Factorial Analysis of Variance Chapter 10 Lecture 10 Jaymie Ticknor Quantitative Methods 2317 Sect 001 2 7 and 9 April 2014 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 recall Main effect for IV 2 IV is pills and DV is retention recall Interaction effect effect of one IV on DV differs across the levels of another IV Interactions 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 design Look at cell means each grouping combination is called a cell Main 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 IV Interaction 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 IV The 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 hamburger Two Way ANOVA 3 F ratios one for main effect for IV 1 IV 2 and one for interaction effect ANOVA is a versatile technique can be used with more than 2 IVs can be used with repeated measured variables Person s deviation from the Grand Mean GM all scores number of all scores is a combination of Person s deviation from its cell mean Person 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 2 M cell mean add scores in cell number of scores in cell SSBetween is split up into 3 parts new SSRows MRow GM 2 SSColumns MColumn GM 2 SSInteraction X GM X M MRow GM MColumn GM 2 Denominator dfWithin df1 df2 dfLast for each cell Numerator dfRows NRows 1 dfColumns NColumns 1 dfInteraction NCells dfRows dfColumns 1 Estimated Population Variance S2 Rows SSRows dfRows S2 S2 S2 FRows S2 FColumns S2 FInteraction S2 Columns SSColumns dfColumns Interaction SSInteraction dfInteraction Within SSWithin dfWithin Rows S2 Within Columns S2 Within Interaction S2 Within IV into a categorical IV Controversy Dichotomizing Continuous IVs some people will convert age a continuous Omnibus overall effect State 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 Columns dfColumns S2 Columns S2 Rows S2 Interaction S2 R2 R2 R2 Interaction dfInteraction S2 R2 2 eta squared ranges from 0 to 1 Rows dfRows S2 Columns dfColumns S2 Within dfWithin Rows dfRows S2 Within dfWithin Interaction dfInteraction S2 Within dfWithin Small Medium Large 01 06 14 2 and 3 and 1 2 and 3 If there are three IVs and one DV there would be four interactions IV 1 and 2 1 and 3