SAS Analysis of Psychology Data: Comparing Linear and Quadratic Effects of Periods - Prof., Exams of Statistics

Download SAS Analysis of Psychology Data: Comparing Linear and Quadratic Effects of Periods - Prof. and more Exams Statistics in PDF only on Docsity! Exam from Psych 5741/5751 Univ of Colorado used with Judd, C.M., & McClelland, G.H. (1989). Data Analysis: A Model Comparison Approach. HBJ. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Final, Spring 1996 — 1 — May 13, 1996 Final Exam Spring 1996 Bread-and-Butter Edition An advantage of the general linear model approach or the neoclassical approach used in Judd & McClelland (1989) is the ability to generate and test complex models which ask sophisticated questions of data. However, we should not forget that the approach also facilitates the basic analyses used in many social science studies. This final exam focuses on those basic analyses and serves as a final review of the general linear model approach applied to bread-and-butter analyses. Question 1 In this study of memory, there are two independent variables: subject mood and emotionality of words. Subjects are randomly assigned to one of 3 mood conditions: sad, neutral, or pleasant. To induce these moods the experiment has the subjects read a series of statements that are either sad, neutral, or pleasant, respectively. Within each mood condition, subjects are further randomly divided into groups asked to memorize either emotional words (such as "love" and "hate") or unemotional words (such as "shoe" and "tree"). The dependent variable is the number of words recalled on a test administered 30 minutes later. There are 18 subjects in this 3 x 2 design. [based on Glenberg (1988), p. 382] A. Your advisor asks you to do a two-way ANOVA. Specify the SAS commands you would use to do the analysis using contrasts. B. Layout the source table, being sure to include rows for all main effects, interactions, and appropriate one-df tests. Fill in the df column. Question 2 [from Kirk (1982), p. 565]. The performance of fifteen clerks on three date-sorting tasks was compared at two times of day: 10 A.M. and 4 P.M. Each clerk completed the date-sorting tasks at each time, but on different days (with the order of the times randomly determined). The task involved Exam from Psych 5741/5751 Univ of Colorado used with Judd, C.M., & McClelland, G.H. (1989). Data Analysis: A Model Comparison Approach. HBJ. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Final, Spring 1996 — 2 — May 13, 1996 sorting a list of random dates written in European form (e.g., 30 1 74 for January 30, 1974). Clerks were randomly assigned to sort the dates into either two, three, or four accounting periods. The dependent variable was the number of dates sorted in a fixed time. (Experiment suggested by Monk, T.H., & Conrad, M.C. (1979). Time of day effects in a range of clerical tasks. Human Factors, 21, 191-194). A. Using the SAS input and output below, construct a complete source table. B. Write a brief summary of the results. C. The periods variable is numeric so instead of using contrast codes, we could have used the SAS command: proc glm; btwn: model w0 = periods periods*periods; wthn: model w1 = periods periods*periods; Put a star, check, or other mark by the rows in your source table which would be different if the above SAS code had been used instead of the proc reg commands which were used in the output below. data clerks; input subj periods am pm; w0 = (am + pm)/sqrt(2); w1 = (am - pm)/sqrt(2); lin = (1/2)*(periods=2) + 0*(periods=3) -(1/2)*(periods=4); quad =(-1/3)*(periods=2) +(2/3)*(periods=3)-(1/3)*(periods=4); label w0 = "Combined Score am + pm" w1 = "Difference Score am - pm" lin = "linear effect of periods" quad = "quadratic effect of periods"; cards; 1 2 171 189 2 2 183 204 3 2 145 154 4 2 158 166 5 2 196 179 6 3 213 249 7 3 224 237 8 3 198 224 9 3 182 198 10 3 172 214 11 4 200 212 12 4 226 224 13 4 213 196 Exam from Psych 5741/5751 Univ of Colorado used with Judd, C.M., & McClelland, G.H. (1989). Data Analysis: A Model Comparison Approach. HBJ. