This document discusses the chi-square test, a non-parametric technique used to determine if there is a significant difference between the expected and observed frequencies in one or more categories. It provides an overview of chi-square, its assumptions, applications including goodness of fit, and an example using SPSS to analyze student preferences of three brands of tracksuits. The chi-square value calculated for this example was 12.727 which is significant, allowing the researcher to conclude that student preferences were not equally distributed among the three brands.

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