CHI SQUARE- A NON PARAMETRIC TECHNIQUE

CHI SQUARE- A NON PARAMETRIC TECHNIQUE

1. DEPARTMENT OF PHYSICAL EDUCATION & SPORTS SCIENCES UNIVERSITY OF DELHI TOPIC: CHI SQUARE (A NON- PARAMETRIC TECHNIQUE) Presented by : Punam Pradhan PhD Scholar Roll no.: 1480

2. An Overview Non-parametric test Criteria for Test selection Introduction to Chi-square Assumptions of Chi-Square Test Application of Chi-square Test Goodness of fit with SPSS Computation of Goodness of Fit Interpretation of findings

3. NON-PARAMETRIC TEST Used when the distribution of the data is not normal , population parameters are unknown & data are qualitative in nature and, Data being measured on nominal or ordinal scales .

4. Criteria for Test selection

5. Chi-square is a statistical test used to test the significance of the difference between the distribution of observed and theoretical frequencies.

6. The chi-square is denoted by the Greek letter x² . Used when the data is nominal (categorical). Chi-square statistic is computed based on frequencies. Chi-square(x²) is computed by the following formula: where, : observed frequency : expected frequency    

7. Assumptions of Chi-Square Test Samples should be randomly drawn from the population. All the observations should be independent of each other. The data should be in terms of frequency. Observed frequencies should not be too small and the sample size, n, must be sufficiently large .

8. Application of Chi-square Test Testing the equal occurrence hypothesis. Testing the significance of association between two attributes. Testing the goodness of fit

9. Goodness of fit with SPSS Consider a study in which response of 110 students were taken to compare the popularity of three different brands of tracksuits among them. Solution: Here, the hypotheses that are required to be tested are as follows: Ho : All three brands are equally popular. H1 : All three brands are not equally popular. Summary of Student’s Response About Their Preferences Brand A Brand B Brand C 50 20 40

10. Computation of Goodness of Fit Click on Variable View to define variables and their properties. Under the column heading ‘Name’ write name of the variable .i.e. Brand. Under the column heading ‘Label’ define full name of variable, .i.e. Brand of Track Suit Under the column heading ‘Values’ define ‘1’ for Brand A, ‘2’ for Brand B, and ‘3’ for Brand C. Under the column heading ‘ Measure’ select the ‘Nominal’ option because Brand is a nominal variable. Define another variable Frequency in the next row as scale variable .

11. Click on Data command, click on Weight Cases option Select the option weight cases by Select variable .i.e. Frequency from the left panel and bring it into “Frequency Variable” section in the right panel. Click on OK and go back to the data file. Frequency

12. Analyze → Nonparametric Tests → Chi‐Square ( you will be taken to next screen) → select Brand variable from left panel and bring it to the ‘ Test variable list ’ section in the right panel → click on option → click ‘Descriptive’ option → click continue → click OK to get the output. Brand of tracksuit

13. * The minimum expected cell frequency is 36.7

14. Interpretation of findings The value of χ2 is 12.727 which is significant at 5% level, as the p value is 0.002 which is less than 0.05. Thus, we may reject the null hypothesis. It can be interpreted that all the three responses are not equally distributed and the fit is not good.

15. References Statistics for Psychology Book, by J.P. Verma Research Methodology (Methods and Techniques) Book, by C.R. Kothari