UW-Madison PSYCH 210 - Factorial ANOVA (4 pages)

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Factorial ANOVA

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Factorial ANOVA


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University of Wisconsin, Madison
Psych 210 - Basic Statistics for Psychology
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PSYCH 210 Lecture 23 Outline of Last Lecture I Finish Within subjects ANOVA a Hypothesis testing steps b Post hoc test c Assumptions II Factorial ANOVA Outline of Current Lecture I Final II Factorial ANOVA a Conceptual Example b New Concepts main effects and interactions c Calculation example with hypothesis testing steps d Post hoc tests e Assumptions Current Lecture I II Final a Same structure as past exams i MC 15 20 cumulative review old MC questions ii Short Answer 3 questions only new material iii Integrative 2 sections 1st one 5 questions includes cumulative all inferential tests starting with z 2nd only on new material ANOVA calculation b 200 pts double the weight c Half cumulative Factorial ANOVA a Conceptual Example i Simplest possible example 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 1 Between Subjects Independent Samples di fps in all situations0 2 Only 2 IV s with 2 conditions ii Social loafing 1 Working in group setting individuals less exert effort in groups than if by themselves 2 Swimming Example iii Experiment Set up 1 IV 1 Type of Race a Levels Individual Relay 2 IV 2 Identifiability of Swimmer a Levels Announcing lap times Not announce Lap time Individual Relay Announced P1 P10 P11 P20 Not Announced P21 P30 P31 P40 b Every Tx contains different people Fully Crossed Design c 2x2 Design i x ii Number of blanks of IVs iii Values within blanks of levels 3 DV Individual lap times 4 Questions a Does the type of race by itself affect the individual race times i Main effect of Type of Race b Does the identifiability of swimmer by itself affect individual race times i Main Effect of ID of Swimmer c Do the variables work together to produce a combined effect on race times i Interaction between Type of Race and ID of Swimmer 5 Eye ball Calculation Individual Relay Announced M 65 M 45 Not Announced M 60 M 70 a Main effect Type of Race i Pretend ID does not exist ii Average 2 Cell Means to calculate Margined Means 1 Individual M 62 5 2 Relay M 57 5 iii Assume means different by at least 10pts is significant 1 No Main Effect ME for Type of Race b Main Effect ID of Swimmer i New Marginal Means 1 Announced M 55 2 Unannounced M 65 a Significant ME for ID of swimmer c Interaction i Graph cell means in line graph 1 Doesn t matter which IV goes on x axis you chose a Other variable identified via legend on graph 2 DV goes on y axis 3 Connect IV dots with a line a Nonparallel lines significant interactions b Parallel no interaction ii Interaction Definition 1 The effect that one IV has on the DV depends on levels of the other IV a The effect that type of race has on individual lap time depends on whether or not swimmer s lap times are announced during the race i Dependent Relationship more complicated than just looking at variables separately or assuming interaction across board iii What if there was no interaction 1 Graph shoes parallel lines 2 Implication a The effect that one IV has on the DV does NOT depend on levels of the other IV b Social loafing occurs no matter what same thing happens across IV ii There are 8 different possible outcomes with a two factor ANOVA 1 Handout a 3 questions are always the same i Whether or not any of them occur is variable b Scenarios i All 3 questions significant ii All 3 not significant iii Any combination in between 1 Ex No ME A No ME B Interaction Sign 2 Main effects and interactions are INDEPENDENT effects a Main effect for first variable does not guarantee ME for 2nd variable or interaction etc b We need to calculate 3 different Fs one for each effect ME A ME B Interaction AxB b Factorial ANOVA Calculation Example i Soccer Skills Example 1 See template handout

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