Question 1 - An educational psychologist is studying the effectiveness of three different reinforcement schedules (I.V.) on certain gender-role (I.V.) behaviors in boys and girls in a middle school. 18 boys and 18 girls were randomly assigned into one of the three reinforcement schedules. In the following table, the psychologist recorded the frequency that the desired behaviors (DV) were demonstrated by individual students. For the data below, use the critical value of .05 in the data analyses.
A. Show a Factorial ANOVA table.
B. Explain the test results for the assumption of homogeneity.
Based upon the sig value of .505 (Sig column, row 1) which is greater than the critical value of .05, equal variances are assumed. F(5,30) = .882, p = .505.
C. Explain your conclusion on the main effects and the interaction from the ANOVA results, including effect size(s).
There was a statistically significant main effect of gender and the frequency of desired behaviors, F(1,30)=4.957, p=.034, partial eta squared = .142. Since this is less than the accepted critical value of .05, this main effect is statistically significant.
There was also a statistically significant main effect of reinforcement schedules and the frequency of desired behaviors, F(2,30)=22.201, p<.001, partial eta squared = .597. Since this is less than the accepted critical value of .05, this main effect is statistically significant.
Finally, there is most likely statistically significant interaction between Gender Role and the Reinforcement mechanism based on the results that show F(2,30)=7.917, p=.002, partial eta squared .345. Since this is less than the accepted critical value of .05, there is most likely a statistically significant interaction.
d. Conduct the post hoc tests using Bonferroni correction and explain your conclusion from the results.
There was a significant interaction between gender and reinforcement schedules on the frequency of desired behaviors, F(2,30)=7.917, p=.002, partial eta squared .345. When running a pairwise comparison with reinforcement and gender role, there is a statistically significant value of <.001. This helps us determine where exactly the significant interaction identified in the Tests of Between Subjects test. It exists in reinforcement schedule 1 for the "Girl" gender.
This is also shown in the fact that the mean for reinforcement level 1 for “Girl” is the lowest mean value (M = 26.50, SD = 1.871). Both the SD and Mean for reinforcement level 1 for “Girl” is different than the others among all of the statistics.
Question 2 - A researcher is interested in whether three methods of teaching are equally effective for students of different reading levels on their reading scores. Students from high, middle, and low reading levels are randomly assigned to one of the teaching methods. For the data below, use the critical value of .05 in the data analyses.
A. Show a Factorial ANOVA table.
B. Explain the test results for the assumption of homogeneity.
Based upon the sig value of .467 (Sig column, row 1) which is greater than the critical value of .05, equal variances are assumed. F(8,27) = .988, p = .467.
C. Explain your conclusion on the main effects and the interaction from the ANOVA results, including F, p, and partial eta squared.
There is not a statistically significant main effect of method and the score, F(2,27)=.243, p=.786, partial eta squared = .018. Since this is greater than the accepted critical value of .05, this main effect is not statistically significant.
There was a statistically significant main effect of reading level and scores, F(2,27)=95.963, p<.001, partial eta squared = .877. Since this is less than the accepted critical value of .05, this main effect is statistically significant.
Finally, there is most likely not a statistically significant interaction between method and reading level on the score based on this test of between subjects effects that show F(4,27)=2.498, p=.066, partial eta squared .270. Since this is not less than the accepted critical value of .05, there is most likely not a statistically significant interaction.
D. Conduct the post hoc tests using Bonferroni correction and explain your conclusion from the results.
When considering the partial eta squared and comparing the values, the "Reading Level" effect shows the highest value, which leads to the assumption that interactions between the Reading Level show the most statistically significant values. When parsing the data between method, then looking at pairwise comparisons of Reading Level there are the most statistically significant values between the high reading levels no matter the method being used. (There is one statistically significant value in the interaction between medium and low Reading Levels with both methods).
Specifically, using any method on high reading level resulted in higher means (M = 34.83, SD = 3.30) than medium reading level results (M = 23.67, SD = 3.85) and low medium reading level results (M = 18.17, SD = 2.25).
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