Question

A market research firm wants to pilot test children’s toys in stores. They collect data on attitude ratings (higher scores reflect more liking) for three different toys and find the following results: Legos (M = 5.5; N = 10), a football (M = 4.5; N = 10), and a NERF gun (M = 6.0; N = 10). They also calculated the between-group and within-group sum of squares (SS_B = 262.2; SS_W =1220.4). Use a one-way ANOVA (where α = .05) to determine if there are significant differences in children ratings of toys.

       1.      Identify the alternative hypothesis (F tests are always nondirectional)

       2.      List your degrees of freedom (within)

       3.      List your degrees of freedom (between)

       4.      List your mean squares between groups

       5.      List your mean squares within groups

       6.      List your F test statistic

       7.      List your critical F value

       8.      Are there statistically significant differences in ratings among different toys? (Yes/No)

       9.      Calculate partial eta-squared (η²) for the effect of toy type on liking ratings (list as decimal, 0.xx)

       10. Calculate Tukey’s HSD

       11. Use Tukey’s HSD to determine if the difference in toy rating between a NERF gun and a football is statistically significant (Yes/No)

You can use the table below to help answer the questions in this scenario

Source	SS	df	MS	F
Between
Within
Total

Answer 1

Answer 2

1. Alternative hypothesis: There is a significant difference in children's ratings of toys.

2. Degrees of freedom (within): 27

3. Degrees of freedom (between): 2

4. Mean squares between groups: 131.1

5. Mean squares within groups: 45.2

6. F test statistic: 2.90

7. Critical F value: 3.10

8. No, there are no statistically significant differences in ratings among different toys because the F test statistic is less than the critical F value.

9. Partial eta-squared (η2): 0.18

10. Tukey's HSD: 1.68

11. Yes, the difference in toy rating between a NERF gun and a football is statistically significant because the difference in means (1.5) is greater than Tukey's HSD (1.68).