Scenario - A results report that does not find any effect and also has small sam

Question

Scenario - A results report that does not find any effect and also has small sample size (possibly no effect detected due to lack of power). A one-way analysis of variance was used to test whether a relationship exists between educational attainment and race. The dependent variable of education was measured as number of years of education completed. The race factor had three attributes of European American (n = 36), African American (n = 23) and Hispanic (n = 18). Descriptive statistics indicate that on average, European Americans have higher levels of education (M = 16.4, SD = 4.6), with African Americans slightly trailing (M = 15.5, SD = 6.8) and Hispanics having on average lower levels of educational attainment (M = 13.3, SD = 6.1). The ANOVA was not significant F (2,74) = 1.789, p = .175, indicating there are no differences in educational attainment across these three races in the population. The results of this study are significant because they shed light on the current social conversation about inequality.

Question - Critically evaluate the sample size in the scenario above .

Explanation / Answer

In this question, we can see that three attributes having the sample size

European American n = 36,

African American n = 23

Hispanic n = 18

So, total sample size is N = 77.

Within groups/Error, the sample size is N-k = 77-3 = 74

Between groups/Treatment, sample size is k-1 = 3-1 = 2

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