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Nonparametric Tests

- HED 489 Biostatistics

- You will remember that two of the major

requirements to use parametric statistical tests

are interval or ratio data and a normal

distribution. However, there are many instances

when you will want to analyze nominal or ordinal

data, or when you are concerned about the shape

of the distribution of your data. Under those

circumstances, nonparametric statistics will save

your life! - In addition to not requiring interval data,

nonparametric statistics do not assume any

particular distribution. They are often referred

to as "distribution-free" tests. As a group,

nonparametric tests are also considered to be

more conservative (less power and higher type II

error) than their parametric equivalents. Because

it's harder to achieve statistical significance

using nonparametric tests, you can be more

confident of the results if your data are

significant. In other words, all other things

being equal, your risk of a Type I error is less

with nonparametric than parametric tests.

Non-parametric Statistics

Difference Tests

Relationship Tests

Causal Tests

Brown Mood

chi-square

chi-square

Spearman Rank- Order Correlation

Mann-Whitney U

Wilcoxon Sign test

Kendalls tau

Kruskall-Wallis Analysis of Variance

As you can see, there are nonparametric

equivalents to parametric tests of difference,

relationship, and cause-effect. Some of these

tests require at least ordinal data, while others

can be used with interval data. I'll give you a

grid at the end of our discussion of

nonparametric tests that you can use. We're

going to cover chi-square, which is a test you

can use to test differences or relationships

Mann-Whitney U, a t-test equivalent Friedman's

ANOVA and two nonparametric correlation

testsSpearman and Kendall.

Follow the Formula

- Click here to follow the formula in Excel. Note

that this is saved as a read-only file. The

reason being is that the formulas are set up so

that you can punch in your own data and it should

(theoretically) calculate your results. - Note that you will be cued to go to the next

Step. - Also, you may see cells with the symbol

in it. This means that the number is too large

to show in the cell. Merely go to the top of the

column of the cell and drag the right line of the

cell so that it is wider.

Use this example

Use the formula in chi2.xls to calculate if there

is a significant difference.

Complex Chi-Square and Contingency Tables

- When there are more than 2 groups on either

variables, the complex chi-square can be used to

test the hypothesis of no relationship between

the variables. If the chi-square test shows that

there is almost likely a relationship between the

variables, then the contingency coefficient can

be computed to give an indication of the degree

of the relationship. Note, if chi-square reveals

no significance, theres no need to run the

contingency coefficient.

Contingency Tables and Odds Ratios

- From contingency tables, one could also calculate

odds ratios. - OR(A/C)/(B/D)
- OR(AD)/(BC)

- Like with the 2 x 2 table chi-square, lets work

through this via Excel. Click here to go to that

spreadsheet.

- OK, thats it for chi-square. Again, this is

used for frequency (nominal or ordinal) data.

Assignment 15a

- Determine the relationship of the following

information - Download template

15b next slide

Assignment 15b

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