Analysis of Variance: Part 2 - psych.westminster.edu · Chapter 8. When to use Repeated Measures...
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Chapter 8 Analysis of Variance: Part 2 Oneway Repeated Measures ANOVA
Transcript of Analysis of Variance: Part 2 - psych.westminster.edu · Chapter 8. When to use Repeated Measures...
Chapter 8
Analysis of Variance: Part 2
Oneway Repeated Measures ANOVA
Chapter 8
Threats to Internal ValidityHistoryMaturationTesting InstrumentationStatistical RegressionExperimental MortalitySelection-maturation interaction
Chapter 8
Instrumentation In which changes in the calibration of a
measuring instrument or changes in the observers or scorers used may produce changes in the obtained measurements.
Chapter 8
Statistical RegressionOperating where groups have been selected
on the basis of their extreme scores.
Chapter 8
Experimental Mortalityor differential loss of respondents from the
comparison groups.
Chapter 8
Partitioning the Variance: Repeated Measures
Total Variance
Chapter 8
Partitioning the Variance: Repeated Measures
Total Variance
BetweenSubjects
WithinSubjects
Chapter 8
Partitioning the Variance: Repeated Measures
Total Variance
BetweenSubjects
WithinSubjects
Treatment
Error
Chapter 8
Between Subjects VarianceThe variance in the data that can be
attributed to differences among the subjects.
Irrelevant to the Hypothesis.
Chapter 8
Within Subjects VarianceVariance between subject’s own scores on
each repeated assessment.– Treatment effects– Error variance
Variances among treatment means for each condition.
Chapter 8
F-Ratio
Treatment VarianceError VarianceF=
Chapter 8
AssumptionsTreatments are not IndependentDependent Variable is measured on at least
an ordinal scaleDependent Variable is normally distributed
Chapter 8
When to use Repeated Measures ANOVA
Same Subjects are in each treatment.There are 2 means or more to compare. (Can use for 2 groups: t is easier)
Chapter 8
How to set up the ANOVA Summary Table
Source
Chapter 8
How to set up the ANOVA Summary Table
Source
Total
Chapter 8
How to set up the ANOVA Summary Table
Source
Total
BetweenWithinTreatmentError
Chapter 8
How to set up the ANOVA Summary Table
Source
Total
Between SSSWithin Treat. SSIVError SSE
Sums ofSquares
SST
Chapter 8
How to set up the ANOVA Summary Table
Source
Total
Between SSSWithin Treat. SSIVError SSE
Sums ofSquares
SST
df
dfS
dfIVdfE
dfT
Chapter 8
How to set up the ANOVA Summary Table
Source
Total
Between SSS dfS Within Treat SSIV dfIV MSIVError SSE dfE MSE
Sums ofSquares
SST
df
dfT
MeanSquares
Chapter 8
How to set up the ANOVA Summary Table
Source
Total
Between SSS dfS MSS Within Treat SSIV dfIV MSIVError SSE dfE MSE
Sums ofSquares
SST
df
dfT
MeanSquares F
F
Chapter 8
Calculating the F StatisticCalculate Sums of SquaresCalculate dfCalculate Mean SquaresCalculate F
Chapter 8
How to Calculate the Sums of Squares Between
Source
Total
Between SSS Within Treat. SSIVError SSE
Sums ofSquares
SST
( )X
kTN
p∑
∑ −
22
Chapter 8
How to Calculate the Sums of Squares Between
Source
Total
Between SSS Within Treat. SSIVError SSE
Sums ofSquares
SST
Sum of scoresfor each subject
( )X
kTN
p∑
∑ −
22
Chapter 8
How to Calculate the Sums of Squares Between
Source
Total
Between SSS Within Treat. SSIVError SSE
Sums ofSquares
SST
T=Total=Sum of all scores.
