12-2 Two-Way ANOVA 629 No (Fail to reject H0 of no interaction effect.) Yes (Reject H0 of no interaction effect.) Start Stop. Don’t consider the effects of either factor without considering the effects of the other. Is there an effect due to interaction between the two factors? Test for effect from row factor using the P-value for the test statistic If the P-value is small (such as less than 0.05), conclude that there is an effect from the row factor. F5 MS (row factor) MS (error) Test for effect from column factor using the P-value for the test statistic If the P-value is small (such as less than 0.05), conclude that there is an effect from the column factor. F5 MS (column factor) MS (error) Test for an interaction between the two factors. Use the P-value for the test statistic If the P-value is small (such as less than 0.05), conclude that there is an interaction effect. F5 MS (interaction) MS (error) FIGURE 12-4 Procedure for Two-Way Analysis of Variance Conclusion: • Reject: If the P-value corresponding to the test statistic is small (such as less than or equal to 0.05), reject the null hypothesis of no effect from the row factor. Conclude that there is an effect from the row factor. • Fail to Reject: If the P-value is large (such as greater than 0.05), fail to reject the null hypothesis of no effect from the row factor. Conclude that there is no effect from the row factor. Column Factor For the column factor, test the null hypothesis H0: There are no effects from the column factor (that is, the column values are from populations with the same mean). Find the P-value corresponding to the test statistic F = MS(column)>MS(error). Conclusion: • Reject: If the P-value corresponding to the test statistic is small (such as less than or equal to 0.05), reject the null hypothesis of no effect from the column factor. Conclude that there is an effect from the column factor. • Fail to Reject: If the P-value is large (such as greater than 0.05), fail to reject the null hypothesis of no effect from the column factor. Conclude that there is no effect from the column factor.
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