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# Two-Way ANOVA

I am having a difficult time with testing the hypothesis within the data. I am able to create the two way anova table for this, however I think I am having difficulties interpreting the information from it.

See Word file for questions.

? Test the hypotheses about significance of Cover main effect with 95% confidence. Remember that you reject the null hypothesis if the p-value is less than the desired level of significance, which is 5% in this case.

? Test the hypotheses about significance of Display main effect with 95% confidence. Remember that you reject the null hypothesis if the p-value is less than the desired level of significance, which is 5% in this case.

? Test the hypotheses about significance of Cover-Display interaction effect with 95% confidence. Remember that you reject the null hypothesis if your p-value is less than the desired level of significance, which is 5% in this case.

1. Explain how two cover designs and two displays affect the magazine sales? Select the cover/display combination that increases sales the most and make suggestions on the promotion of the magazine.

2. From the excel file, Estimate the size of the Cover-Display interaction effect. Is there any sizeable interaction effect? Is Blue&Red cover attractive even in the parking lot and White&Black cover id not appealing even at the check-out line?

3. Estimate two-way ANOVA model for the sales' data. Use 0.05 alpha and 15 rows per sample.

#### Solution Preview

? Within the COLUMNS row, locate F-statistics and its p-value. (This is 108.824, 9.66)
? Test the hypotheses about significance of Cover main effect with 95% confidence. Remember that you reject the null hypothesis if the p-value is less than the desired level of significance, which is 5% in this case.
Two-way ANOVAs are similar to one-way ANOVAs. However, when using a one-way ANOVA, you only have one factor and are testing whether or not it has an effect on the variable. In a two-way ANOVA, you are testing two factors. Either (or both) of the factors might effect the variable. We need to look at the main effect of each factor and any interaction between them.

For the main effect of Cover, we are testing the hypotheses:
Null hypothesis: the population means of the different values of "Cover" are equal; i.e. there is no main effect for "Cover"
Alternative hypothesis: the population means of the different values of "Cover" are different; i.e. there is a main effect for "Cover"

Look at the p-value in the "Columns (cover main effect)" row of the ANOVA table. The p-value is p = 9.66 x 10^(-15). This is less than p = 0.05. Therefore, we can reject the null hypothesis and assume that there is a main effect of Cover.

? Within the SAMPLE row, locate F-statistics and its p-value. (This is 49.1369706 and 3.33
? Test the hypotheses about significance of Display main ...

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