Nonparametric Tests

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Nonparametric Tests

• HED 489 Biostatistics

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• 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.

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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.
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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.

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Use this example
Use the formula in chi2.xls to calculate if there
is a significant difference.
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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.

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Contingency Tables and Odds Ratios

• From contingency tables, one could also calculate
  odds ratios.
• OR(A/C)/(B/D)
• OR(AD)/(BC)

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• Like with the 2 x 2 table chi-square, lets work
  through this via Excel. Click here to go to that
  spreadsheet.

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• OK, thats it for chi-square. Again, this is
  used for frequency (nominal or ordinal) data.

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Assignment 15a

• Determine the relationship of the following
  information
• Download template

15b next slide
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Assignment 15b