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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

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

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

Box 9.1, page 324

Problem 13

9.2

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

Box 9.2, page 331

Problem 15 (2 x 2)

Problem 22 (more than 2 groups)

9.2

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

- 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

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

Box 9.4, page 341

Problem 36

9.3

- 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 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

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

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