Factorial Designs and ANOVA

Factorial Designs 4 Very efficient design –Multiple comparison groups –Multiple independent variables 4 Avoids some of the artificiality of traditional experiment where x varies and all other things held constant.

Researcher can: 4 Analyze effects of two or more variables simultaneously 4 Determine if variables interact to produce differences in outcome that would not occur if effects of each variable were considered separately 4 Test several hypotheses

Research Example: Damrosh Nursing students’ perceptions of an act of rape 48 nursing students were given four different vignettes about a rape to read. 32 yo female raped in her car outside all night drug store Group A--rape occurred at 10PM, car door left unlocked Group B--rape occurred at 12 Mid., car door left unlocked Group C--rape occurred at 10PM, car door locked Group D--rape occurred at 12 Mid., car door locked Subjects questioned as to how responsible the victim was How much they liked and identified with the victim How severly the rapist should be punished

What are the independent variables 10 Pm 1 Time 2 treatment conditions 12 Mid 2 Condition of Lock 2 treatment conditions locked unlocked

Graphic Representation

Number of cells 4 Equal to the number of independent variables X tx conditions 4 2 indep var x 2 tx cond = 4

Compare Mean scores for each group Mean scores for each time period 10 A+C 12 B+D Mean scores for each locked condition unlocked A+B locked C+D

Answers research questions 4 What is the main effect of time variable? 4 What is the main effect of locked condition variable? 4 Is there an interactive effect of time with locked condition?

Hypotheses 4 One for each independent variable (main effects) 4 One for the interactive effect never more than one interaction

ANOVA Analysis of Variance Decomposes the variability into variability caused by independent variable from that caused by all other sources

F ratio= variance between groups variance within groups F=MS b between group variance MS w within group variance

F ratio The higher the value of f, the greater the probability that the measures being compared are significantly different from each other, and variance is caused by independent variable f<1=never statistically significant

Factorial designs 4 Sound basis for external validity 4 Mortality a real threat to validity (should have the same number in each cell) Now try your hand at quiz three for class discussion for # 7 a. What are the independent variables and their treatment conditions? (diagram the study) B. Is there a main effect to each? C. Is there an interactive effect?