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QIM 511 SPSS: Chi-Square Test Presented By: ANG LING POH ONG MEI YEAN SOO PEI ZHI 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 Chi-square Tests 2 Main types 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 3 assumptions to deal before conducting chi-square tests: 1) 2) 3) Random sampling Independence of observations Size of expected frequencies 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: 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 5) Then, select Analyze menu 6) Click on Nonparametric Tests and then Chi Square 7) Select the required variable to move into Test Variable List box 1) 2) 3) 4) 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 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 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. Color preference of 150 people Category Color Observed Frequencies Expected Frequencies Yellow 35 30 Red 50 45 Green 30 15 Blue 10 15 White 25 45 Calculate chi-square 2 = Chi-square O = Observed frequency E = Expected frequency k = number of categories, groupings, or possible outcomes Calculate chi-square Category Color O E (O-E) (O-E)2 (O-E)2 E Yellow 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 2 = 26.95 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 Critical 2 values 2 = 26.95 , df = 4 , p < 0.05 Critical 2 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. 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. Chi-square Test for Relatedness or Independence Steps to conduct chi-square test for goodness of fit: 1. 2. 3. 4. 5. 6. 7. 8. 9. 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. 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. 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 86 250 = 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 Critical 2 Chi-square value is bigger than critical chi-square value, reject null hypothesis. 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