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# HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D. - PowerPoint PPT Presentation

Fox/Levin/Forde, Elementary Statistics in Social Research, 12e. Chapter 9: Nonparametric Tests of Significance. HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D. 4/28/2014 , Spring 2014. CHAPTER OBJECTIVES. 9 .1. Understand the logic of nonparametric tests. 9 .2.

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HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D.

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Fox/Levin/Forde, Elementary Statistics in Social Research, 12e

• Chapter 9: Nonparametric Tests of Significance

## HLTH 300 Biostatistics for Public Health Practice,Raul Cruz-Cano, Ph.D.

4/28/2014, Spring 2014

CHAPTER OBJECTIVES

9.1

• Understand the logic of nonparametric tests

9.2

• Conduct one-way and two-way chi-square tests

9.3

• Perform the median test

9.4

• Perform the Mann-Whitney U and Kruskal-Wallis tests

• Learning Objectives

• After this lecture, you should be able to complete the following Learning Outcomes

• 9.1

9.1

### Nonparametric Tests

t tests and F ratios require:

• Normality (or especially large samples)

• Interval level data

What if these requirements cannot be met?

• We must use nonparametric tests

• Chi-square

• The median test

• Mann-Whitney U test

• Kruskal-Wallis test

Nonparametric tests are less powerful than parametric

• Power = the probability of rejecting the null hypothesis when it is actually false and should be rejected

• Learning Objectives

• After this lecture, you should be able to complete the following Learning Outcomes

• 9.2

9.2

### The One-Way Chi-Square Test

Observed frequency: the set of frequencies obtained in an actual frequency distribution

Expected frequency: the frequencies that are expected to occur under the terms of the null hypothesis

• In general, this is found by dividing N by the number of categories

Chi-square allows us to test the significance of differences between observed and expected frequencies

### Examples

Box 9.1, page 324

Problem 13

9.2

### The Two-Way Chi-Square Test

How can we compare observed and expected frequencies for more than one variable?

• Two-way chi-square test

• This involves cross-tabulations

The methods for calculating one-way and two-way chi-squares are very similar

• In fact, the same formula is used

• The only major difference is in how we calculate expected frequencies

For each cell:

df=(# of rows -1 )(# of columns -1)

• 9.2

Table 9.2

### Examples

Box 9.2, page 331

Problem 15 (2 x 2)

Problem 22 (more than 2 groups)

9.2

### Correcting for Small Expected Frequencies

One of the few demands on the chi-square test is that the sample size should not be too small

• Be wary of expected frequencies that are less than 5

• In this case, it might be best to collapse categories

• When expected frequencies are greater than 5 but less than 10, use Yate’s correction

• Reduces the size of the chi-square value

• Only used for 2 X 2 tables, hence df= 1

Page 329

9.2

### Requirements for the Use of Two-Way Chi-Square

• A Comparison between Two or More Samples

• Nominal Data

• Random Sampling

• The Expected Cell Frequencies Should Not Be Too Small

• Learning Objectives

• After this lecture, you should be able to complete the following Learning Outcomes

• 9.3

9.3

### The Median Test

Used when dealing with ordinal data

• Determines the likelihood that two or more random samples have been taken from populations with the same median

First, determine the median of the two groups combined

Then, create a cross-tabulation with the two categories and the scores that fall above the median and the scores that do not fall above the median

Finally, conduct a chi-square test

• Using Yate’s corrections if there are any expected frequencies that are less than 10

### Example

Box 9.4, page 341

Problem 36

9.3

### Requirements for the Use of the Median Test

• A Comparison between Two or More Medians

• Ordinal Data

• Random Sampling

• Learning Objectives

• After this lecture, you should be able to complete the following Learning Outcomes

• 9.4

9.4

### The Mann-Whitney U Test

The median test ignores the specific rank-order of cases

This test examines the rank-ordering of all cases

• It determines whether the rank values for a variable are equally distributed throughout two samples

The smaller of the two U values is used for testing the differences between groups

• This value is compared against the critical U value found in Table G in Appendix C

We won’t study but be aware of its existence when comparing your work vs. answers in the back of the book

9.4

### The Kruskal-Wallis Test

Can be used to compare several independent samples

• Requires only ordinal-level data

The H statistic is compared to the critical values of chi-square found in Table F in Appendix C

We won’t study but be aware of its existence when comparing your work vs. answers in the back of the book

### Homework

Problem 14, 19, 28, 35

CHAPTER SUMMARY

• Nonparametric tests of significance can be used to analyze data that are not normally distributed or are not measured at the interval level

9.1

• One-way and two-way chi-square statistics can be calculated for variables measured at the nominal level

9.2

• The median test can be used to examine data measured at the ordinal level

9.3

• The Mann-Whitney U and Kruskal Wallis tests are more powerful than the median test and can also be used to examine ordinal data

9.4