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This presentation discusses the assumptions used in repeated measures design and the procedure of testing them using SPSS.

- 1. Presented by Dr.J.P.Verma MSc (Statistics), PhD, MA(Psychology), Masters(Computer Application) Professor(Statistics) Lakshmibai National Institute of Physical Education, Gwalior, India (Deemed University) Email: vermajprakash@gmail.com
- 2. 1. Assumptions on data type IV - 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 sets 4. Normality assumption 5. Sphericity assumptions 2
- 3. The type I error increases Power of the test decreases Internal and External validities are at stake 3
- 4. Some assumptions are design issues and Some can be tested by using SPSS or other software Lets Learn to use SPSS first 4
- 5. 5 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
- 6. 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 6
- 7. 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 steps a. Define all variables by clicking on “VariableView” b. Feed data by clicking on “DataView” 7
- 8. 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 Values iv. Define data type of each variable in Measure Step 1 Figure 3.2 Option for defining variables and coding 8
- 9. Step 2 Figure 3.3 Format for data feeding 9
- 10. By skewness and Kurtosis By Means of Kolmogorov-Smirnov test and Shapiro-Wilk test Normal Q-Q plot 10
- 11. Most of the statistical tests are based upon the concept of normality To test the normality Check the significance of Skewness Kurtosis 11
- 12. One of the characteristics of normal distribution 3 2 2 3 1 Symmetrical distribution How to measure skewness? Skewed curves Positively skewed curve Negatively skewed curve 01 01 - ∞ + ∞ - ∞ + ∞ 11 01 12
- 13. 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=58.3 Remark: Most of the scores are more than the mean value 01 01 13
- 14. 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 14
- 15. 2 2 4 2 One of the characteristics of the normal distribution How to measure the spread of scores? 322 02 02 02 15
- 16. Kurtosis is significant if its value is more than two times its standard error )(SE2 22 )5n)(3n( 1n )(SE2)(SE)Kurtosis(SE 2 12 16
- 17. Self image (in nos.) Height(in ft.) 24.00 5.40 30.00 5.50 22.00 5.50 42.00 5.60 38.00 5.60 21.00 5.60 24.00 5.70 30.00 5.70 22.00 5.70 24.00 5.70 23.00 5.80 23.00 5.80 28.00 5.80 24.00 5.90 21.00 5.90 45.00 6.00 24.00 5.80 23.00 5.50 28.00 5.60 30.00 5.60 22.00 5.70 28.00 5.70 24.00 5.70 45.00 5.80 42.00 5.90 Analyze Descriptive statistics Explore Figure 3.4 Initiating commands for testing normality and identifying outliers 17
- 18. Figure 3.5 Option for selecting variables and detecting outliers Check for identifying outliers through Box-Plot Click on for outlier options 18
- 19. 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 19
- 20. Table 3.3 Tests of normality _________________________________________________ Kolmogorov-Smirnov Shapiro-Wilk Statistics df Sig. Statistic df 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 ofTesting 20
- 21. 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 results Limitation 21
- 22. 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 22
- 23. 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 23
- 24. 24 To buy the book Repeated Measures Design for Empirical Researchers and all associated presentations Click Here Complete presentation is available on companion website of the book