Analysis of Variance

1
Analysis of Variance

• ANOVA and the F Distribution

Supernova Image from http//legacy.gsfc.nasa.gov/d
ocs/snr_images.html
2
Lets Review

• Independent Variable (IV)
• What you are doing to the subjects, or
• How you are grouping the subjects
• Dependent Variable (DV)
• What you are measuring
• Between Subjects Design
• Within Subjects Design

3
The F Distribution

• z distribution
• t distribution
• f distribution
• Based on the ratio of two variances
• Shape
• Properties

4
The F Distribution

• Uses
• Homogeneity of variance
• ANOVA

5
Concepts Related to Variability

• Causes of Variability

6
Assumptions of ANOVA

• Random selection
• Random assignment
• Case independence
• Normal distribution
• Homogeniety of Variance
• Interval or ratio level data
• gt 30 cases per group

7
TerminologyOne Independent Variablewith More
than Two Levels
Oneway ANOVA for __________
Independent Samples or Repeated Measures
8
TerminologyMore than One Independent Variable
__________ ANOVA for __________
Two way or Three way or N - way
Independent Samples or Repeated Measures or Mixed
Design
9
Number of Levels of the IV (Name of the IV)
_____(__________) X _____(__________)
__________ ANOVA for __________
Two way or Three way or N - way
Independent Samples or Repeated Measures or Mixed
Design
10
Some Examples

• 2(Sex) X 2(Level of Caffeine) two way ANOVA for
  independent samples
• 2(Amount of Alcohol) X 3(Type of Setting) two way
  ANOVA for a mixed design
• 2(Age Group) X 3(Type of Class) X
  2(Pretest/Posttest) three way ANOVA for a mixed
  design
• 2(Reward Type) X 2(Time of Day) two way ANOVA for
  repeated measures

11
Oneway ANOVA for Independent Samples(Independent
Measures)

• When to use it
• One independent variable
• The independent variable has 3 or more levels
  (conditions/groups)
• Each subject experiences only one level or
  condition (i.e., a between subjects design)

12
Oneway ANOVA for Independent Samples

• Research Question
• Hypotheses
• Variables
• Entering data
• Conducting the test
• Reporting results
• Drawing conclusions

13
Descriptives
14
Test of Homogeneity of Variances
15
ANOVA
16
Oneway ANOVA for Independent Samples

• Research Question
• Hypotheses
• Variables
• Entering data
• Conducting the test
• Reporting results
• Drawing conclusions

17
Summary Table
18
Summary Table
19
Sum of Squares Between
20
Summary Table
21
Sum of Squares Within
22
Summary Table
23
Sum of Squares Total
24
Summary Table
25
Summary Table
26
Summary Table
27
Summary Table
28
Summary Table
29
Summary Table
30
Summary Table
31
Post Hoc Tests

• What is it?
• Why do it?
• How to calculate it?
• What does it mean?

32
Multiple Comparisons LSD
33
Effect Size

• What is it?
• Why do it?
• How find it?
• What does it mean?

34
Variance Accounted For

• What is it?
• Why do it?
• How to calculate it?
• What does it mean?

35
How do you know which test to use?

• What type of data do you have for the DV?
• Is the question a difference question or a
  relationship question?
• For difference questions
• How many independent variables do you have?
• If only one, then ask How many groups/conditions
  are you comparing?
• If only two, use a t test.
• If more than two, use a one way ANOVA.
• What type of IVs are they (between subjects or
  within subjects)
• For different groups One way ANOVA for
  independent samples.
• For the same group repeatedly One way ANOVA for
  repeated measures.