Experiments with more than two groups

1
Experiments with more than two groups or levels
of the independent variable
2
Why conduct studies with more than two groups?

• Can answer more sophisticated questions with a
  multiple group designmore efficient.
• Compare more than 2 kinds of treatment in one
  study.
• Compare 2 (or more) kinds of treatment and a
  control group.
• Compare a treatment vs. placebo vs. control
  group.
• To go from a two groups design to a multiple
  groups design, you add another level to your IV.
• Two groups IV has only 2 levels
• Multiple groups IV has 3 (or more) levels

3
Multiple groups Designs

• Between-subjects design
• Advantages
• simpler to run
• no issues of carryover effects
• Disadvantages more variability in distribution

• Within-subjects design
• Advantages
• participants are more equated
• less variability in distribution
• Disadvantages more chance of carryover effects

4
Analysis of Variance

• Multiple-groups designs are measured with the
  analysis of variance (ANOVA).
• One-way ANOVA 1 independent variable
• Two-way ANOVA 2 independent variables
• A one-way ANOVA for between-subjects design is
  known as a one-way randomized ANOVA.
• A one-way ANOVA for within-subjects design is
  known as a one-way repeated measures ANOVA.

5
Completely Randomized ANOVA

• Three groups of 8 salesclerks measured once
• Independent groups participants in one group are
  not same as participants in the other group.
• IV dress style of customers
  
• 3 levels
• Sloppy Clothing customers
• Dressy Clothing customers
• Casual Clothing customers
• DV response time of clerks to help customers

6

Grand mean 53.50
No individual score is exactly equal to group
mean or grand mean. Is the variability due to
the independent variable (clothing style) or is
it due to error variance (chance, confounds,
individual differences) ?
7

Grand mean 53.50

Within-groups variance - although salesclerks
within the group were exposed to the same
participants, the differences in reaction time
from one salesclerk to another are due to error
variance (individual differences more or less
motivated salesclerks). - variance within each
condition provides an estimate of the population
error variance.
8

Grand mean 53.50
Between-groups variance - compares the means
between the groups. - If IV had an effect, the
group means should differ from grand mean
(Systematic variance due to manipulation of IV).
- If IV had no effect, group means would differ
from grand mean just by chance (Error variance)
Between-groups variance systematic variance
error variance
9
Rationale of ANOVA

• F between-groups variance
• within-groups variance
• F systematic variance error variance
• error variance
• IV has an effect F gt 1 must pass a cutoff for
  statistical significance.
• IV has no effect or small effect F 1

10

11
Degrees of Freedom for one-way randomized ANOVA

• F(2, 21) 4.71
• Degrees of freedom F((k-1), k(n-1))
• k number of groups or levels of IV
• n number of participants in each group
• Between-groups degrees of freedom k - 1 k 3
• 3 1 2
• Within-groups degrees of freedom k(n-1) n 8
• 3( 8 1) 21
• F(2, 21)

12

Post Hoc Tests

• Post hoc after the fact t-tests
• Compares each of the groupswith each other to
  see if they
• differ significantly from each other.
• There are many kinds of post hoc tests
• Tukey (HSD) honestly significant difference.
• Ex significant difference between groups 1 2
  2 3

13
Results of ANOVA for randomized groups in APA
style

• The effect of different clothing on salespersons
  response time was significant, F(2, 21) 4.71, p
  lt .05. Post-hoc comparisons indicated that clerks
  waiting on customers dressed in sloppy clothing
  (M 63.25) responded more slowly than clerks
  waiting on customers in dressy clothing (M
  48.38) or casual clothing (M 48.88). Clerks
  waiting on customers in dressy and casual
  clothing did not differ from each other.

14
Repeated measures ANOVA

• One group of 8 salesclerks measured three times
• Repeated measures the same participants are
  tested in all three conditions.
• IV dress style of customers
  
• 3 levels
• Sloppy Clothing customers
• Dressy Clothing customers
• Casual Clothing customers
• DV response time of clerks to help customers

15

16

• Same rationale
• F between-groups variance
• within-groups variance
• All variances obtained the same way, except for
  within-groups variance.
• Difference
• Within-groups variance has 2 sources of variance
  
• - subject variance
• - error variance
• Error variance is used to calculate F ratio

Post hoc tests apply when ANOVA is significant.
17
Degrees of Freedom for repeated measures ANOVA

• F(2, 14) 19.71
• Degrees of freedom F((k-1), (k -1)(n-1))
• k number of groups/levels
• n number of participants in each group
• Between-groups DF k 1 k 3
• 3 1 2
• Within-groups DF (k-1)(n-1)
• (3-1)(8-1) (2)(7) 14
• F(3-1, (3-1)(8-1)) F(2, 14)

18
Results of repeated measures ANOVA groups in APA
style

• The effect of three different clothing styles on
  clerks response times was significant, F(2, 14)
  19.71, p lt .05. Post-hoc comparison showed
  that clerks took longer to respond to customers
  dressed in sloppy clothing (M 63.25) than to
  customers in dressy clothing (M 48.38) or
  customers in casual clothing (M 48.88).
  Response times did not differ between clerks
  waiting on customers in dressy or casual
  clothing.
• --------------------------------------------------
  --------------------------------------