repeated measures anova
DESCRIPTION
Repeated Measures ANOVA - overview with SPSS and writeupTRANSCRIPT
• Repeated measures• Matched samples
Independent-measures analysis of
variance
Repeated measures designs
Individual differences
Total Variability
Between Treatments
Within Treatments
Oneway ANOVA
Independent Samples
Compare two groups that are unrelated to each other
Numerator is difference between groups
Does not control for the impact of individual differences
Related Samples
Compare two measures from one person or one related pair of people
Numerator is difference within pair
Controls for the impact of individual differences
Null hypothesis: in the population, there are no
mean differences among the treatment groups
Alternate hypothesis states that there are
mean differences among the treatment groups.
...: 3210 H
H1: At least one treatment mean μ
is different from another
removed) sdifference l(individua
effect, treatmentno withexpected es)(differenc variance
s treatmentbetween es)(differenc varianceF
F ratio based on variances
• Same structure as independent measures
• Variance due to individual differences is
not present
Participant characteristics that vary from
one person to another.
• Not systematically present in any treatment
group or by research design
Characteristics may influence
measurements on the outcome variable
• Eliminated from the numerator by
the research design
• Must be removed from the denominator
statistically
Numerator of the F ratio includes
• Systematic differences caused by treatments
• Unsystematic differences caused by random factors (reduced because same individuals in all treatments)
Denominator estimates variance reasonable to expect from unsystematic factors
• Effect of individual differences is removed
• Residual (error) variance remains
Total Variability
Between Treatments
Within Treatments
Between Subjects
Error Variance
Repeated Measures ANOVA
(Equations follow)
First stage
• Identical to independent samples ANOVA
• Compute SSTotal =SSBetween treatments + SSWithin treatments
Second stage
• Removing the individual differences from the denominator
• Compute SSBetween subjects and subtract it from SSWithin treatments to find SSError
N
GXSStotal
22
treatment each insidetreatmentswithin SSSS
N
G
n
TSS treatmentsbetween
22
Note that this is the
Computational Formula
for SS
N
G
k
PSSbetween
22
subjects
subjectsbetweentreatments withinerror SSSSSS
dftotal = N – 1
dfwithin treatments = Σdfinside each treatment
dfbetween treatments = k – 1
dfbetween subjects = n – 1
dferror = dfwithin treatments – dfbetween subjects
error
errorerror
df
SSMS
treatments between
treatments betweenntstreatme between
df
SSMS
error
mentstreat between
MS
MSF
OVERVIEW
This study investigated the cognitive effects of stimulant
medication in children with mental retardation and
Attention-Deficit/Hyperactivity Disorder. This case study
shows the data for the Delay of Gratification (DOG) task.
Children were given various dosages of a drug,
methylphenidate (MPH) and then completed this task as
part of a larger battery of tests. The order of doses
was counterbalanced so that each dose appeared equally
often in each position. For example, six children received
the lowest dose first, six received it second, etc. The
children were on each dose one week before testing.
This task, adapted from the preschool delay task of the
Gordon Diagnostic System (Gordon, 1983), measures the
ability to suppress or delay impulsive behavioral responses.
Children were told that a star would appear on the
computer screen if they waited “long enough” to press a
response key. If a child responded sooner in less than four
seconds after their previous response, they did not earn a
star, and the 4-second counter restarted. The DOG
differentiates children with and without ADHD of normal
intelligence (e.g., Mayes et al., 2001), and is sensitive to MPH treatment in these children (Hall & Kataria, 1992).
QUESTIONS TO ANSWER
Does higher dosage lead to higher cognitive performance
(measured by the number of correct responses to the DOG task)?
DESIGN ISSUES
This is a repeated-measures design because each participant performed the task after each dosage.
VARIABLE DESCRIPTION
d0 Number of correct responses after taking a placebo
d15Number of correct responses after taking .15 mg/kg of the drug
d30Number of correct responses after taking .30 mg/kg of the drug
d60Number of correct responses after taking .60 mg/kg of the drug
Analyze
Descriptives
Explore
Follow steps on diagram at right
Much more output than you want
Need to ask for some Options to get SPSS to do as much of the work as possible.
• Descriptives
• Plots
• Multiple Comparisons
• Effect Size
Follow the SPSSinstructions in Cronk
Choose Options according to thebox at the rightclick the choicesshown at right.
Percentage of variance explained by the
treatment differences
Partial η2 is percentage of variability that has
not already been explained by other factors
error
treatments between
subjectsbetweentotal
treatments between
SS
SS
SSSS
SS
2
Determine exactly where significant
differences exist among more than two
treatment means
• Tukey’s HSD can be used (almost always
same number of subjects) or Scheffé if
dropouts mean unequal measures.
• Substitute SSerror and dferror in the formulas
Does methylphenidate (MPH) have an impact on Delay of
Gratification for children with a diagnosis of ADHD?
Researchers compared DOG for of 24 children when they
received a placebo (M=39.75, s=11.315) and doses of 15mg/kg
(M=39.67, s=9.135), .30mg/kg (M=____, s=__) and .60mg/kg
(M=___, s=__); see Figure 1. The differences were/were not
significant (F(__ ,__)=______, p = _____). Post-hoc tests
with Bonferroni correction showed that ____________ The
impact of the MPH dosage was _____, with about ____% of
the variability in DOG related to the dosage of MPH (partial
2=._____). Dosage of MPH ______________
The observations within each treatment
condition must be independent.
The population distribution within each
treatment must be normal.
The variances of the population
distribution for each treatment should be
equivalent.
• Repeated measures• Matched samples