One-way Repeated Measures Design Presented by Dr.J.P.Verma MSc (Statistics), PhD, MA(Psychology), Masters(Computer Application) Professor(Statistics) Director, Centre for Advanced Studies Lakshmibai National Institute of Physical Education, Gwalior, India (Deemed University) Email: [email protected]This Presentation is based on the book titled Repeated Measures Designs for Empirical Researchers by Wiley USA For Details Kindly click here
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es Effect of one factor on some dependent variable is investigated
Example Effect of Time(morning, evening and evening) on the
memory retention
One-way Repeated Measures Design
Also known as within-group design or within-subjects design
Subjects are repeatedly tested in all the treatment conditions Subject receives treatment in a random fashion
Levels of the factor can be different treatments or different time durations
Advantages of One-Way Repeated Measures Design
Pattern of behaviour due to intervention over the period of time can be detected.
Useful where getting more subjects is an issue Experimental error reduces as subjects serve their own control
Efficient than independently measured designs if subjects variability is significant. Design is sensitive in nature hence slight variation in dependent variable due to manipulation of independent variable can be detected.
Due to carryover effect performance of the subjects may be affected in different treatment conditions.
Weaknesses of Repeated Measures Design
Since same subjects are tested in all treatment conditions hence large number of levels of a factor cannot be investigated.
The design will be inefficient if the subject’s variability is not significant
In a clinical experiment the drug efficacy can be tested by taking hourly blood samples for 12 hours after its administration.
Application of Design
To compare recovery pattern of soccer players under light exercise, autogenic relaxation and underwater exercise A physiologist may study an intervention of pranayama in the relief of asthma
Pizza company may investigate the taste of different types of pizza on youngsters.
When to use One-way RMD
To compare the taste of different pizza in a specific age category of the subjects. Six subjects participate in the study.
Example
Case I: Levels of within-subjects factor are different treatment conditions
Used in Two Types of Situations
Layout Design
Issues in the Design
Carryover effect
controlled b
y
Keeping sufficient gap
between treatments
Order effect
controlled b
y
Counterbalancing
1. Divide sample into groups2. Randomized
treatments on these groups.
Designing procedure
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Factor 1: Pizza
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Testing protocol
First phase testing
Second phase testing
Third phase testing
ChickenPan Cheese
Subjects
Figure 4.1 Layout design
When to use One-way RMD
To investigate the effect of time on efficacy of drug in 2 hours, 4 hours and 6 hours during an experiment. Five subjects participate in the study.
Example
Case II: Levels of within-subjects factor are different time durations
Used in Two Types of Situations
2 hours
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4 hours 6 hours
Subjects
Before
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Factor 1: Time
Testing protocol
Figure 4.2 Layout design
Steps in One Way RMDTest normality assumption
Describe layout design
Write research questions
Write H0 to be tested
Decide familywise error rates (α)
Use SPSS to generate outputs
Descriptive statistics
Mauchly's test of sphericity
F table for within-subjects effect
Pair-wise comparison of means
Means plot
Steps in One Way RMD
Test Sphericity assumption
Is p<.0
5Test 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
Solving One-way RMD with SPSS
To investigate the effect of time(two, four and six weeks) on the reasoning ability during an intervention of meditation programme on 10 sample.
Objective
Table 4.1 Data on reasoning ability ___________________________________Zero day2nd Week4th Week 6th Week___________________________________
a. Data type The IV must be categorical having three or more levels
and DV should be on interval or ratio scale
IV : Time(Zero, Two, Four and Six Week)DV : Reasoning ability measured on interval scale
First assumption is satisfied
Testing Assumptions
Sample has been randomly selected Observations have been independently obtained
Second assumption is also fulfilled
b. Independence of Observations The subjects are randomly selected and are independent
to each other
Testing Assumptions c. Normality Assumption For each level of the independent variable the dependent variable must follow approximately normal distribution and should not have outlier.
Table 4.2 Tests of normality for the data on reasoning ability__________________________________________________________________ Kolmogorov-Smirnov Shapiro-Wilk
Statistics df Sig. Statistic df Sig.(p value) (p value)
Epsilona( )Within Subjects Mauchly's W Approx. Chi- df Sig. Greenhouse- Huynh- Lower- Effect Square Geisser Feldt bound_________________________________________________________________________________ Time .062 21.441 5 .001 .546.650 .333
_________________________________________________________________________________Assumption of Sphericity is violated because chi-square is significant
Output of Repeated Measures in SPSS
Table 4.5 F-Table for testing significance of Within-Subjects Effects Measure: Reasoning_ability_________________________________________________________________________________________
Source Type III df Mean Square F Sig. Partial SS Eta Squared
df for Error = ε × 8 = 0.535 × 8 = 4.28Due to correction in degrees of freedom p values
increases.
)1n)(1r(SS
)1r(SS
FError
Time
)1n)(1r(SS
)1r(SS
FError
Time
)1n)(1r(SS
)1r(SS
Error
Time
a. If sphericity is assumed
b. If sphericity exists the modified degrees of freedom for SStime and SSError gets modified by multiplying them by F remains same irrespective of the fact whether sphericity exists or not.
Testing Significance of Within-Subjects Effect
After Greenhouse-Geisser correction the F is significant p=.009(<.05)
Partial Eta Square is .447, indicates very high effect size
The effect of time is meaningful to enhance reasoning ability with meditation intervention.
Conclusion
What Next ?Apply t test with Bonferroni correction for
pair-wise comparison of marginal means
Eta square Value .02 .13 .26Status Small Medium
Large
Pair-wise Comparison of Marginal Means
Table 4.6 Pair wise Comparison of marginal means Measure: Reasoning_ability_____________________________________________________________________________
Mean Diff. 95% CI for Differencea
(I) Time (J) Time (I-J) Std. Error Siga Lower BoundUpper Bound_____________________________________________________________________________Zero_day Week_two .100 .875 1.000 -1.879 2.079
_____________________________________________________________________________Based on estimated marginal meansa. Adjustment for multiple comparisons: Bonferroni*. The mean difference is significant at the .05 level.
Marginal means plot
P>.05
P=.00
1
Zero_day Week_two Week_four Week_six
Time
P>.05
P=.000
Estim
ated
mar
gina
l mea
ns o
f rea
soni
ng a
bilit
y
Variable: Reasoning ability
Marginal means plot
Meditation intervention program significantly affects the reasoning ability of the subjects.
The significant effect was observed only after the six weeks of the intervention program.
Inference
Figure 4.10 Marginal means plot
Thank You
This Presentation was based on the book titled Repeated Measures Designs for Empirical Researchers by Wiley USA