1. Presented By: ang ling poh ong mei yean soo pei zhi
QIM 511
SPSS: Chi-Square Test
Presented By: ang ling poh ong mei yean soo pei zhi

2. Nonparametric Techniques
Is used when having serious violations of distribution assumptions or not normal
Appropriate for data measured on scales that are not interval or ratio.
Selection of nonparametric techniques are:
Chi-square tests
Mann-Whitney test
Wilcoxon signed-rank test
Kruskal-Wallis test
Friedman test
Spearman’s rank-order correlation

3. Chi-square Tests 2 Main types
3 assumptions to deal before conducting chi-square tests:
Random sampling
Independence of observations
Size of expected frequencies
Chi-square test for goodness of fit
For analysis of a single categorical variable
Chi-square test for independence or relatedness
For analysis of the relationship between 2 categorical variables

4. Chi-square test for Goodness of Fit
used to compare observed and expected frequencies in each category.
sample size is usually small

5. Chi-square test for Goodness of Fit
Steps to conduct chi-square test for goodness of fit:
Select the Data menu
Click on Weight Cases to open the dialogue box
Click on the Weight cases by radio button
Select the relevant variable and move to Frequency Variable
Then, select Analyze menu
Click on Nonparametric Tests and then Chi Square
Select the required variable to move into Test Variable List box

6. Goodness of fit chi square Output file will look like this:
You can see from the output that the chi-square value is no significant (p > .05).

7. Interpreting Chi square test for Goodness of Fit
Example
Color preference of 150 people, p < 0.05
Category Color
Observed Frequencies
Expected Frequencies
Yellow 35
20%
Red 50
30%
Green 30
10%
Blue 10
White 25

8. Color preference of 150 people
Chi-square requires that you use numerical values, not percentage or ratios.
Chi-square should not be calculated if the expected value in any category is less than 5.
Color preference of 150 people
Category Color
Observed Frequencies
Expected Frequencies
Yellow 35 30
Red 50 45
Green 15
Blue 10
White 25

9. Calculate chi-square 2 = Chi-square O = Observed frequency
E = Expected frequency
k = number of categories, groupings, or possible outcomes

10. Calculate chi-square Category Color O E (O-E) (O-E)2 2 = 26.95 Yellow35 30 5 25
0.83
Red 50 45
0.56
Green 15
225
Blue 10 -5
1.67
White
-20
400
8.89
2 = 26.95

11. Calculate Degrees of freedom (df)
Refers to the number of values that are free to vary after restriction has been placed on data.
Defined as N- 1, the number in the group minus one restriction.
df = N – 1
= 5 – 1
= 4

12. Critical 2 values 2 = 26.95 , df = 4 , p < 0.05
If chi-square value is bigger than critical value, reject null hypothesis.
If chi-square value is smaller than critical value, fail to reject null hypothesis.

13. Chi-square Test for Relatedness or Independence
Used to evaluate group differences when the test variable is nominal, dichotomous, ordinal, or grouped interval.
A test of the influence or impact that a subject’s value on one variable has on the same subject’s value for a second variable.

14. Chi-square Test for Relatedness or Independence
Steps to conduct chi-square test for goodness of fit:
Select the Analyze menu
Click on Descriptive Statistics and then Crosstabs
Select a row and column variable to move into the respective box
Click on Statistics command pushbutton to open Crosstabs: Statistics subdialogue box
Click on the Chi-square check box then Continue
Click on the Cells subdialogue box
In the Counts box, click on the Observed and Expected check boxes
In the Percentages box, click on the Row, Column andTotal check boxes
Click on Continue and then OK.

15. Interpreting Chi square test for Relatedness or Independence
Example
Incidence of three types of malaria in three tropical regions.
H0 : The two categorical variables are independent.
H1. : The two categorical variables are related.

16. Calculate expected frequency
c = frequency for that column
r = frequency for that row
n = total number of subjects in study

17. Calculate expected frequency
250
= 30.96

18. Calculate chi-square
2 =

19. Calculate Degrees of freedom (df)
df = (r-1)(c-1)
= (3-1)(3-1)
= (2)(2)
= 4
r = number of categories in the row variable
c = number of categories in the column variable

20. Find critical 2 values 2 = 125.516 , df = 4 , p < 0.05
Chi-square value is bigger than critical chi-square value, reject null hypothesis.

21. REFERENCES
Green, S. B., Salkind, N. J., & Akey, T. M. (2000). Using SPSS for Windows: Analyzing and understanding data (2nd ed.). New Jersey: Prentice Hall.
Coakes, S. J., Steed, L., & Ong, C. (2010). SPSS:analysis without anguish: version 17.0 for Windows (Version 17.0 ed.). McDougall Street, Milton, Qld: John Wiley & Sons Australia, Ltd.
Hinkle, Wiersma, & Jurs. Chi-square test for goodness of fit. Retrieved from
Penn State Lehigh Valley. Chi-square test. Retrieved 9 March, 2011, from
Maben, A. F. Chi-square test. Retrieved from
Bench, M. Interpreting the chi-square test. Retrieved 9 March, 2011, from