Final answer:
To decide on the ANOVA outcome, compare the calculated F-statistics for each factor and the interaction with the critical F-values from an F-distribution table. Without the critical values at the 0.05 significance level and the context, we cannot definitively conclude whether to reject or fail to reject the null hypothesis.
Step-by-step explanation:
The question involves deciding upon the correct action after conducting a 2 × 2 between-subjects ANOVA. Given the Mean Squares for factor A (MSA), factor B (MSB), the interaction between factors A and B (MSA×B), and the Mean Square Error (MSE), we determine the F-statistics for each factor and for the interaction. The F-statistic is calculated by dividing the Mean Square of the factor by the Mean Square Error (e.g., FA = MSA / MSE).
For factor A, FA = 24 / 6 = 4. For factor B, FB = 20 / 6 = 3.33. For the interaction, FA×B = 30 / 6 = 5. These F-statistics will be compared with critical F-values from an F-distribution table, corresponding to the degrees of freedom and the significance level (α = 0.05). Since each group has eight participants, the degrees of freedom for the numerator (between groups) is the number of groups minus one. Here, we have two levels for each factor, thus for each main effect, we have 1 degree of freedom, and for the interaction, we have 1 (A levels - 1) × 1 (B levels - 1) = 1, and for the denominator (within groups), degrees of freedom is total number of participants minus number of groups, which is 32 minus 4, giving us 28.
If the calculated F-statistics are greater than the critical values, we would reject the null hypothesis. If they are smaller, we would fail to reject the null hypothesis. Thus, based off the given information alone, without the critical F-values, we cannot definitively answer the question without more data or context.
If the student is asked to make a decision at 0.05 significance level, they would usually compare the calculated F-statistics with the critical F-value from an F-distribution table for the corresponding degrees of freedom. If the F-statistic value is higher than the critical F-value, they would reject the null hypothesis. If it is lower, they would fail to reject it. Additional steps such as conducting a post hoc test or increasing the sample size depend on the context and results of the ANOVA.