A one-way within-groups ANOVA on 3 and 18 degrees of freedom results in an F statistic of 3.12.What decision should be made about the hypothesis based on this statistic?
A) Fail to reject the null hypothesis because the F statistic does not exceed the critical cutoff.
B) Fail to reject the null hypothesis and conclude there is no effect of the independent variable.
C) Reject the null hypothesis and conclude there are differences among the levels of the independent variable.
D) Reject the null hypothesis and conclude the independent variable has no effect.

Question

Quizplus · Accepted Answer

To determine whether to reject the null hypothesis, one must compare the calculated F statistic to the critical F value at a given significance level (usually .05) for the specific degrees of freedom (df between and df within). Without the critical F value or significance level provided, the most cautious decision is to fail to reject the null hypothesis if the F statistic does not clearly exceed common critical values for these degrees of freedom. Typically, an F of 3.12 with 3 and 18 degrees of freedom would not be considered significantly high enough to reject the null hypothesis at the .05 level, hence the choice to fail to reject.

A One-Way Within-Groups ANOVA on 3 and 18 Degrees of Freedom