ADVANCED ANOVA APPLICATIONS
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1 TWO FACTOR ANOVA
2 ADVANCED ANOVA APPLICATIONS Repeated-Measures designs Compare 2 measurements from each participant Related-Samples, or Repeated-Measures, t-test Compare more than 2 measurements from each participant Repeated-Measures ANOVA Independent Samples designs Compare 2 independent groups on one factor Independent-Measures t-test Compare more than 2 independent groups on one factor One-Way ANOVA Compare independent groups on two factors Two-Factor, Independent Samples (or Two-Way) ANOVA
3 TWO-FACTOR (OR TWO-WAY) ANOVA (WITH INDEPENDENT SAMPLES) Research Design has two factors (independent and/or classification/quasi-experimental variables) Each factor has at least two levels Also called a factorial design Each combination of factor levels is tested with a separate group of participants (only one piece of data from each participant) One dependent variable is measured
4 RESEARCH SITUATION We are interested in the effects of both diet and exercise on percentage of body fat. A sample of 20 male high school sophomores is randomly selected. The participants are randomly assigned to one of four different treatment conditions, based on two independent variables. This study is a 2 (Level of Exercise: Exercise, No Exercise) X 2 (Calories in Diet: Below 2000, Above 2000) design, with both independent variables being manipulated in a between-subjects manner. After a 3-month period, each subject is measured for percentage of body fat compared to total weight.
5 RESEARCH SITUATION Factor B: Calories in Diet Below 2000 Above 2000 Factor A: Level of Exercise Exercise n = 5 X = 10, 12, 14, 12, 10 M = 11.6 n = 5 n = 5 X = 12, 14, 15, 16, 14 M = 14.2 n = 5 No Exercise X = 16, 18, 20, 22, 20 X = 22, 24, 24, 22, 24 M = 19.2 M = 23.2
6 3 HYPOTHESIS TESTS The two-factor ANOVA tests for: Mean difference between the two levels of Factor A MAIN EFFECT OF EXERCISE LEVEL Mean difference between the two levels of Factor B MAIN EFFECT OF CALORIE LEVEL Any other mean differences that may result from a unique combination of a specific calorie level and a specific exercise level INTERACTION BTW CALORIE LEVEL AND EXERCISE LEVEL
7 F-RATIOS Three F-Ratios: For the main effect of Factor A (Exercise Level): F = variance (differences) between the means for Factor A variance (differences) expected by chance/error For the main effect of Factor B (Calorie Level): F = variance (differences) between the means for Factor B variance (differences) expected by chance/error For the interaction of Factors A and B: F = variance (differences) not explained by main effects variance (differences) expected by chance/error
8 EXERCISE/CALORIE DATA 25 Body Fat Percentage Exercise No Exercise Parallel or nearparallel lines indicate no interaction between factors Main effect of Exercise Main effect of Calorie Level 0 Below 2000 Above 2000 Calorie Level
9 EXERCISE/CALORIE DATA 25 Body Fat Percentage Exercise No Exercise Parallel or nearparallel lines indicate no interaction between factors Main effect of Exercise Main effect of Calorie Level 0 Below 2000 Above 2000 Calorie Level
10 RESEARCH SITUATION We are interested in whether the drug Ritalin has any effect on reducing the activity levels of hyperactive adolescents. Further, we want to see if the drug s effect is similar for two age groups. A random sample of 40 participants is selected, with 20 under the age of 16 and 20 older than 16. Each age grouping is further divided into two groups of 10 participants each and randomly assigned to either the Ritalin condition or the placebo condition. This study is a 2 (Age: Under 16, Over 16) X 2 (Drug: Placebo, Ritalin) design, with both factors measured in a between-subjects manner. After two months, the participants are measured on their activity levels on a scale of 0 to 50, with high scores indicating higher levels of activity.
11 DATA & MAIN EFFECTS Factor B: Drug Placebo Ritalin Factor A: Age Under 16 Over 16 M = 35 M = 27 M = 33 M = 37 M A1 = 31 M A2 = 35 M B1 = 34 M B2 = 32
12 RITALIN/AGE DATA Under 16 Over 16 Non-parallel lines indicate an interaction between factors Hyperactivity No main effect of Age Group No main effect of Drug 5 0 Placebo Drug Ritalin
13 RITALIN/AGE DATA Under 16 Over 16 Non-parallel lines indicate an interaction between factors Hyperactivity No main effect of Age Group No main effect of Drug Placebo Drug Ritalin
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