A researcher conducts a 2 $\times$ 4 between-subjects ANOVA in which 12 participants were observed in each group.If = 18 and = 264,then what is the decision for Factor A at a .05 level of significance using the two-way between-subjects ANOVA?
A)Reject the null hypothesis.
B)Retain the null hypothesis.
C)There is not enough information to answer this question.

Question

A researcher conducts a 2 $\times$ 4 between-subjects ANOVA in which 12 participants were observed in each group.If  = 18 and  = 264,then what is the decision for Factor A at a .05 level of significance using the two-way between-subjects ANOVA?
A)Reject the null hypothesis. 
B)Retain the null hypothesis. 
C)There is not enough information to answer this question.

Quizplus · Accepted Answer

Without knowing the specific statistics (e.g. means, standard deviations) for each group, we cannot calculate the F-value for Factor A. However, since we are given the overall sum of squares for Factor A (18) and the total sum of squares (264), we can calculate the sum of squares error (SSE) as 264-18 = 246. With 2 levels of Factor A and 11 degrees of freedom for error (12 participants per group - 2 groups), we can use an F-table to find the critical F-value for a .05 level of significance. Assuming equal variances across groups, the critical F-value is 4.75. If the calculated F-value for Factor A is greater than 4.75, we reject the null hypothesis (i.e. there is a significant effect of Factor A).

A Researcher Conducts a 2 ×\times× 4 Between-Subjects ANOVA in Which 12 Participants Were Observed in Which

A Researcher Conducts a 2 $\times$ 4 Between-Subjects ANOVA in Which 12 Participants Were Observed in Which