PSYCH 210 Lecture 18 Outline of Last Lecture I. Related-Samples Designa. Criteriab. Examplec. AssumptionsII. Variant on Related-Samples Designa. Matched-pairs tOutline of Current Lecture I. Analysis of Variancea. Why do we need a new test?b. Conceptual rationale for ANOVAc. Sources of variabilityCurrent LectureI. Start of 3rd exam material: Introduction to Analysis of Variance (ANOVA)a. Why do we need a new test?i. Tests we know so far1. One Tx groupa. z testb. One-sample t2. Two Tx groupsa. Independent-samples tb. Related samples tA. Matched-pairs tii. What if we want to use more than two experimental groups?1. Ex) helping study in elevator (Bystander Effect)These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.a. IV = # of bystanders A. CD alone (0 Bystander) (+P)B. CD + 1 confederate (1 B) (+P)C. CD + 2 confederate (2 B) (+P)D. CD + 3 confederate (3 B) (+P)b. DV = # of coins picked up by Pc. Independent-samples would require 6 different tests! (and would violate some rules of statistics)A. A vs. B, A vs. C, A vs. D, B vs C, B vs D, C vs Dd. Testwise vs. experimentwise alphaA. Alphas for each test are additive1. 0.05 x 6 = 0.3 = experimentwise alpha (way too big!)iii. New procedure: Analysis of Variance (ANOVA)1. Do the sample means come from the same population?a. If Tx WorksA. MA from Pop A, MB Pop B, MC from Pop C, MD from Pop Db. If Tx has no effectA. MA MB, MC, MD all from same population2. Basic t formulaa. t = [(M1 – M2) – (μ1 – μ2)]/SM1-2A. (actual diff. btwn means)/(Std. Error = Diffs. expected by chance)b. =FA. = (Variance btwn groups)/(Variance within groups)3. How do we switch from using mean differences to using variances? (How can we use variance to test for difference btwn means)a. Sample data (helping example continued)A. 6, 7, 8, 6, 8, >> MA = 7 B. 4, 3, 6, 3, 4 >> MB = 4C. 0, 1, 3, 1, 0 >> MC = 1b. Scenario 2A. MA = 70B. MB = 40C. MC = 10c. In which scenario would s2 (variability) be greater?A. Scenario 21. Smaller variance = numbers less spread out (less difference btwn numbers)2. Larger variance = numbers more spread out4. Two types of variability in the F ratioa. Between-groups variabilityA. Variability across groupsB. Why do participants in one condition (Tx group) get different scores?1. 6, 7, 8 2. 4, 3, 63. 0, 1, 3 a. Sources of Variabilityi. Treatment Effectii. Individual Differencesiii. Chance (error)b. Within – groups variabilityA. Why do participants in the SAME Tx group get different scores?1. 6, 7, 82. 4, 3, 63. 0, 1, 3 a. Sources of Variabilityi. Individual Differencesii. Chance (error)5. How to use ANOVA formulaa. F = [Tx effect + Indv diffs + Error]/[Indv diffs + Error]b. Enter specific sources of variability into F ratioA. What should be approximate value for F is H0 true(no Tx)?1. F = [0 + A + B]/[A + B]2. H0 : F ~ 1B. If H0 false? (Tx effect)1. H1: F >
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