Data Analysis in Psychology: A Case Study on Protein Consumption and Weight Gain in Rats -, Exams of Statistics

Download Data Analysis in Psychology: A Case Study on Protein Consumption and Weight Gain in Rats - and more Exams Statistics in PDF only on Docsity! Psych 5741/5751: Data Analysis University of Colorado @ Boulder Gary McClelland & Charles Judd First Exam, Spring 1993 Question 1 Much of the statistical methodology used in psychology and the social sciences was borrowed from early work by statisticians analyzing agricultural experiments. So we've borrowed a test question from a classic textbook of that genre--Snedecor & Cochran. A study was done to compare the weight gain in rats as a function of level and source of protein in the diet. There were two levels of protein (high and low) and there were three types of sources (beef, cereal, and pork). Each diet was fed to separate groups of 10 rats each for a week. The dependent variable is weight gain (in grams) at the end of one week. In analyzing the resulting data, weight GAIN was regressed on five contrast-coded predictors. LEVPROT codes level of protein (+1 if high, -1 if low); ANMLVEG codes whether the source of the protein is animal (+1 if beef, +1 if pork) or vegetable (-2 if cereal); X3 codes the two different sources of animal protein (+1 if beef, -1 if pork, 0 if cereal). LEVAMVEG is the interaction between LEVPROT and ANMLVEG and LEVBFPK is the interaction between LEVPROT and BEEFPORK. The following SAS output resulted from this analysis. Model: MODEL1 Dependent Variable: GAIN 1-week weight gain in grams Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 5 4612.93333 922.58667 4.300 0.0023 Error 54 11586.00000 214.55556 C Total 59 16198.93333 Root MSE 14.64772 R-square 0.2848 Dep Mean 87.86667 Adj R-sq 0.2185 C.V. 16.67039 [continued on next page] Prepared to accompany Judd & McClelland (1989) — 1 — Psych 5741/5751: Data Analysis University of Colorado @ Boulder Gary McClelland & Charles Judd Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 87.866667 1.89101188 46.465 0.0001 LEVPROT 1 7.266667 1.89101188 3.843 0.0003 ANMLVEG 1 1.483333 1.33714732 1.109 0.2722 BEEFPORK 1 0.250000 2.31600710 0.108 0.9144 LEVAMVEG 1 3.133333 1.33714732 2.343 0.0228 LEVBFPK 1 0 2.31600710 0.000 1.0000 Squared Partial Variable DF Type II SS Corr Type II INTERCEP 1 463233 . LEVPROT 1 3168.266667 0.21473562 ANMLVEG 1 ??? 0.02228123 BEEFPORK 1 2.500000 0.00021573 LEVAMVEG 1 1178.133333 ??? LEVBFPK 1 0 0.00000000 Variable Variable DF Label INTERCEP 1 Intercept LEVPROT 1 hi protein vs lo prot contrast ANMLVEG 1 source: animal vs vegetable BEEFPORK 1 source: beef vs pork LEVAMVEG 1 level by anim vs veg source LEVBFPK 1 level by beef vs pork Table of Means Level of Level of -------------GAIN------------ LEVEL SOURCE N Mean SD high beef 10 100.0000000 15.1364167 high cereal 10 85.9000000 15.0218360 high pork 10 ??? 10.9163486 low beef 10 79.2000000 13.8868443 low cereal 10 83.9000000 15.7088086 low pork 10 78.7000000 16.5465673 A. Write out the complete source table for a two way analysis of variance of these data, including the omnibus main effect test for source of protein and the omnibus interaction test. Make sure to include PRE values for each F* statistic. Notice that there are a few pieces of missing information in the printout, marked by ???, which you must calculate in other ways in order to complete the source table. Prepared to accompany Judd & McClelland (1989) — 2 — Psych 5741/5751: Data Analysis University of Colorado @ Boulder Gary McClelland & Charles Judd Question 3 A cognitive psychologist is interested in factors affecting the transfer of skill from one task to another. He believes that if a subject trains on one task, the acquired skill should transfer to a second task only if the second task is similar to the first. Additionally, skill transfer should occur most efficiently if the subject is asked, during training on the first task, to verbalize the concrete steps involved in the acquired skill. Finally, the researcher believes that verbalization should make a difference on skill transfer only if the second task and the first are similar to each other. If the two tasks are dissimilar, then verbalization should not increase the amount of transfer as a function of training. To test these ideas, he conducts an experiment in which subjects are trained on one task and then their skill on a second is assessed. The following three independent variables are crossed in a factorial design: Amount of training on task 1: none, 10 min, 20 min Similarity of task 2 to task 1: dissimilar, similar Verbalization during task 1 training: yes, no Ten subjects are randomly assigned to each of the resulting 12 cells of the research design. Assuming that the researcher's hypotheses are correct and that he conducts a traditional three-way analysis of variance (albeit with single degree of freedom contrasts) on the data he collects, answer the following questions. A. Write out the rows of the resulting source table, indicating for each row only the source of the sum of squares (i.e., the effect that is tested) and the associated degrees of freedom. (Be clear about what the contrast is for each effect listed in the table, e.g., linear effect of amount of training.) Prepared to accompany Judd & McClelland (1989) — 5 — Psych 5741/5751: Data Analysis University of Colorado @ Boulder Gary McClelland & Charles Judd B. Which of the single degree of freedom tests in this source table do you expect to be reliable, assuming that the data confirm the researcher's hypotheses? Circle each row in the table where you expect a reliable F * . Prepared to accompany Judd & McClelland (1989) — 6 —