( )X
kTN
p∑
∑ −
22
Chapter 8
How to Calculate the Sums of Squares Between
Source
Total
Between SSS Within Treat. SSIVError SSE
Sums ofSquares
SST
k=number treatments
( )X
kTN
p∑
∑ −
22
Chapter 8
How to Calculate the Sums of Squares Between
Source
Total
Between SSS Within Treat. SSIVError SSE
Sums ofSquares
SST
N= Total number of scores
( )X
kTN
p∑
∑ −
22
Chapter 8
How to Calculate the Sums of Squares Total
Source
Total
Between SSS Within Treat. SSIVError SSE
Sums ofSquares
SST X TN
22
∑∑ −
Chapter 8
How to Calculate the Sums of Squares Total
Source
Total
Between SSS Within Treat. SSIVError SSE
Sums ofSquares
SST X TN
22
∑∑ −
Sum of all scoressquared first
Chapter 8
How to Calculate the Sums of Squares Within
Source
Total
Between SSS Within Treat. SSIVError SSE
Sums ofSquares
SST
X
nTN
j∑
∑
−
2
2
Total for treatment j
Chapter 8
How to Calculate the Sums of Squares Within
Source
Total
Between SSS Within Treat. SSIVError SSE
Sums ofSquares
SST
X
nTN
j∑
∑
−
2
2
Number of subjects
Chapter 8
How to Calculate the Sums of Squares Within
Source
Total
Between SSS Within Treat. SSIVError SSE
Sums ofSquares
SST
SST-SSIV-SSE
Chapter 8
How to Calculate the Degrees of Freedom
Source
Total
Between SSS Within Treat. SSIVError SSE
Sums ofSquares
SST
df
dfT
n-1
Chapter 8
How to Calculate the Degrees of Freedom
Source
Total
Between SSS Within Treat. SSIVError SSE
Sums ofSquares
SST
df
dfT
n is the number of subjects
n-1
Chapter 8
How to Calculate the Degrees of Freedom
Source
Total
Between SSS Within Treat. SSIVError SSE
Sums ofSquares
SST
df
dfT
k-1
n-1
Chapter 8
How to Calculate the Degrees of Freedom
Source
Total
Between SSS Within Treat. SSIVError SSE
Sums ofSquares
SST
df
dfT
k-1
n-1
(n-1)(k-1)
Chapter 8
How to Calculate the Degrees of Freedom
Source
Total
Between SSS Within Treat. SSIVError SSE
Sums ofSquares
SST
df
k-1
n-1
(n-1)(k-1)
N-1
Chapter 8
How to Calculate the Mean Squares
Source
Total
Between SSS dfS Within Treat SSIV dfIV MSIVError SSE dfE MSE
Sums ofSquares
SST
df
dfT
MeanSquares
Chapter 8
How to Calculate F
Source
Total
Between SSS dfS MSS Within Treat SSIV dfIV MSIVError SSE dfE MSE
Sums ofSquares
SST
df
dfT
MeanSquares F
F=
Chapter 8
Determining the Critical FAlpha = .05Find Column for df TreatmentFind Row for df ErrorCompare Critical F to Obtained F
Chapter 8
Statistical Decision Making If Critical F > Obtained F
– failed to reject null hypothesis If Critical F < Obtained F
– reject the null hypothesis
Chapter 8
Interpreting the ResultsGraph MeansUse a multiple Comparison test
– to determine which means are– significantly different
Chapter 8
Multiple ComparisonsHonestly Significant Difference TestHSD
HSD q MSna
error=
Chapter 8
Multiple ComparisonsHonestly Significant Difference TestHSD
HSD q MSna
error=
StudentizedRange Statistic(from Table)
Chapter 8
Multiple ComparisonsHonestly Significant Difference TestHSD
HSD q MSna
error=
Mean Square Error(from ANOVA)
Chapter 8
Multiple ComparisonsHonestly Significant Difference TestHSD
HSD q MSna
error=
Number ofSubjects
