|PART FIVE -- Essentials|--Nonparametric Statistics
Parameter: population characteristic
Nonparametric test: does not require any particular population characteristics
Advantage: no required population characteristics
Disadvantage: not as powerful as parametric tests (t-test, ANOVA)
Power: ability of a test to detect when Ho is false, and give the correct
conclusion (rejection of Ho)
Power of any test can be increased by increasing the sample size.
If two different tests are applied to the same data, the more powerful test will
produce a lower p-value.
Sign Test--for differences between population means, paired-difference design
Based on the binomial distribution
Ho: the population means are equal.
Ha: the population means are not equal (2-sided). 1-sided tests are also possible.
Wilcoxon Signed-Rank Test--test for differences between population means,
paired-difference design
Ho: the population means are equal.
Ha: the population means are not equal (2-sided).
1-sided tests are also possible.
Procedure--see “notes”
Mann-Whitney "U" Test--test for differences between population means, unpaired
design
Ho:the population means are equal.
Ha: the population means are not equal (2-sided).
1-sided tests are also possible.
Procedure--see ”notes”
Runs Test (not in textbook)--test for independence in a series of binomial events
Procedure--see ”notes”
Terminology--explain each of the following:
Sign Test--application, nonparametric, parametric, sign test, binomial distribution, paired-difference design, power, ranking, tied observations, tied rankings, Wilcoxon Signed-Rank Test--application, Mann-Whitney “U” Test--application, Runs Test--application, run, positive dependence, negative dependence, independence.
Skills and Procedures
- given appropriate data, conduct a Sign Test and interpret the results
- given appropriate data, conduct a Wilcoxon Signed-Rank Test and interpret the results
- given appropriate data, conduct a Mann-Whitney “U” Test and interpret the results
- given appropriate data, conduct a Runs Test and interpret the results
Concepts
- describe the advantage of nonparametric tests
- describe the disadvantage of nonparametric tests
- explain how the disadvantage of nonparametric tests may be overcome
- explain the theory of the sign test
- explain the concept of “power” and tell why nonparametric tests are generally less powerful than their parametric equivalents
- describe what is meant by “randomness” in a series of binomial events
- describe what is meant by “positive dependence” in a series of binomial events
- describe what is meant by “negative dependence” in a series of binomial events