c. The factor is the type of TV program that was watched. The treatment is the embedded commercials in the TV programs.

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1 STAT E Statistical Methods Assignment 9 Solutions Exercises 12.8, 12.13, For each test: Include appropriate graphs to see that the conditions are met. Use Tukey's Honestly Significant Difference test to investigate pairwise differences. Exercise 12.8 a. The experimental units are 324 adult TV viewers b. The dependent variable is the number of brand names recalled in commercial messages, with scores from 0 (no brands recalled) to 9 (all nine brands recalled). c. The factor is the type of TV program that was watched. The treatment is the embedded commercials in the TV programs. d. You need to compare the variation within each group as well as the variation between groups. e. The test statistic F = with p value reported as.000. f. Since the p value is close to zero, the null hypothesis (H 0 : μ V = μ S = μ neither ) is rejected. The data indicates that the mean number of brand names recalled is not the same for all three types of TV shows. The boxplots suggest that the variances are similar, and the Homogeneity of Variance test confirms this: since p is large, the null hypothesis of equal variances is not rejected. Test of Homogeneity of Variances Levene Statistic df1 df2 Sig

2 ANOVA Sum of Squares df Mean Square F Sig. Between Groups Within Groups Total Tukey's Honestly Significant Difference test indicates that there is a difference between the means of Group 1 and Group 3, and Group 2 and Group 3, but not Group 1 and Group 2. Multiple Comparisons Tukey HSD Mean 95% Confidence Interval (I) FACTOR (J) FACTOR Difference (I-J) Std. Error Sig. Lower Bound Upper Bound * * * * *. The mean difference is significant at the 0.05 level.

3 12.13 H 0 : μ simple = μ elaborate = μ pairwise H a : the means are not all equal The results show F = with a p-value of.001, and so the null hypothesis is rejected. This data indicates that the mean percent of names recalled is not the same for the three name retrieval methods. However, the boxplots suggest that the equal variance condition is not met. Also, the p-value for the test of homogeneity of variances is.026; since this value is less than α =.05, the null hypothesis of equal variances is rejected. This indicates that the conditions for a One-Way ANOVA are not met. ANOVA Sum of Squares df Mean Square F Sig. Between Groups Within Groups Total Test of Homogeneity of Variances Levene Statistic df1 df2 Sig

4 Tukey's HSD test indicates that there is a significant difference between the means of Groups 1 and 3, and between Groups 2 and 3, but not Groups 1 and 2. Tukey HSD Multiple Comparisons Mean 95% Confidence Interval (I) GROUP (J) GROUP Difference (I-J) Std. Error Sig. Lower Bound Upper Bound * * * * *. The mean difference is significant at the 0.05 level. Exercise H 0 : μ angry = μ disgusted = μ fearful = μ happy = μ sad = μ neutral H a : the means are not all equal The results show F = with a p-value of.007, and so the null hypothesis is rejected. This data indicates that the mean dominance ratings are not the same for the six facial expressions. RATING ANOVA Sum of Squares df Mean Square F Sig. Between Groups Within Groups Total

5 Multiple Comparisons However, although the boxplots suggest that the equal variance condition is not met, the p- value for the test of homogeneity of variances is.566; since this value is greater than α =.05, the null hypothesis of equal variances is not rejected. This test indicates that the conditions for a One-Way ANOVA are met. Test of Homogeneity of Variances RATING Levene Statistic df1 df2 Sig The results of Tukey's HSD test (shown on the next page) indicate that the only significant difference is between the means for Happy faces and Sad faces. Although the following analysis was not required, you can see that a two-sample t-test shows that a significant difference is found between the means for these two groups (p =.005):) Group Statistics FACE N Mean Std. Deviation Std. Error Mean RATING H S Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means RATING Equal variances assumed Equal variances not assumed Sig. (2- Mean Std. Error 95% Confidence Interval of the Difference F Sig. t df tailed) Difference Difference Lower Upper

6 RATING Tukey HSD Mean 95% Confidence Interval (I) FACE (J) FACE Difference (I-J) Std. Error Sig. Lower Bound Upper Bound A D F H S * N D A F H S N F A D H S N H A D F S * N S A * D F H * N N A D F H S

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