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Repeated Measures lectures notes

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Vak
(PSMM2)

Instelling
Rijksuniversiteit Groningen (RuG)

This document entails elaborative lecture notes of the course Repeated Measures, for the masters Clinical Forensic Psychology and Victimology, Klinische Neuropsychologie, Clinical Neuropsychology en Klinische Psychologie.

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Repeated Measures lecture notes
Lecture 1 Review of ANOVA
Univariate = 1 dependent variable (DV)

Multivariate = multiple DVs

Lectures are most important! Background is in book, still important.

Recall ANOVA

Between-factor one-way ANOVA:

Purpose: Comparison of group means (independent populations).

Factor, e.g., gender, for females and males.

One-way means 1 factor like gender, or intervention (group with intervention, and group without), or
educational level with three levels (low, average, high).

→ two way is with two factors, e.g., gender and educational level in the design. A participant is
always put in a group. Between subject-variable, e.g., you a female of male.

Within-variable: pops up in different moments/categories, e.g., within factor is time, before and after
treatment.

To wat extent do the means differ, e.g., between high and low education.

µj = population mean of the group

 = subject-specific residual

SS = the variability in sum of scores.

SS partition: SST = SSG + SSE

SSG – between groups, explained part

SSE – within groups, unexplained part

F = MSG/MSE =

95% confidence interval (CI) = 95% sure that the population mean will fall between the sample mean
and 95% CI interval.

SS/df = means square (MS)

,F = mean square / residual

Example one-way ANOVA

- Study on the effects of instructional material on how well students learn statistical concepts.
- Variables:
o DV continuous: Y (test scores on statistical concepts)
o IV discrete: group (2) (instructional conditions)
- Perform an univariate ANOVA:
o Test whether the two population means are equal
o ANOVA table:
SS, df, MS, F, p-value, Partial eta squared (.01: Small; .06: Medium; .14: Large effect
size)

Samples scores on Y per group + output

Significance test and effect size

p > .05 HO = not rejected, no significant difference.

Small sample = lower power, could give larger effect size

- P-value: indicates the significance of a factor.
o What is the probability of these samples means or more extreme if the population
means would be equal in the population?
- Effect size: indicates the size of the effect
o In ANOVA: How large is the difference between the groups in the population?
o Population means relative to within group variable. How much do groups differ from
each other? The further apart the normal distributions are, the bigger the effect size.
o Effect size measures in ANOVA
▪ ɳ2 = SSeffect/SStotal: proportion of variance explained of effect
▪ Partial ɳ2: proportion of variance explained, after accounting for variance
explained by possible other factors
▪ And other measures

,Follow-up on significant ANOVA

What to do if the omnibus F test rejects H0?

- Evidence that at least 1 group differs from the other groups, based on one or more effects
(main/interaction). One group significantly differs, where is the difference?
Via:
o Visual inspection
o (Muliple) comparisons (tests or CI’s)
1. Planned → contrasts
2. Post hoc comparisons

Assumptions ANOVA

1. Independent observations
2. Within each group the scores are normally distributed
a. Check per group via QQ-plot or test on skewness and kurtosis
3. The variances of the scores are equal across all groups
a. Check sample variances between groups: max/min <2 is ok
b. Levene’s test: be cautious, use of significant test to confirm H0. → quite dangerous

Experimental designs

Experiments have 3 characteristics:

1. Manipulation of treatment levels:
– researcher controls nature and timing of each treatment level
2. Random assignment of cases to levels (groups):
– to remove bias
– average out differences among cases
3. Control of extraneous variables:
– only treatment level changes during experiment

Observational: apparently groups differ from each other.

Experimental: you can infer causality.

How to control extraneous variables:

- Hold them constant
- Counter effect their effects
- Turn them into an extra factor

When all 3 characteristics hold (i.e., manipulation, random assignment, control), differences in scores
are attributed to differences in treatment levels.

Proof of causal relationship? → still hazardous until study is successfully replicated

, Between subject design

Differences due to treatments are tested between groups of subjects: Different cases in every level.

Designs:

- Experimental: Cases are randomly assigned to
treatment levels
- Nonexperimental (also denoted: correlational
or observational): No random assignment
(e.g., gender; patient/control)
- Factorial designs:
o Treatment levels are determined by
more than one factor
o Main effects of each factor, and interaction(s)

Factorial ANOVA

- Usually more than one factor (defining different groups)
o For two factors: then a x b groups, and main effects and interaction effects can be
tested. → is denoted: two-way ANOVA.
▪ Main effects are best interpreted when there is NO interactions between
variables.
- Why several factors?
o Statistical reason: Reduction of error variance
o Substantive reason: Study interplay between variables

Source of variance

Identifying source of variance

1. List each factor as source
2. Examine each combination of factors: complete crossed → include interactions as source
3. When effect is repeated, with different instances, at every level or another factor → include
factor as source
Main effects are best interpreted when there is NO interaction between variables.

Example:

- Factor A, factor B, and subjects S
- A and B completely crossed: A, B, AB, and S
- Different S, at each level of A and B: A, B, AB, and S(AB)

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