August+4th - Quantitative Methods in Psychology Psychology...

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Unformatted text preview: Quantitative Methods in Psychology Psychology August 4th, 2009: ANOVA week! Jeff Vietri corresponding to Chapter 14 in the corresponding text text Effect Size Effect SSbetween η= SSbetween + SS within 2 • Gives the percent variance explained by Gives the treatment (just like r2) the --the variability accounted for by the treatment --the differences differences 0.01 < η2 < 0.09 small effect 0.01 0.09 < η2 < 0.25 medium effect 0.09 η2 > 0.25 large effect Repeated Measures ANOVA Repeated Up until now we’ve just covered one-way Up ANOVA (the most basic type) ANOVA – This ANOVA merely determines if there are This significant differences between samples significant However, its possible that differences However, between samples could be attributed to the people in each group the Repeated-Measures ANOVA Repeated-Measures Just like repeated-samples t-test, Just Repeated-measures ANOVA uses the same people in different treatment conditions conditions – This reduces or may even eliminate extra This error error – This is an extremely powerful test – Often the same people are assessed at Often different points in time (or under different conditions) Repeated Measures ANOVA Repeated Recall: Independent measures ANOVA ANOVA In repeated measures, individual difference ONLY contributes to differences within treatments, because same individuals are used in all treatments. Variance-between Variance-within Independent measures Treatment effect + Experimental error + individual differences Experimental error + individual differences Repeated measures Treatment effect + Experimental error Experimental error + individual differences Now: Repeated-measures ANOVA Now: Repeated-measures ANOVA F= Variance between treatments Variance due to chance/error Now, we can eliminate individual differences in repeated measures ANOVA differences F= Variance between treatments (without individual differences) Variance due to error (without individual differences) = Treatment effect + error (excluding individual differences) Error (excluding individual differences) = Variance between treatments Variance within treatments – Variance between individuals Repeated Measures: SSTotal Repeated • SSTotal = sum of squares for the entire set of scores (without regard to group) of Same as with one-way ANOVA SSTotal = ΣX SSTotal 2 ( ΣX ) − N 2 G = ΣX − N 2 2 G = Grand Total G = ΣX dftotal = N - 1 Repeated Measures: SSBetween Repeated • SSBetween is the sum of squares of group mean differences differences Pretending that each mean of a group is an Pretending individual score you use the same process for the sum of squares the • dfbetween = k – 1 Again, same formula as with one-way ANOVA SS Between T12 T2 2 T3 2 G 2 − = + + n n2 n3 N 1 T = group total Repeated Measures: SSWithin Repeated Within Groups variance in One-way Within ANOVA is attributed to both individual differences and random error differences Repeated-measures ANOVA attempts to Repeated-measures separate out these two components separate • SSwithin = SSerror + SSsubjects • SSsubjects = individual differences – This analyses accounts for individual This differences which strengthens the test differences Repeated Measures: SSWithin Repeated • SSwithin is the sum of squares for each group added together group • SSwithin = SS1 + SS2 + SS3 + …+ SSk SS within • dfwithin = N – k Same as with regular ANOVA Repeated Measures: SSBetween Subjects Repeated Represents individual differences so they can be Represents removed removed 2 SS BetweenSubjects 2 2 Pn1 P P2 G2 =1+ + ... + − k k k N • dfbetween subjects = n1 – 1 P represents person totals represents For each person, square the person’s total and For divide by the number of samples Add all these up Add • Subtract [G2/N] Repeated Measures: SSError Repeated • SSError = SSwithin – SSbetween subjects • dferror = (N – k) – (n1 – 1) error – “N” is the number of people in study – “n1” is the number of people in each group For a repeated-measures ANOVA, which of the following is computed differently, compared to an independent-measures ANOVA? independent-measures A. total SS B. between treatment between SS SS C. within treatment SS D. the denominator of the the F ratio the Example Example Effect Size Effect Just like with other statistical tests, Just Repeated Measures ANOVA has a way to calculate effect size calculate Effect size gives a way to get a sense of Effect how important your results are how Just because they are significant does not Just mean that your IV has a huge impact on your DV your Post Hoc Tests Post Tukey’s HSD can be used for Repeated Tukey’s Measures Measures • Again, same formula as One-way ANOVA Again, except must use MSError instead of MSWithin except • Also, df for q-table is dferror not dfwithin for MS error HSD = q n1 Two-way ANOVA Two-way Two-way ANOVA Two-way Up until now we have only discussed One-way Up ANOVA ANOVA Where one discrete IV (“factor”) predicts one DV However, often times in research we not just However, concerned with one variable, researchers may want to study more than one at once to Remember confounding variables? We can include Remember them into our design them Two-way ANOVA Two-way One-way ANOVA design: Does my drug affect cholesterol levels (control, 5mg, Does 10mg)? 10mg)? Two-way ANOVA design: Does my drug affect cholesterol levels (control, 5mg, Does 10mg)? 10mg)? Does an exercise program affect cholesterol levels? Does drug affect cholesterol levels differently for people Does on exercise program vs. those not on exercise program? on Two-way ANOVA Two-way Two-way ANOVA is looking at two IVs and Two-way their effect on the DV their Two-way ANOVA has three null hypotheses: H0a: μA1 = μA2 = μA3 H0b: μB1 = μB2 = μB3 H0c: There is no interaction between A and B. There This last hypothesis tests what is called an This interaction interaction Two-way ANOVA Two-way Since we are looking at two variables at the Since same time, we need to know the effect of the first variable, the second variable, and the combined effects of both variables combined Example Example makes you feel good makes you feel good + = ? Example Example makes you feel good makes you feel good + makes you dead = Interaction Interaction An interaction means that the relationship An between one variable and the dependent variable is affected by another variable variable Q: What is the relationship of X and Y? If the answer is “it depends”, then you have If an interaction an What is the relationship between temperature and test scores? (A) Higher temperatures are associated with lower scores. (B) IT DEPENDS! If there is high humidity then higher temperatures are associated with lower scores. If there is low humidity, there is no relationship between temperature scores. Effect Size Effect SSbetween η= SSbetween + SS error 2 Same as formula for One-way ANOVA except replace SSwithin by SSerror Formula give the percent of variance explained Similar to the r2 of the t-test effect size “How much variation in the DV is explained by the IV?” Assumptions Assumptions Observations within each treatment condition Observations must be independent must – Independent observations Distribution of scores within each group must be Distribution normal normal – Normality Variances of scores within each group must be Variances normal normal – Homogeneity of variance – Test with Fmax test (just like t-test) but we won’t be doing that in this course doing Exercise Treatments Participant A B C D _________________________________________ 1 6 3 3 0 P=12 ΣX2 = 172 2 4 4 2 2 P=12 G = 44 3 4 2 0 2 P=8 4 6 3 3 0 P=12 _________________________________________ T = 20 T = 12 T = 8 T = 4 SS = 4 SS = 2 SS = 6 SS = 4 Are there significant differences among treatments? Alpha = .05 Compute the percentage of variance explained by the treatment (η2). ...
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This note was uploaded on 11/17/2011 for the course PSYCHOLOGY 830:200 taught by Professor Staff during the Fall '11 term at Rutgers.

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