2. Describe the similarities between an F-ratio and a t statistic. 4. Calculate SS total SS between and SS within for the following set of data: Treatment 1 Treatment 2 Treatment 3 N=30 N=10, T=10, SS=27 N=10, T=20 SS=16 N=10, T=30, SS=23 G=60 X=206 6. A researcher reports an F ratio with df between=2 and df within=30 for an independent measures ANOVA. a. How many treatment conditions were compared in the experiment? b. How many subjects participated in the experiment? 8. A research report from an independent measure study states that there are significant differences between treatments, F(3, 48)=2.95, p<.05 a. How many treatment conditions were compared in the study? b. What was the total number of participants in the study? 10. A researcher conducts an experiment comparing four treatment conditions with a separate sample of n = 6 in each treatment. An ANOVA is used to evaluate the data, and the results of the ANOVA are presented in the following table. Complete all missing values in the table. Hint: Begin with the values in the df column. 12. A developmental psychologist is examining the development of language skills from age 2 to age 4. Three different groups of children are obtained, one for each age, with children in each group. Each child is given a language-skills assessment test. The resulting data were analyzed with an ANOVA to test for mean differences between age groups. The results of the ANOVA are presented in the following table. Fill in all missing values. N=18 children in each group. Source SS df MS 48 ____ _ ____ _ Within treatme nts ____ _ ____ _ ____ _ Total 252 ____ _ Betwee n treatme nts F= ___ _ 14. The following data were obtained from an independent measures research study comparing three treatment conditions. Use an ANOVA with a= .05 to determine whether there are any significant mean differences among the treatments. Treatment 1 Treatment 2 Treatment 3 N=18 N=8, T=16, SS=40 N=6, T=24 SS=24 N=4, T=32, SS=16 G=72 X=464 16. Several factors influence the size of the F-ratio. For each of the following, indicate whether it would influence the numerator or the denominator of the F-Ratio, and indicate whether the size of the F-ratio would increase or decrease. a)Increase the difference between the sample means. b)Increase the size of the sample variances. 18. The following data were obtained from an independent-measures research study comparing three treatment conditions: Treatment 1 Treatment 2 Treatment 3 4 4 9 2 0 3 6 3 6 4 1 6 N=8, T=16, SS=40 N=18 N=6, T=24 SS=24 N=4, T=32, SS=16 G=72 M=4 M=2 M=6 X=260 T=16 T=8 T=24 SS=8 SS=10 SS=18 20. The following data summarize the results from an independent-measures study comparing three treatment conditions. I II III n=10 n=10 n=10 M=2 M=3 M=4 T=20 T=30 T=40 S squared=2.67 S squared=2.00 S ssquared=1.33 A. Use an ANOVA with alpha level at 0.05 to determine whether there are any significant differences among the three treatment means. B. Calculate n^2 to measure the effect size for this study. 22. The following values are from an independent-measures study comparing three treatment conditions. I II III n=8 n=8 n=8 a. Compute the variance for each sample. SS=42 SS= 28 SS=98 b. Compute MS within (the denominator of the f ratio for an anova). 24. The following scores are from an independent measures study comparing two treatment conditions. a. Use an independent measures t test with an alpha = 0.5 to determine whether there is a significant mean difference between the two treatments. b. Use an ANOVA with alpha =0.5 to determine whether there is a sginifigant difference between the two treatments. You should find that F=t squared. I II 1 12 6 5 6 6 3 9 N=8 G=48 X=368