Contrast Codes in One-Way ANOVA: CU Boulder Psych Data Analysis Course Solutions - Prof. G, Study notes of Statistics

Download Contrast Codes in One-Way ANOVA: CU Boulder Psych Data Analysis Course Solutions - Prof. G and more Study notes Statistics in PDF only on Docsity! Psych 5741/5751: Data Analysis University of Colorado @ Boulder Gary McClelland & Charles Judd Practice Problems: Answers One-Way ANOVA Contrast Code Problems This file contains the original problems and the answers for the one- way ANOVA coding problems. Note that many other answers are possible. In particular, any row for a code given below can be multiplied by any constant, including -1, to produce an equivalent contrast code in terms of orthogonality. For example, the code (1/3, 1/3, -2/3) is equivalent to the code (5, 5, -10) and to the code (-1, -1, 2). Also some problems allow you to ask alternative questions that might not be the same questions for which I have suggested codes. 1. An advertising director tests the effectiveness of three types of ads: those with color pictures, those with black and white photos, and those with no pictures. Subjects rate each type of ad. Specify a contrast code to test picture vs. no picture and specify the other orthogonal contrast code. What does the other contrast code test? Color B&W NoPhoto 1/3 1/3 -2/3 Picture vs. No Picture 1/2 -1/2 0 Color vs. B&W 2. A drug company wishes to test the side effects of a new drug. They used five groups: a control group which received no medication (C1), a control group which received an inert placebo (C2), a treatment group which received the regular formulation of Drug A (A1), another treatment group which received a buffered version of Drug A (A2), and a final treatment group which received a different Drug B which is presumed to have the same therapeutic effects as Drug A (B). Generate a set of contrast codes for groups C1, C2, A1, A2, and B to answer these questions: 1. Do the drug groups differ from the control groups? 2. Do the two control groups differ from each other? 3. Do the Drug A groups differ from the Drug B group? 4. Do the two formulations of Drug A differ from each other? Verify that all of your contrast codes are orthogonal to each other. C1 C2 A1 A2 B -3/5 -3/5 2/5 2/5 2/5 Drugs vs. Conrols (#1) 1/2 -1/2 0 0 0 Control1 vs. Control2 (#2) 0 0 1/3 1/3 -2/3 Drug A (both) vs. Drug B (#3) 0 0 1/2 -1/2 0 Drug A1 vs. Drug A2 (#4) Prepared to accompany Judd & McClelland (1989) — 1 — Psych 5741/5751: Data Analysis University of Colorado @ Boulder Gary McClelland & Charles Judd To verify orthogonality, multiply each pair of codes, element-by-element, and sum them. They are orthogonal if that sum is zero. For example, to show that #1 and #3 are orthogonal (-3/5)(0) + (-3/5)(0) + (2/5)(1/3) + (2/5)(1/3) + (2/5)(-2/3) = 0 + 0 + 2/15 + 2/15 - 4/15 = 0. 3. Subjects are given some material to learn for 10 trials, with the independent variable intertrial interval (the interval between successive trials) being manipulated at intervals of 0 seconds (massed practice) and 20, 40, and 60 seconds (distributed or spaced practice). 80 subjects are randomly assigned to one of the four groups for a total of 20 subjects per group. Specify a code for testing the hypothesis that performance will steadily increase as the intertrial interval increases (linear trend). Specify another code that will test the hypothesis that performance will be better for the middle levels than for either extreme (quadratic trend). If you can, specify the third code that will complete the set of contrast codes (cubic trend), but you may need a table of orthogonal polynomials to find the third code. 0 20 40 60 -3/2 -1/2 1/2 3/2 Linear Trend -1/2 1/2 1/2 -1/2 Quadratic Trend -1/2 3/2 -3/2 1/2 Cubic Trend These polynomial contrasts are availabile in Table A.1 on p. 92 of Contrast Analysis by Rosenthal and Rosnow. 4. Fifth-grade students representing five ethnic groups are compared in terms of school attitude. The five ethnic groups are Afro- Americans, Hispanics, Native Americans , Asian-Americans, and Whites. Generate any complete set of contrast codes which you believe would be appropriate for analyzing these data. Indicate the question asked by each code you generate. Prepared to accompany Judd & McClelland (1989) — 2 —