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Final, Spring 1996 — 5 — May 13, 1996 Question 3 [And now a problem for our students from business; from Neter, Wasserman, & Kutner (1983), p. 330] An economist was interested in the speed with which a particular insurance innovation was adopted. Of particular interest was whether stock companies adopted innovations slower or faster than mutual companies. Also available was information on the size of the company (in millions of dollars of insurance policies in force). Relevant SAS input commands and output folllow the questions. A. Without controlling for size of firm, is there a difference between the time to adopt the innovation for mutual as compared to stock companies? Give the appropriate PRE, F*, and p. B. Using ANCOVA, is there a difference between the time to adopt the innovation for mutual as compared to stock companies when controlling for size of firm? Give the appropriate PRE, F*, and p. Give the adjusted means that are compared in this analysis. C. Explain in non-technical terms, such as in a memo to a CEO, why questions A and B have different answers. D. Is there any evidence for a violation of the heterogeneity of regression assumption? Give the appropriate PRE, F*, and p. E. Is the relationship between size and time to adopt the innovation different for mutual and stock companies? Give the appropriate PRE, F*, and p. data firms; input time size type$; MvsS = (1/2)*(type="Mutual") - (1/2)*(type="Stock"); SizeMvsS = size * MvsS; label time = "Months to Adopt" size = "Size of Firm ($1,000,000s)" MvsS = "Mutual vs. Stock Contrast" SizeMvsS ="Size by Mutual vs. Stock Interaction"; cards; 17 151 Mutual 26 92 Mutual 21 175 Mutual 30 31 Mutual 22 104 Mutual 0 277 Mutual 12 210 Mutual Exam from Psych 5741/5751 Univ of Colorado used with Judd, C.M., & McClelland, G.H. (1989). Data Analysis: A Model Comparison Approach. HBJ. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Final, Spring 1996 — 6 — May 13, 1996 19 120 Mutual 4 290 Mutual 16 238 Mutual 28 164 Stock 15 272 Stock 11 295 Stock 38 68 Stock 31 85 Stock 21 224 Stock 20 166 Stock 13 305 Stock 30 124 Stock 14 246 Stock ;; proc means; var time size; by type; proc reg; title 'Simple Comparison'; model time = MvsS; proc reg; title 'ANCOVA Comparison'; model time = MvsS size/ss2 pcorr2 tol; output out=temp h=lever r=resid p=timehat rstudent=rstudent cookd=cookd; proc reg data=firms; title2 'with Interaction Added'; model time = MvsS size SizeMvsS/ss2 pcorr2 tol; The SAS System TYPE=Mutual Variable Label N Mean Std Dev -------------------------------------------------------------------- TIME Months to Adopt 10 16.7000000 9.2981480 SIZE Size of Firm ($1,000,000s) 10 168.8000000 84.7909848 -------------------------------------------------------------------- Variable Label Minimum Maximum ---------------------------------------------------------------- TIME Months to Adopt 0 30.0000000 SIZE Size of Firm ($1,000,000s) 31.0000000 290.0000000 ---------------------------------------------------------------- TYPE=Stock Variable Label N Mean Std Dev -------------------------------------------------------------------- TIME Months to Adopt 10 22.1000000 9.1706052 SIZE Size of Firm ($1,000,000s) 10 194.9000000 85.9863684 -------------------------------------------------------------------- Variable Label Minimum Maximum ---------------------------------------------------------------- TIME Months to Adopt 11.0000000 38.0000000 SIZE Size of Firm ($1,000,000s) 68.0000000 305.0000000 ---------------------------------------------------------------- Exam from Psych 5741/5751 Univ of Colorado used with Judd, C.M., & McClelland, G.H. (1989). Data Analysis: A Model Comparison Approach. HBJ. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Final, Spring 1996 — 7 — May 13, 1996 Simple Comparison Model: MODEL1 Dependent Variable: TIME Months to Adopt Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 1 145.80000 145.80000 1.710 0.2075 Error 18 1535.00000 85.27778 C Total 19 1680.80000 Root MSE 9.23460 R-square 0.0867 Dep Mean 19.40000 Adj R-sq 0.0360 C.V. 47.60101 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 19.400000 2.06491862 9.395 0.0001 MVSS 1 -5.400000 4.12983723 -1.308 0.2075 Variable Variable DF Label INTERCEP 1 Intercept MVSS 1 Mutual vs. Stock Contrast Exam from Psych 5741/5751 Univ of Colorado used with Judd, C.M., & McClelland, G.H. (1989). Data Analysis: A Model Comparison Approach. HBJ. