Presented toMs Maryium Gul
Presented by Aamna Haneef
Roll no: 05MS (2012-2014)
Lahore College for Women University
Repeated Measures ANOVA
Repeated measures ANOVA is also referred to as a • “within-subjects ANOVA”,• “Dependent groups” or • “ANOVA for correlated
samples”
Other Names
Why the repeated factor is called a “within” subjects factor?
Because comparisons are made multiple times ("repeated") “within” the same subject rather than across ("between") different subjects
In within subject design
• Each participant is measured more than once
• Same subjects across the levels of the IV
• Levels can be ordered like time or treatment
• Or levels can be un-ordered (e.g. cases take three different types of depression inventories)
What RM ANOVA does?Like T-Tests, repeated measures ANOVA gives the statistic tools to determine whether or not change has occurred over timeT-Tests compare average scores at two different time periods
RM ANOVA compared the average score at multiple time periods
The logic of RM ANOVA
Any differences that are found between treatments can be explained by only two factors:1. Treatment effect2. Error or Chance
Cont…
A particular subject’s scores will be more alike than scores collected from multiple subjects
Less variability decrease in sampling error
Cont…
Subject A B C
Each row
represents
one
subject
measured
under
each of k
conditions.
1subj1 under
condition A
subj1 under
condition B
subj1 under
condition C
2subj2 under
condition A
subj2 under
condition B
subj2 under
condition C
3subj3 under
condition A
subj3 under
condition B
subj3 under
condition C
And so on…
Assumptions
Dependent variableIt should be measured at the interval or ratio level (continuous), such as • revision time • Intelligence• exam performance • weight
Assumptions Cont…
Independent variable It should consist of at least two categorical, "related groups" or "matched pairs“• 10 individuals' performance in a
spelling test before and after new form of computerized teaching method
• measuring changes in blood pressure due to an exercise-training program
Assumptions Cont…
No significant outliers differencesData values that are "far away" from the main group of data• Distorting the differences between the related groups• Reduces the accuracy of results
Assumptions Cont…Normally distributed Dependent
variable• The dependent variable between the
two or more related groups should be approximately normally distributed
• It is quite "robust" to violations of normality
• The Shapiro-Wilk test of normality can test for normality
Assumptions Cont…
Sphericity• Refers to differences between
variances in levels of the repeated-measures factor (Time)
• Violation of the assumption of sphericity, causes the test to become too liberal (leads to an increase in the Type I error)
• Mauchly's Test of Sphericity can help to test for its violation
Hypothesis for RM ANOVA
The repeated measures ANOVA tests for whether there are any differences between related population means
H0: µ1 = µ2 = µ3 = … = µk
H0: There are no differences between population means.HA: At least one treatment or observation mean is significantly different
Sources of Variability• In repeated measure ANOVA, there are
three potential sources of variability: 1. Treatment variability: between columns, 2. Within subjects variability: between
rows, and 3. Random variability: residual(chance
factor or experimental error beyond the control of a researcher) .
• A repeated measure design is powerful, as it controls for all potential sources of variability.
FORMULA
variance between treatmentsF = ------------------------------------------
Error variance • A large F value indicates that the
differences between treatments/observations are greater than would be expected by chance or error alone.
Approaches to RM ANOVA
SPSS conducts 3 types of tests if the within-subject factor has more than 2 levels• The standard univariate ANOVA test• The alternative univariate tests• The multivariate test
Advantages • Using the same participants in
different experimental manipulations • Exclude the effects of individual
differences • This design is also very economical • Removing variance due to differences
between subjects from the error variance greatly increases the power (probability of correctly rejecting a false null hypothesis)
Disadvantages
• Practice effects causing participants’ results to improve • Carry-over effects (bias)• Demand characteristics (more
exposure, more time to think about meaning of the experiment).• Boredom and lack of concentration
Tidbits
Why it is always called F statistic?
The F statistic was named after Ronald A. Fisher, who mainly developed ANOVA
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