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

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3 Apr 2018
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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
ā¢ More than two groups so far, one or two groups (or two sets of
scores)
ā¢ What about comparing three groups?
o Control group
o Treatment 1
o Treatment 2
ā¢ Would need three different t tests for one study
o Ad bc more tests you do, more likely you are going to come
ā¢ New procedure affords one test to detect any difference
Analysis of Variance (ANOVA)
ā¢ Used to test differences among means (2+)
o One independent variable (factor)
o 2+ levels (conditions, groups) (k= # levels)
o one dependent variable
ā¢ no population information is available
ā¢ shift from emphasis on means to variances
o back-door method of testing differences among means
Different Types of ANOVAS
ā¢ One-way between-subjects
o One factor is tested (with k= 2+ levels)
o Different subjects in each level
āŖ Independent samples, independent measures
ā¢ One-way within-subjects
o One factor (with k= 2+ kevels)
o Same subjects in each level
āŖ Related samples, repeated measures
ā¢ Two-way between-subjects (two factors)
An introduction to analysis of variance
ā¢ Selecting independent samples
o Quasi-Experiment
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o Experiment
Changes in Notation
ā¢ n= number of participants per level (group
ā¢ N=number of total participants in a study
o When n is the same in each level, N= k * n
ā¢ k= number of levels (groups)
Sources of Variation and the Test Statistic
ā¢ 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
āŖ Regardless of group
āŖ This is called ātotal varianceā
o Parse how much of the total variance is from
āŖ Difference between levels
āŖ Differences within levels
Sources of Variation and the Test Statistic
ā¢ Sources of variation
o Between groups variation- differences between means
o Within groups (error) variation- differences within group
ā¢ Calculation of difference between groups
o Inherently has difference within groups
o Cannot separate them mathematically
o Can do this:
āŖ Weighted average of variance in each group
āŖ Variance attributed to chance
What to do now?
ā¢ Mathematically, inappropriate to subtract
o Group/within variation- within variation
ā¢ Instead, calculate ratio- F ratio
o Note: this is not the calculation formula
āŖ Fobt= variance attributed to group differences
ļŗ Variance attributed to chance
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