One-way Repeated Measures MANOVA Design

Presented by

Dr.J.P.VermaMSc (Statistics), PhD, MA(Psychology), Masters(Computer Application)

Professor(Statistics)

Lakshmibai National Institute of Physical Education, Gwalior, India

(Deemed University)Email: vermajprakash@gmail.com

One-way Repeated Measures MANOVA Design

Also known as repeated MANOVA or rMANOVA

Also known as

To investigate the effect of an independent factor (having different levels) on a group of dependent variables

Why to Use

Same subjects are tested under each level of the independent variable.

Independent variable can either be different treatment conditions or different time points.

Features

 DVs : Number of correct recalling of name, colour and shape of objectsIV : Four and Six seconds visual time

Example Which visual time is more effective for memory retention of the object’s characteristics?

One-way rMANOVA Design

When to use One-way Repeated Measures MANOVA?

When individuals vary widely on the experimental variable.

When several dependent variables (DVs) measure different aspects of some cohesive theme.

Where improvement trend needs to be investigated. Example of DVs

personality (Extraversion, Psychoticism, Neuroticism)

health(blood pressure, heart rate, vital capacity)

product features(economy, comfort, attractiveness)

fitness(cardio respiratory endurance, flexibility, strength)

nature(extrovert, optimism, creativity) academic achievement(English, Maths,

Commerce) Example: To study the change in physiological status((heart rate, blood pressure and vital capacity) of subjects while undergoing an exercise programme over a period of time.

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This Presentation is based on

Chapter 7 of the book

Repeated Measures Design for Empirical Researchers

Published by Wiley, USA

Complete Presentation can be accessed on

Companion Website

of the Book

Precaution in using One-way RM MANOVA

Choose DVs carefully in the study

DVs should be moderately correlation (.3 to .7)among themselves

Highly correlated DVs

Weaken the power of the analysisUncorrelated

DVsMANOVA has nothing to offer

Word of Caution

Thumb Rule

Even if dependent variables are moderately

Don’t be tempted to use RM MANOVA

If combining DVs can not be justified

Consider using series of univariate ANOVAs

Why to Use Repeated Measures MANOVA?

1. Due to demand of research question being investigated.

2. Variables explaining latent variable are often correlated hence separate rANOVA's will be redundant and difficult to integrate.

3. None of the individual ANOVAs may produce a significant effect on the DV, but if combined they might.

4. By using MANOVA, family wise error rate(α) can be controlled.

5. The sphericity assumption in rANOVA is often violated whereas RM MANOVA does not require this assumption.

Application

To investigate as to how the personality(Extraversion, Psychoticism and Neuroticism) transformation takes place during one year of training in communication skill.

To investigate as to which naturopathy intervention (pranayama, meditation and relaxation exercise) is more effective in improving mood state(confusion, depression and fatigue)

An educational consultant may wish to investigate performance(numerical aptitude, reasoning and English comprehension) trend of subjects during a training programme for a competitive examination.

Assumptions

Data type : There should be two or more continuous DVs and one categorical IV.

 Sample Size Number of observations must be higher than the number of DVs. Recommended sample size of at least 20.

 Independence of Measurement  Missing Data This design requires complete data for all

the subjects.  Outliers No outlier should exist in any group  Linearity All DVs are linearly related among themselves

in each group of the independent variable.  Normality There should be multivariate normality.  Multicollinearity There should be no multicollinearity

among the DVs.  Sphericity There should be no sphericity in data.

Case I: Levels of the within-subjects variable are different treatment conditions

Example: To investigate the effect of naturopathy intervention in improving mood state of six subjects

When to use One-way rMANOVA

Each subject is tested on multiple dependent variables in each treatment condition

Issues in the DesignCarryover effect – Controlled by having sufficient gap between any two treatmentsOrder effect – Controlled by counterbalancing

IV : Naturopathy intervention (pranayama, meditation and relaxation exercise) DVs : Mood state parameters(confusion, depression and fatigue)

