What is the association between involvement in high school extracurricular activities and GPAs in high school seniors in Texas? This is an ideal question for a one-way ANOVA because:
- One-way ANOVA tests can accommodate one independent variable, divisible into as many nominal categories as required. In this case, the independent variable is the extracurricular activity the participants are involved in, divided into sports, student government (student council, yearbook committee), musical group (choir, orchestra, band), and academic groups (Mathletes, language clubs, science clubs). This fits the qualitative, nominal characteristic requirement for the one-way ANOVA independent variable.
- The dependent variable must be a ratio or interval scale. The dependent variable in this study is GPA, which is quantitative, continuous ratio data measured from 0-4.0.
- One-way ANOVA tests require that the groups in question have a homogeneity of variance, or that the “groups should all have reasonably similar standard deviations”(Sukal, 2013, p. 211).
- Finally, one-way ANOVA tests work off of the assumption that the samples are pulled from a population that is normally distributed (Sukal, 2013). The population is high school seniors in Texas, and while not yet confirmed with the actual data collection, it is assumed that the population will yield a normal distribution.
The null hypothesis posits that there is no difference in GPAs across the 4 groups of extracurriculars. It is annotated in the following manner: H0=µsports= µgovt= µmusic= µacademic. Meanwhile, the alternate hypothesis, Ha=µsports ≠µgovt ≠µmusic ≠µacademics, suggests that the differences in GPAs across the extracurricular groups are statistically significant.
Running a statistical t-test with the same data multiple times (to account for the multiple categories within the independent variable) increases the potential for TypeI errors; running a single test with the ANOVA technique controls this inflation (Sukal, 2013). Granted, the ANOVA test itself will not indicate which means are significantly different, but follow-up post-hoc tests can provide that data (Sukal, 2013). Assuming that the groups are meet the homogeneity of variance and normal distribution requirements, Type I errors will be minimal and remain at the original alpha level (p=.05 in most cases) (Laerd Statistics, 2018).
Laerd Statistics. (2018). One-way ANOVA. Retrieved from Laerd Statistics: https://statistics.laerd.com/statistical-guides/one-way-anova-statistical-guide-2.php
Sukal, M. (2013). Research Methods: Applying Statistics in Research. Bridgepoint Education.