PSYC 210 - ANOVA Class Notes

PSYC 210 - ANOVA Class Notes - ANOVA (Day 1) Let's say you...

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ANOVA (Day 1) Let’s say you have 4 treatments you want to evaluate: IV: Treatment Medication Cognitive Behavioral Combination of only Therapy only medication and CBT Placebo DV: Depression M 1 M 2 M 3 M 4 You would like to know what treatments work best. Now that you know t-tests you could do a t-test for each of the following: M1 vs. M2 M2 vs. M3 M3 vs M4 M4 vs M1 M1 vs. M3 M4 vs. M2 Why shouldn’t you do so (compute 6 separate t-tests)? Analysis of Variance (ANOVA) involves analyzing different sources of variance. Variance = a measure of variability = standard deviation squared (s 2 ) Let’s revisit the initial example. Consider these depression scores: Med. only CBT only Combination Control 10 13 19 15 12 11 10 20 15 9 14 18 13 18 10 23 12 12 12 17 M 1 = 12.4 M 2 = 12.6 M 3 = 13.0 M 4 = 18.6 Two sources of variance: 1) Between group variance Differences between group means Caused by the independent variable plus some error 2) Within group variance Spread or dispersion of scores within each group Caused by error (individual differences, sampling error, uncontrolled variables, etc.) The F Statistic F = pVariance WithinGrou upVariance BetweenGro Conceptually, this is very similar to t. It is a measure of differences between groups relative to error. Just like t , the value of F is influenced by the differences between means as well as the spread of scores in each group.
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Computing F within between MS MS F = Where: Variance between treatments (Between group variance) = MS between = between between df SS SS between = sum of squares between groups df between = degrees of freedom between groups = number of groups – 1 = k - 1 MS between = mean square between groups Variance with treatments (Within group variance) = MS within = within within df SS SS within = sum of squares within groups df within = degrees of freedom within groups = N - number of groups = N - k MS within = mean square within groups ANOVA summary table Source SS df MS F Between 1 SS between df between MS between F Within 2 SS within df within MS within Total SS total df total = SS b +SS w = N - 1 1 In an actual summary table, the name of the IV is used to label the between group source of variance. 2
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This note was uploaded on 02/23/2012 for the course WMST 101 taught by Professor Burns during the Fall '08 term at UNC.

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PSYC 210 - ANOVA Class Notes - ANOVA (Day 1) Let's say you...

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