still a valid option?. Psicothema, 2017, vol. 29, num. 4, p. 552-557.

Statistics, L. (2019). One-way ANOVA in SPSS Statistics–Understanding and reporting the output.