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Presented By : ang ling poh ong mei yean soo pei zhi

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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
- 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

- 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
- Then, select Analyze menu
- Click on Nonparametric Tests and then Chi Square
- 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).

- 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

Calculate chi-square percentage or ratios.

2 = Chi-square

O = Observed frequency

E = Expected frequency

k = number of categories, groupings, or possible outcomes

Calculate chi-square percentage or ratios.

2 = 26.95

Calculate Degrees of freedom ( percentage or ratios.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 percentage or ratios.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.

Critical 2

Chi-square Test for Relatedness or Independence percentage or ratios.

- 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 percentage or ratios.

- 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.

Interpreting Chi square test for Relatedness or Independence percentage or ratios.

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 percentage or ratios.

e = expected frequency

c = frequency for that column

r = frequency for that row

n = total number of subjects in study

Calculate chi-square percentage or ratios.

2 = 125.516

Calculate Degrees of freedom ( percentage or ratios.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 percentage or ratios.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 percentage or ratios.

- 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

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