• 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