UNT PSYC 2317 - Chapter #10 : Factorial Analysis of Variance
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Jaymie TicknorQuantitative Methods 2317 Sect. 0012, 7, and 9 April 2014Lecture #10Chapter #10 : Factorial Analysis of Variance :Two or more independent variables but still one DV; we have to estimate 3 effects:Main effect for IV #1: this independent variable on dependent variable alone; across all levels of other IV, ignoring other IV; IV is alcohol and DV is retention recallMain effect for IV #2: IV is pills and DV is retention recallInteraction effect: effect of one IV on DV differs across the levels of another IVInteractions: In order to examine main effects and interactions, you must look at the cell means, and graph the interaction; non-parallel lines suggest interaction (lines cross each other)2 IVs: IV #1 has 2 levels while IV #2 has 3 levels: 2 x 3 factorial designLook at cell means; each grouping combination is called a cellMain effect: examine the row and column totals (called marginal means); if marginal means are different across levels of an IV, there is a main effect for that IVInteraction: examine the cell means for each level of each IV; if the cell means increase or decrease at different rates for each level of IV, there is interaction for that IVThe effect of IV (time since last meal) on DV (liking of meal) depends on the level of another IV (type of food); if the time since the last meal is short, one prefers a small steak; if the time since the last meal is long, one prefers a big hamburgerTwo-Way ANOVA: 3 F-ratios: one for main effect for IV #1, IV #2, and one for interaction effectANOVA is a versatile technique; can be used with more than 2 IVs; can be used with repeated measured variablesPerson’s deviation from the Grand Mean (GM = all scores / number of all scores) is a combination of:Person’s deviation from its cell meanPerson’s cell mean’s deviation from the GM (person’s row mean’s deviation from the GM; person’s column mean’s deviation from the GM; remaining deviation = interaction effect)SSTotal = SSWithin + SSBetween → ∑(X – GM)2 = ∑(X – M)2 + ∑(M – GM)2M = cell mean (add scores in cell / number of scores in cell)SSBetween is split up into 3 parts [new]SSRows = ∑(MRow – GM)2SSColumns = ∑(MColumn – GM)2SSInteraction = ∑ [(X – GM) – (X – M) – (MRow – GM) – (MColumn – GM)]2Denominator: dfWithin = df1 + df2 + … + dfLast (for each cell)Numerator: dfRows = NRows – 1dfColumns = NColumns – 1dfInteraction = NCells – dfRows – dfColumns – 1Estimated Population Variance: S2Rows = SSRows / dfRowsS2Columns = SSColumns / dfColumnsS2Interaction = SSInteraction / dfInteractionS2Within = SSWithin / dfWithinFRows = S2Rows / S2WithinFColumns = S2Columns / S2WithinFInteraction = S2Interaction / S2WithinControversy: Dichotomizing Continuous IVs: some people will convert age (a continuousIV) into a categorical IVOmnibus = overall effectState Null and Research Hypothesis: three different null (and research) hypotheses:No difference in happiness between men and women (IV #1)No difference in happiness between people who watch 24 and people who watch Grey’s Anatomy (IV #2)Difference in happiness between people who watch 24 and people who watch Grey’s Anatomy will be the same for men and women (Interaction)Effect Size for Two-Way ANOVA:R2Columns = (S2Columns * dfColumns) / [(S2Columns * dfColumns) + (S2Within * dfWithin)]R2Rows = (S2Rows * dfRows) / [(S2Rows * dfRows) + (S2Within * dfWithin)]R2Interaction = (S2Interaction * dfInteraction) / [(S2Interaction * dfInteraction) + (S2Within * dfWithin)]R2 (η2 (eta squared)) ranges from 0 to 1Small .01Medium .06Large .14If there are three IVs and one DV, there would be four interactions (IV #1 and 2, 1 and 3, 2 and 3, and 1, 2, and

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# UNT PSYC 2317 - Chapter #10 : Factorial Analysis of Variance

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