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Psych 100A
Winter 2010
Lecture 15: OneFactor Between
Subjects Analysis of Variance
Onefactor multilevel design
• Onefactor multilevel design
is also called a oneway
multilevel design
– A type of experiment with one independent variable
that has three or more levels
–A
t
test cannot be used to analyze this kind of design
– Instead, an analysis of variance
(ANOVA) is used to
test statistical hypotheses with this experimental design
The problem with using Many t
tests
• When we have three groups there are 3 two
way comparisons
• Four groups 6 twoway comparison
Four groups, 6 two way comparisons
• N groups, N*(N1)/2 twoway comparisons
Type I error rate increases
Better Alternative: Onefactor
BetweenSubjects ANOVA
• Assumptions regarding the study design
– The scores in each sample are drawn randomly
from the population
– The scores are drawn independently
– The scores in the populations sampled are
normally distributed
– The variances of the scores in the population
are equal
Graphical Depiction
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Terms
• Grand mean
– Symbolized as
– The mean for all of the scores in the experiment
• Mean square
G
X
– Symbolized as
MS
– Another term for variance, used in ANOVA
• Withingroups error variance
– Symbolized as
MS
Error
– Measures only the error variance
Terms (continued)
• Betweengroups variance
– Symbolized as
MS
A
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 Winter '10
 FIRSTENBERG,I.
 Statistics, Normal Distribution, Variance

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