Please help by answering the following questions in this problem set. Thank you!
Problem Set 2—Specify Ho whenever appropriate.
1. An experiment is conducted to compare the efficacy of five treatments for depression: (1) prozac, (2) elavil, (3) zoloft, (4) prozac plus psychotherapy, and (5) zoloft plus psychotherapy. An ANOVA yields a significant main effect. The experimenter plans to conduct the following four comparisons:
(i) treatments with psychotherapy vs. treatments without psychotherapy
(ii) treatments with prozac vs. treatments without prozac
(iii) treatments with zoloft vs. treatments without zoloft
(iv) prozac and zoloft (both without psychotherapy) vs. elavil
For each comparison, fill in the coefficients for the appropriate linear contrast. (i) ψ = (M1) + (M2) + (M3) + (M4) + (M5)
(ii) ψ = (M1) + (M2) + (M3) + (M4) + (M5)
(iii) ψ = (M1) + (M2) + (M3) + (M4) + (M5)
(iv) ψ = (M1) + (M2) + (M3) + (M4) + (M5)
Do these contrasts form an orthogonal set? You will be penalized for doing unnecessary calculations. Do NOT test the contrasts.
2. To test whether rats consume equal amounts of different sweettasting solutions, a researcher assigns 10 different rats to each of 3 groups. She records the amount consumed (in milliliters) by each rat. The means are (1) sucrose: 9.1, (2) saccharin: 7.6, and (3) polycose:
9.9. The ANOVA reveals a significant main effect, F(2, 27) = 3.466, p = .046. Use the NewmanKeuls test to determine which groups differ. If you use the Tukey’s HSD test instead, do your results change? Explain.
3. From the “creativity” example presented in class, add a sixth child to each age group. The 4
yearold has a score of 6, the 6yearold has a score of 12, the 8yearold has a score of 11, and the 10yearold has a score of 5. Conduct the ANOVA on your computer. By hand, test the
same hypothesis we tested in class (i.e., creativity peaks at 7 years of age, symmetrical function of age) with orthogonal contrasts.
4. Here is a set of data collected in a betweensubjects design.
Conduct a oneway ANOVA by hand and on your computer. You don’t actually have to do the calculations by hand (e.g., you can use Excel), but make it clear that you know what needs to be done and go through all of the steps. Compare the means by hand using Fisher’s LSD, Scheffé’s, Tukey’s HSD, and the NewmanKeuls tests. Check your work on your computer (if you’re using JASP, it won’t do LSD or NK, don’t worry about it). Provide a summary statement
indicating how many pairwise comparisons were significant with each method. 2/2 3/2
Questions from Pagano text: (pp. 436 – 439)
11—on computer only
20—Run an ANOVA on the computer with these data. Conduct Tukey’s and the Scheffé test by hand and on the computer. Do the solutions differ? Explain.
21—Run an ANOVA on the computer with these data. By hand, use contrasts to compare the normalsleep group with the two sleepdeprived groups, and the two sleepdeprived groups with each other. Make a conclusion. In two different ways, show that the contrasts are orthogonal.
24—Run an ANOVA on the computer with these data. Conduct all possible pairwise comparisons by hand using multiple ttests in three ways: uncorrected, corrected using the Bonferroni method, and corrected using the BonferroniHolm method. Do the three methods lead to different solutions? Explain. You’ll need to get exact pvalues on SPSS (from Fisher’s LSD) or with the online app from the lecture slides.
5. A social psychologist studied the effectiveness of three different reinforcement schedules on
prosocial behaviours in children. She looked at 36 children; 6 boys and 6 girls in each of the three schedules. The dependent variable was the number of times that the desired behaviors were demonstrated (within a specified interval) following exposure to the particular reinforcement schedule. The data, some calculations, and the computer output are provided below.
Schedule 1: 32 36 38 30 38 35 (∑X = 209, ∑X2 = 7333)
Schedule 2: 34 36 39 40 31 33 (∑X = 213, ∑X2 = 7623)
Schedule 3: 40 42 36 35 38 41 (∑X = 232, ∑X2 = 9010)
Schedule 1: 25 27 28 29 26 24 (∑X = 159, ∑X2 = 4231)
Schedule 2: 40 29 33 38 34 37 (∑X = 211, ∑X2 = 7499)
Schedule 3: 43 41 37 36 39 45 (∑X = 241, ∑X2 = 9741) Source Sumofsquares DF Meansquare Fratio P GENDER 51.361 1 51.361 4.957 0.034 SCHEDULE 460.056 2 230.028 22.201 0.000 GENDER* SCHEDULE 164.056 2 82.028 7.917 0.002 Error 310.833 30 10.361
The significant interaction tells us that the "schedule" variable works differently for boys than for girls. Use simple effects to investigate the interaction further by examining the effect of the "schedule" variable separately for boys and then again for girls, using the simplest and fewest calculations possible. State the null hypotheses and make the appropriate conclusions. Do not make any unnecessary calculations. Cal
Questions from Pagano text: (pp. 473474)
11—by hand (or on Excel) and on the computer. Calculate effect sizes (etasquared and omegasquared) by hand and on the computer (SPSS won’t do this, don’t worry about it). If the
interaction is significant, conduct the appropriate tests of simple effects by hand. Create a figure by hand or on the computer (the YAxis should go from 0 to 20).
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