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

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

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

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

- Chapter 9: Nonparametric Tests of Significance

4/28/2014, Spring 2014

CHAPTER 12eOBJECTIVES

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 12e
- After this lecture, you should be able to complete the following Learning Outcomes

- 9.1

9 12e.1

Nonparametric Testst 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 12e
- After this lecture, you should be able to complete the following Learning Outcomes

- 9.2

9.2 12e

The One-Way Chi-Square TestObserved 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

9.2 12e

The Two-Way Chi-Square TestHow 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 12e

Table 9.2

9.2 12e

Correcting for Small Expected FrequenciesOne 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

Example 12e

Page 329

9 12e.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 12e
- After this lecture, you should be able to complete the following Learning Outcomes

- 9.3

9.3 12e

The Median TestUsed 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

9 12e.3

Requirements for the Use of the Median Test- A Comparison between Two or More Medians

- Ordinal Data

- Random Sampling

- Learning Objectives 12e
- After this lecture, you should be able to complete the following Learning Outcomes

- 9.4

9.4 12e

The Mann-Whitney U TestThe 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 12e

The Kruskal-Wallis TestCan 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 12e

Problem 14, 19, 28, 35

CHAPTER SUMMARY 12e

- 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

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