Lecture 16Psyc 300A

What a Factorial Design Tells You

• Main effect: The effect of an IV on the DV, ignoring all other factors in the study. (Compare means of different levels of IV, while ignoring [collapsing across] other IVs [ i.e., compare marginal means])

• Interaction effect: When the effect of one IV on a DV differs depending on the level of a second IV.

• Interpret the interaction first

Group Activity: Main Effects and InteractionsMake graphs of the

following situations: Study 1

Study 2

Study 3

Study 4

Var A Var B AxB interaction

p < .05 n.s. p < .05

p < .05 p < .05 p < .05

n.s. p < .05 n.s.

n.s. n.s. p < .05

Factorial Designs: Naming Conventions

• The first number is the number of levels in first IV, second number is number of levels in second IV, etc.

• 2 x 2• 2 x 3• 2 x 2 x 3• Between-subjects,

repeated measures (within), mixed

A 2 x 3 Interaction

0

2

4

6

8

10

Relaxation Focus Affirmation

Coping Technique

Rat

ing hi stress

lo stress

Analysis of Variance (ANOVA)

• Test statistic for ANOVA is F• Is related to t-test• ANOVA is for multiple levels of IV and

multiple IVsMSbetween

F =MSwithin

• It compares the amount of variability between groups to amount within groups

Interpreting the F statistic (ANOVA)• Hand calculations

– Calculate F (this is Fobtained).

– Compare value with F in table (Table B.3. This is Fcritical). To do this need to know alpha and df.

– If Fobtained > Fcritical, a significant effect.

• In SPSS– Look at source (summary) table– Effects with significance values less

than .05 are significant.

ANOVA (one way) ExampleDo preschoolers benefit from extra practice in language

skills?Groups: 1=5hrs; 2=10 hrs; 3=20 hrs

1 87 2 87 3 891 86 2 85 3 911 76 2 99 3 961 56 2 85 3 871 78 2 79 3 891 98 2 81 3 901 77 2 82 3 891 66 2 78 3 961 75 2 85 3 961 67 2 91 3 93

ANOVA Source (or Summary) Table

_______________________________________Source df SS MS F .

Between groups 2 1133.07 566.54 8.80

Within groups 27 1738.40 64.39Total 29 2871.47_______________________________________

Oneway ANOVA: SPSS Output

Post hoc comparisons

• When there are more than two conditions, a significant F-test tells you that at least two means are different, but not which ones

• To discover which are different, we use post hoc comparisons

• Some of these include Scheffe, Newman-Keuls, Duncan, Tukey tests

SPSS: Factorial ANOVA, All Between-Subjects IVs (Weight loss data)

Female trainer Female trainer Male trainer Male trainer

Female client Male client Female client Male client

76 65 88 65

78 90 76 67

76 65 76 67

76 90 76 87

76 65 56 78

74 90 76 56

74 90 76 54

76 79 98 56

76 70 88 54

55 90 78 56

SPSS Data File: Weight Loss Study

SPSS Weight Loss Study Plot

SPSS Output File: Weight Loss Study