Statistics: T-Tests and ANOVA
T-Tests and ANOVA: Statistics
Independent sample t-tests and ANOVA are both used to test for differences in means of unrelated, independent groups. However, ANOVA has been shown to be more effective than the t-test when the number of groups is more than two. This is because ANOVA controls the risk of type I error by holding the probability constant at a .05 significance level. This text explores the differences between the two tests, and the specific situations when each one is more effective.
Independent Sample t-Tests
My week 1 research questions were geared at assessing the impact of community youth sporting programs on adolescents' academic performance, discipline, and social well-being. RQ4 was selected to be used for this particular analysis. It read:
"Are there any significant differences between the levels of discipline of adolescents who engage in community youth sporting activities and those that do not?"
Well, this research question lends itself effectively to both ANOVA and the independent sample t-tests. However, ANOVA is preferred when the number of groupings being tested is more than 2; that is, when three or more unrelated groups are being measured on the same independent variable (Sukal, 2013). In our case, however, there are only two groupings of data -- i) adolescents who engage in community sporting activities and ii) adolescents who do not engage in community sports activities, which implies that the sample t-test can be used effectively (Sukal, 2013).
Variables and their Attributes: it is evident, from the research question, that community youth sporting activities is the independent variable, whereas the level of discipline is the dependent variable. The independent variable would be measured based on whether or not a participant engages in any of the state-funded youth sporting events in their community, be it rugby, football, tennis, hockey or basketball. The variable will be composed of two groups -- 1) a Yes group, for adolescents who participate in any of the aforementioned sporting events; and 2) a No group for adolescents who do not participate in any youth sporting event in the community. This would make the variable a discrete, nominal variable because there is a finite number of possible options (just two) and the numbers 1 and 2 are nothing but category identifiers with no quantitative significance.
The dependent variable, level of discipline, on the other hand, would be defined in terms of an individual's ability to self-regulate...
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