S2

S5

S1

S6

S3

S4

Relaxation Exercise

First phase testing

S2

S5

S1

S6

S3

S4

S2

S5

S1

S6

S3

S4

Second phase testing

Third phase testing

Testing protocol

Treatment: Naturopathy intervention

Confusion Depression Fatigue

S1

S6

S3

S4

S2

S5

S1

S6

S3

S4

S2

S5

S1

S6

S3

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S2

S5

Confusion Depression Fatigue

S3

S4

S2

S5

S1

S6

S3

S4

S2

S5

S1

S6

S3

S4

S2

S5

S1

S6

Confusion Depression Fatigue

MeditationPranayama

Layout of One-way rMANOVA Design

Figure 7.1 Layout design

1. Divide sample into groups2. Randomized treatments on these groups and take measurements on all

dependent variables

Designing procedure

S1

S2

S3

S4

S5

S6

4 week

Testing protocolTreatment: Time

Numerical Reasoning English Aptitude Compre

2 weekZero week

Numerical Reasoning English Aptitude Compre

Numerical Reasoning English Aptitude Compre

S1

S2

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S1

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S1

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S6

Case II: levels of the within-subjects variable are different time periods

When to use One-way rMANOVA

Example: To investigate the performance trend of subjects during a training programme for a competitive examination. DVs : Performance parameters (numerical aptitude, reasoning and English comprehension)IV : Time(zero week, 2 week, 4 week)

Figure 7.2 Layout design

Steps in One-way rMANOVA Test assumptions of design

Describe layout design

Write research questions to be investigated

Write hypotheses to be tested

Specify familywise error rates (α)

Use SPSS to generate outputs

Descriptive statistics

MANOVA table containing Wilk’s Lambda Continue

…

Is Wilk’s Lambda

Significant

Terminate further analysis

N

YApply rANOVA for each dependent

variable

Use SPSS to generate following outputs

Mauchly's test of

sphericity

F table in rANOVA for each

dependent variable

Pair-wise comparisons of means for each

dependent variable.

Means plot for each dependent

variable

Steps in One-way rMANOVA

Steps in One Way RMD

Test Sphericity assumption in each rANOVA

Is p<α/

kTest F ratio by

assuming sphericity N

Y

Check

<.75 Test F by using Huynh-

Feldt correctionNTest F by using

Greenhouse-Geisser correction

Y

If F is significant use Bonferroni correction for comparison of means

Report findings

k: number of DVs

Table 7.1 Marks obtained by the students in different subjects tested at different times of the day _____________________________________________________________________________________ Time of the day Morning(7 AM) Afternoon(1 PM) Evening(7 PM)_____________________________________________________________________________________Maths English Reasoning Maths English Reasoning Maths EnglishReasoning

12 12 15 15 15 11 17 14 1213 14 16 17 13 12 16 12 1014 10 17 18 14 14 15 15 1513 9 15 15 14 13 16 16 1214 8 17 14 13 11 14 13 1415 11 15 18 12 10 16 15 1513 10 14 17 15 9 15 13 1012 13 15 15 12 8 13 12 1313 12 13 16 15 11 15 16 1215 11 14 18 16 12 16 15 13

_____________________________________________________________________________________

One-way rMANOVA Design

Objective : To see the effect of time of the day on the student’s performance in different subjects.

- An Illustration with SPSS

S1

S3

S2

S4

S5

S6

Evening

First phase testing

S1

S3

S2

S4

S5

S6

S1

S3

S2

S4

S5

S6

Second phase testing

Third phase testing

Testing protocol

Treatment: Time of the day

Maths English Reasoning

S2

S4

S5

S6

S1

S3

S2

S4

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S6

S1

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AfternoonMorning

Maths English Reasoning

Maths English Reasoning

Layout Design

All subjects are tested on all the three DVs but not in a particular sequence.  

S1 and S3 are tested on all DVs in the morning, S2 and S4 in the afternoon and

S5 and S6 in the evening. Similarly treatments(time) are randomized in other phases.

Procedure

Figure 7.3 Layout of the one-way rMANOVA design in the illustration

Research Questions

Whether time of testing affects student’s academic performance together in all the three subjects?”

Whether time of testing affects student’s performance in each of the subject; Maths, English and Reasoning?

Which time of the day improves performance of the students in each subject?

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