Using repeated measures anova with spss

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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

Transcript of Using repeated measures anova with spss

Page 1: Using repeated measures anova with spss

One-way Repeated Measures Design

Presented by

Dr.J.P.VermaMSc (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

Page 2: Using repeated measures anova with spss

An extension of paired t testFeatur

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

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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.

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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

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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.

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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

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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

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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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Subjects

Before

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Factor 1: Time

Testing protocol

Figure 4.2 Layout design

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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

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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

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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___________________________________

31 36 35 3731 34 34 3532 31 37 3530 32 36 3534 33 37 3735 34 36 3836 31 31 3836 35 30 4032 31 35 3633 32 34 36

___________________________________

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Testing Assumptions

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

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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

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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)

_____________________ _____________________________________________ Zero day .178 10 .200* .924 10 .3932nd Week .192 10 .200* .905 10 .2464th Week .216 10 .200* .879 10 .1286th Week .166 10 .200* .902 10 .228__________________________________________________________________

Since no p-value is significant for S-W statistic hence data is normal

Normality assumption is satisfied

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Testing Assumptions Sphericity Assumption The sphericity should not exist among the data

Variances of the differences between all combinations of related groups must be equal.

or

All correlations among the repeated measures are equal.

Meaning of Sphericity Assumption

This assumption shall be tested while using

the outputs of SPSS later

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Solving RMD with SPSS

Data on reasoning ability_________________________Zero Two Four Sixweek week week week

_________________________31 36 35 3731 34 34 3532 31 37 3530 32 36 3534 33 37 3735 34 36 3836 31 31 3836 35 30 4032 31 35 3633 32 34 36________________________

Layout of Design

Hypothesis to be Tested

Factor 1: Time

Testing protocol

Subjects

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Week6Week4Week2day_Zero0 ththnd:H

H1: At least one group mean differs

Figure 4.3 Layout of the design for the study

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Distribution of SS in Repeated Measures Design

Data on reasoning ability_________________________Zero Two Four Sixweek week week week

_________________________31 36 35 3731 34 34 3532 31 37 3530 32 36 3534 33 37 3735 34 36 3836 31 31 3836 35 30 4032 31 35 3633 32 34 36________________________

SSTime df=r-1

Total SS df = N-1

SSWithin df= nr-r

39

3 36

SSError df= (n-1)(r-1)SSSubjects df= n-1 9 27

Figure 4.4 Scheme of distributing total SS and df

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Level of SignificanceThe level of significance = .05

No Post hoc test in RMD hence

t test used for group comparisonsIt inflates

αTo control error rate

Bonferroni correction is usedWhat correction it does? t is tested at new α (=α/k)k: no of group comparisons

This correction is automatically taken care of by increased

P-value if Bonferroni correction is used in SPSS.

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Steps in SPSS Screenshot 1

Analyze General Linear Model Repeated Measures

Figure 4.5 Screen for initiating commands for one-way rANOVA

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Steps in SPSS Screenshot 2

Figure 4.6 Options for defining dependent and independent variables

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Steps in SPSS Screenshot 3

Write repeated factor ‘Time’Write levels of the repeated factor ‘4’ and click on AddWrite name of the dependent variable

Click on Add to define this variables

Figure 4.7 Options for adding independent and dependent variables

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Figure 4.8 Option for selecting within subjects variables (Time) and obtaining means plot

Steps in SPSS Screenshot 4

Bring these variables from left panel to this location

Click on Plots for means plotBring ‘Time’ factor at this location

Click on Continue

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Steps in SPSS Screenshot 5

Figure 4.9 Option for descriptive statistics and pair wise Comparison of means using Bonferroni correction

Click on Options

Bring ‘Time’ factor at this location

Check these options

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SPSS outputs and Interpretation

Descriptive Statistics Mauchly's Test of Sphericity F Table for testing within-subjects

effects Table for pair-wise comparison of

means Marginal means plot

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Output of Repeated Measures in SPSS

Output 1: Descriptive Statistics

Table 4.3 Descriptive statistics_____________________________________

Mean SD N_____________________________________Zero_day 33.0000 2.16025 10Week_two 32.9000 1.79196 10Week_four 34.5000 2.36878 10Week_six 36.7000 1.63639 10_____________________________________ 

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Output of Repeated Measures in SPSS

Output 2: Mauchly's Test

Measure: Reasoning_ability Table 4.4 Mauchly's test of Sphericitya

_________________________________________________________________________________

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

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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

_________________________________________________________________________________________Time Sphericity Assumed 94.475 3 31.4927.281 .001 .447

Greenhouse-Geisser 94.475 1.637 57.7257.281.009 .447Huynh-Feldt 94.475 1.951 48.423 7.281 .005 .447Lower-bound 94.475 1.000 94.475 7.281 .024 .447

 Error(Time)Sphericity Assumed 116.775 27 4.325

Greenhouse-Geisser 116.775 14.730 7.928Huynh-Feldt 116.775 17.559 6.650Lower-bound 116.775 9.000 12.975

__________________________________________________________________________________________

Output 3: rANOVA Table for testing within-subjects effects

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Why F Remains Same After Applying Correction

Greenhouse Geisser: df for Treatment = ε × 2= 0.517 × 2= 1.03 df for Error = ε × 8 = 0.517 × 8 = = 4.14Huynh- Feldt: df for Treatment = ε ×2 = 0.535 × 2 = 1.07

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.

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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

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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

Week_four -1.500 1.267 1.000 -4.366 1.366Week_six -3.700* .367 .000 -4.529 -2.871

Week_twoZero_day -.100 .875 1.000 -2.079 1.879Week_four -1.600 1.013 .893 -3.892 .692Week_six -3.800* .573 .001 -5.097 -2.503

Week_four Zero_day 1.500 1.267 1.000 -1.366 4.366

Week_two 1.600 1.013 .893 -.692 3.892Week_six -2.200 1.153 .532 -4.808 .408

Week_six Zero_day 3.700* .367 .000 2.871 4.529Week_two 3.800* .573 .001 2.503 5.097Week_four 2.200 1.153 .532 -.408 4.808

_____________________________________________________________________________Based on estimated marginal meansa. Adjustment for multiple comparisons: Bonferroni*. The mean difference is significant at the .05 level.

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Marginal means plot

P>.05

P=.00

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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

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Thank You

This Presentation was based on the book titled Repeated Measures Designs for Empirical Researchers by Wiley USA

For Details Kindly click here