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Final, Spring 1996 — 10 — May 13, 1996 F. The following SAS output of residuals and plots was for a preliminary analysis like the one above. Comment on how well the assumptions were satisfied for this preliminary analysis and comment on any outliers. What next step would you recommend? ANCOVA Comparison OBS MVSS SIZE SIZEMVSS TIME TIMEHAT RESID LEVER RSTUDENT COOKD 1 0.5 151 75.5 17 19.0997 -2.0997 0.11192 -0.27543 0.00337 2 0.5 92 46.0 26 21.5492 4.4508 0.14869 0.60159 0.02189 3 0.5 575 287.5 21 1.4964 19.5036 0.57858 9.83323 6.67537 4 0.5 31 15.5 30 24.0818 5.9182 0.21282 0.84060 0.06480 5 0.5 104 52.0 22 21.0510 0.9490 0.13920 0.12620 0.00091 6 0.5 277 138.5 0 13.8685 -13.8685 0.11660 -2.04340 0.15479 7 0.5 210 105.0 12 16.6502 -4.6502 0.10001 -0.61153 0.01438 8 0.5 120 60.0 19 20.3867 -1.3867 0.12814 -0.18335 0.00175 9 0.5 290 145.0 4 13.3288 -9.3288 0.12353 -1.29132 0.07538 10 0.5 238 119.0 16 15.4877 0.5123 0.10304 0.06672 0.00018 11 -0.5 164 -82.0 28 23.3829 4.6171 0.10341 0.60826 0.01477 12 -0.5 272 -136.0 15 18.8990 -3.8990 0.12121 -0.51721 0.01285 13 -0.5 295 -147.5 11 17.9441 -6.9441 0.13576 -0.94664 0.04721 14 -0.5 68 -34.0 38 27.3685 10.6315 0.15747 1.52923 0.13506 15 -0.5 85 -42.5 31 26.6628 4.3372 0.14310 0.58396 0.01975 16 -0.5 224 -112.0 21 20.8918 0.1082 0.10302 0.01408 0.00001 17 -0.5 166 -83.0 20 23.2998 -3.2998 0.10298 -0.43218 0.00751 18 -0.5 305 -152.5 13 17.5289 -4.5289 0.14326 -0.61041 0.02156 19 -0.5 124 -62.0 30 25.0436 4.9564 0.11794 0.65962 0.02006 20 -0.5 246 -123.0 14 19.9785 -5.9785 0.10932 -0.79657 0.02653 ANCOVA Comparison Normal-Normal Quantile Plot Variable=RESID Residual Normal Probability Plot 22.5+ | * +++++ | *++++++ | ++++*++ | +****+** * | **+**** | *++*+*++ -12.5+ +*+++++ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 Exam from Psych 5741/5751 Univ of Colorado used with Judd, C.M., & McClelland, G.H. (1989). Data Analysis: A Model Comparison Approach. HBJ. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Final, Spring 1996 — 11 — May 13, 1996 ANCOVA Comparison Plot of Residuals vs. Predicted Plot of RESID*TIMEHAT. Legend: A = 1 obs, B = 2 obs, etc. | | 20 + | A | | | | 15 + | | | | | A 10 + | | | | R | A e 5 + A A s | A A i | d | u | a | A A l 0 + A | | A | A | A | A A -5 + A | A | A | | | A -10 + | | | | | A -15 + | -+-----------+-----------+-----------+-----------+-----------+-----------+ 0 5 10 15 20 25 30 Predicted Value of TIME Exam from Psych 5741/5751 Univ of Colorado used with Judd, C.M., & McClelland, G.H. (1989). Data Analysis: A Model Comparison Approach. HBJ. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Final, Spring 1996 — 12 — May 13, 1996 Question 4 [also from Neter, et al., p. 364] In a study of the effectiveness of coupons offering a price reduction on a given product, 1000 homes were selected and a coupon and advertising material for the product were mailed to each. The coupons offered different price reductions (5, 10, 15, 20, and 30 percent) for specific automobile maintenance services; 200 homes were randomly assigned to each of the price reduction categories. The response variable was whether the coupon was redeemed within six months. A. Is the price reduction percentage related to the rate at which coupons were redeemed? Give the appropriate test statistic and p. B. Is there any evidence that the effectiveness of the price reduction did not increase linearly (in terms of logits)? Give the appropriate test statistic and p. C. Your boss decides that a 25% price reduction is the most your firm can afford. What is the expected proportion of coupons that would be redeemed if a 25% reduction were offered? data coupons; input reduce count redeem; reducesq = reduce * reduce; cards; 5 32 1 5 168 0 10 51 1 10 149 0 15 70 1 15 130 0 20 103 1 20 97 0 30 148 1 30 52 0 ;; proc logistic; model redeem = reduce; weight count; proc logistic; model redeem = reduce reducesq; weight count;