## 1/2 Problem Set 2Specify Ho whenever appropriate. Chapter 15 1. An experiment is conducted to compare the efficacy of five treatments for depression:...

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Problem Set 2—Specify Ho whenever appropriate.

Chapter 15

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.

X1

X2

X3

X4

20

11

18

10

21

14

17

9

26

15

12

13

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

19—by hand

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.

Chapter 16

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.

BOYS

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)

GIRLS

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 &quot;schedule&quot; variable works differently for boys than for girls. Use simple effects to investigate the interaction further by examining the effect of the &quot;schedule&quot; 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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