PY 211 Lecture Notes - Lecture 27: Analysis Of Variance, Repeated Measures Design, Test Statistic

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Chapter 12: Analysis of Variance (ANOVA)
One-way Between-Subjects Design 4/10/2017 4:56:00 PM
Increasing k: a shift to analyzing variance
More than two groups so far, one or two groups (or two sets of
scores)
What about comparing three groups?
o Control group
o Treatment 1
o Treatment 2
Would need three different t tests for one study
o Ad bc more tests you do, more likely you are going to come
up with wrong answer
New procedure affords one test to detect any difference
Analysis of Variance (ANOVA)
Used to test differences among means (2+)
o One independent variable (factor)
o 2+ levels (conditions, groups) (k= # levels)
o one dependent variable
no population information is available
shift from emphasis on means to variances
o back-door method of testing differences among means
Different Types of ANOVAS
One-way between-subjects
o One factor is tested (with k= 2+ levels)
o Different subjects in each level
Independent samples, independent measures
One-way within-subjects
o One factor (with k= 2+ kevels)
o Same subjects in each level
Related samples, repeated measures
Two-way between-subjects (two factors)
An introduction to analysis of variance
Selecting independent samples
o Quasi-Experiment
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o Experiment
Changes in Notation
n= number of participants per level (group
N=number of total participants in a study
o When n is the same in each level, N= k * n
k= number of levels (groups)
Sources of Variation and the Test Statistic
Variation in the Dependent Variable
o Scores from DV vary from subject to subject, and level to
level (group to group)
o Calculate the variance of all the scores from the study
Regardless of group
This is called “total variance”
o Parse how much of the total variance is from
Difference between levels
Differences within levels
Sources of Variation and the Test Statistic
Sources of variation
o Between groups variation- differences between means
o Within groups (error) variation- differences within group
Calculation of difference between groups
o Inherently has difference within groups
o Cannot separate them mathematically
o Can do this:
Weighted average of variance in each group
Variance attributed to chance
What to do now?
Mathematically, inappropriate to subtract
o Group/within variation- within variation
Instead, calculate ratio- F ratio
o Note: this is not the calculation formula
Fobt= variance attributed to group differences
Variance attributed to chance
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