testing assumptions in repeated measures design using spss
TRANSCRIPT
Testing Assumptions in Repeated Measures 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: [email protected]
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Assumptions in Repeated Measures Design
1. Assumptions on data typeIV - categorical with three or more
levels. DV - interval or ratio
2. Observations from different participants are independent to each other
3. No outliers in data sets4. Normality assumption5. Sphericity assumptions
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What happens if Assumptions are Not Satisfied?
The type I error increases Power of the test decreases Internal and External validities
are at stake
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How to Test These Assumptions
Some assumptions are design issues
and
Some can be tested by using SPSS or other software
Lets Learn to use SPSS first
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This Presentation is based on
Chapter 3 of the book
Repeated Measures Design for Empirical Researchers
Published by Wiley, USA
Complete Presentation can be accessed on
Companion Website
of the Book
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Learning SPSS – Initial Steps
Step 1: Activate SPSS by clicking on the following command sequence.
Start All Programs IBM SPSS Statistics
Figure 3.1 Option for creating/opening data file
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Advantage of Experimental Research
Step 2: Prepare data file Choose the option “Type in data” if data file is
prepared first time Choose the option “Open an existing data source” if
existing data file to be used
Step 3: Prepare data file in two stepsa. Define all variables by clicking on “Variable View”b. Feed data by clicking on “Data View”
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Defining Variables in Data File
i. Define short name of the variable under column Name Name should not start with number or any special character Only special character that can be used is underscore “_” If the name consists of two words it must be joined with
underscore ii. Define full name of the variable, the way you feel like under Label iii. If variable is nominal define coding under heading Valuesiv. Define data type of each variable in Measure
Step 1
Figure 3.2 Option for defining variables and coding
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Data Feeding Format in Data View Step
2
Figure 3.3 Format for data feeding
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Procedure of checking Normality
By skewness and Kurtosis By Means of Kolmogorov-Smirnov test and Shapiro-Wilk test Normal Q-Q plot
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Testing Normality with Skewness and Kurtosis
Most of the statistical tests are based upon the concept of normality
To test the normality
Check the significance of
Skewness
Kurtosis
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Skewness- Measure of symmetricityOne of the characteristics of normal distribution
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Symmetrical distribution
How to measure skewness?
Skewed curves
Positively skewed curve
Negatively skewed curve
01
01
- ∞ + ∞ - ∞ + ∞
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01
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Interpretation of Skewness
Positively skewed curve
- ∞ + ∞X: 3,2,3,2,4,6,3,5,5,4,6,4,3,8,90
Mean=14.6
Remark: Most of the scores are less than the mean value
Negatively skewed curve
- ∞ + ∞X: ,3,2,65,68,66,70,67,64,65,69,72,70
Mean=58.3Remark: Most of the scores are more than the
mean value
01
01
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How to test the significance of the skewness?
Skewness is significant if its value is more than two times its standard error
)3n)(1n)(2n()1n(n6)(SE)Skewness(SE 1
)(SE2 11
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Kurtosis –Measure of spread around mean
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One of the characteristics of the normal distribution
How to measure the spread of scores?
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02
02
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How to test the significance of kurtosis?
Kurtosis is significant if its value is more than two times its standard error
)(SE2 22
)5n)(3n(1n)(SE2)(SE)Kurtosis(SE
2
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Kolmogorov-Smirnov test and Shapiro-Wilk test
Self image (in nos.) Height(in ft.)
24.00 5.4030.00 5.5022.00 5.5042.00 5.6038.00 5.6021.00 5.6024.00 5.7030.00 5.7022.00 5.7024.00 5.7023.00 5.8023.00 5.8028.00 5.8024.00 5.9021.00 5.9045.00 6.0024.00 5.8023.00 5.5028.00 5.6030.00 5.6022.00 5.7028.00 5.7024.00 5.7045.00 5.8042.00 5.90
Analyze Descriptive statistics Explore
Figure 3.4 Initiating commands for testing normality and identifying outliers
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Option for finding Outlier through BoxPlot
Figure 3.5 Option for selecting variables and detecting outliers
Check for identifying outliers through Box-Plot
Click on for outlier options
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Option for Shapiro test and Q-Q Plot
Check this option for generating outputs of Shapiro test and Q-Q plots
Click on for normality test and QQ Plots option
Figure 3.6 Options for computing Shapiro-Wilk test and the Q-Q plot
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Shapiro-Wilk Test for Normality
Table 3.3 Tests of normality_________________________________________________ Kolmogorov-Smirnov Shapiro-Wilk
Statistics df Sig. Statisticdf Sig.
_________________________________________________Self image .269 25 .000 .785 25 .000
Height .140 25 .200 .963 25 .484 _________________________________________________
If Shapiro-Wilk statistic is not significant (p>.05) then normality exists.
Result: Height is normally distributed but the self image is not
Criteria of Testing
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Limitations of Kolmogorov-Smirnov test and Shapiro-Wilk test
Shapiro-Wilk Test is appropriate for small sample sizes (n< 50) but can be used for sample sizes as large as 2000
In large sample more likely to get significant resultsLimitation
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Normal Q-Q Plot for Normality
Normal Q_Q plot for self image
Normal Q_Q plot for height
Figure 3.7 Normal Q-Q Plot for the data on self image and height
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What is an Outlier?
A data which is unusual
How to detect ? Most of the behavioral variables are
normally distributed
And therefore
If a random sample is drawn then any score that lies outside 3σ or 2σ limits is an outlier
If population mean, µ is 40 and standard deviation,σ is 5 then
Any value outside the range 30 to 50 or outside the range 25 to 55 may be an outlier
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