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 statements for meaningfulness in the scenario above

Explanation / Answer

The statement that ANOVA is not significant means that there is no stastical difference in education across three races. It cannot be said with certainity that the eduactional difference across three races differ.

However, since there are differences in mean, it can be inferred that the eduaction levels differ. We should do a stastical test with a higher sample size to say with certainity that eduaction levels differ.

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