Presented By:

ANG LING POHONG MEI YEANSOO PEI ZHI

QIM 511SPSS: Chi-Square Test

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 testsMann-Whitney test Wilcoxon signed-rank testKruskal-Wallis testFriedman testSpearman’s rank-order correlation

Chi-square Tests

2 Main types

3 assumptions to deal before conducting chi-square tests:1) Random sampling2) Independence of observations3) 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

Chi-square test for Goodness of Fit

used to compare observed and expected frequencies in each category.

sample size is usually small

Chi-square test for Goodness of Fit Steps to conduct chi-square test for goodness

of fit:1) Select the Data menu2) Click on Weight Cases to open the dialogue box3) Click on the Weight cases by radio button4) Select the relevant variable and move to

Frequency Variable5) Then, select Analyze menu6) Click on Nonparametric Tests and then Chi

Square 7) Select the required variable to move into Test

Variable List box

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).

Interpreting Chi square test for Goodness of Fit

ExampleColor preference of 150 people, p < 0.05Category

ColorObserved

FrequenciesExpected

FrequenciesYellow 35 20%

Red 50 30%

Green 30 10%

Blue 10 10%

White 25 30%

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.

Category Color

Observed Frequencies

Expected Frequencies

Yellow 35 30

Red 50 45

Green 30 15

Blue 10 15

White 25 45

Color preference of 150 people

Calculate chi-square

2 = Chi-square

O = Observed frequency

E = Expected frequency

k = number of categories, groupings, or possible outcomes

Category Color

O E (O-E) (O-E)2 (O-E)2

EYellow 35 30 5 25 0.83

Red 50 45 5 25 0.56

Green 30 15 15 225 15

Blue 10 15 -5 25 1.67

White 25 45 -20 400 8.89

Calculate chi-square

2 = 26.95

Calculate Degrees of freedom (df)

df = N – 1

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.

= 5 – 1= 4

Critical 2 values2 = 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.

Critical 2

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.

Steps to conduct chi-square test for goodness of fit:1. Select the Analyze menu2. Click on Descriptive Statistics and then Crosstabs3. Select a row and column variable to move into the

respective box4. Click on Statistics command pushbutton to open

Crosstabs: Statistics subdialogue box5. Click on the Chi-square check box then Continue6. Click on the Cells subdialogue box7. In the Counts box, click on the Observed and

Expected check boxes8. In the Percentages box, click on the Row, Column

andTotal check boxes9. Click on Continue and then OK.

Chi-square Test for Relatedness or Independence

Interpreting Chi square test for Relatedness or IndependenceExample

H0 : The two categorical variables are independent.H1. : The two categorical variables are related.

Incidence of three types of malaria in three tropical regions.

Calculate expected frequency

e = expected frequency

c = frequency for that column

r = frequency for that row

n = total number of subjects in study

Calculate expected frequency

e =90 x 86250

= 30.96

Calculate chi-square

2 = 125.516

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

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.

Critical 2

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 http://www.phy.ilstu.edu/slh/chi-square.pdf

Penn State Lehigh Valley. Chi-square test. Retrieved 9 March, 2011, from http://www2.lv.psu.edu/jxm57/irp/chisquar.html

Maben, A. F. Chi-square test. Retrieved from http://www.enviroliteracy.org/pdf/materials/1210.pdf

Bench, M. Interpreting the chi-square test. Retrieved 9 March, 2011, from http://www.mathbench.umd.edu/mod106_chisquare/page10.htm