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
𝑓0
𝑓𝑒

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