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Understand the idea of a non-parametric test and appreciate situations in which such a test might be useful (e.g., when sampling from a population which cannot be assumed to be normally distributed)
Understand the basis of the sign test, the Wilcoxon signed-rank test and the Wilcoxon rank-sum test (including knowledge that Wilcoxon tests are valid only for symmetrical distributions)
Use a single-sample sign test and a single-sample Wilcoxon signed-rank test to test a hypothesis concerning a population median (including the use of normal approximations where appropriate; questions will not involve tied ranks or observations equal to the population median value being tested)
Use a paired-sample sign test, a Wilcoxon matched-pairs signed-rank test and a Wilcoxon rank-sum test, as appropriate, to test for identity of populations (including the use of normal approximations where appropriate; questions will not involve tied ranks or zero-difference pairs)
Parametric tests are hypothesis tests carried out when the underlying distribution of the population is known. These tests involve parameters such as the population mean μ and assume an underlying normal distribution. Examples include z-tests and t-tests that we studied in Chapter 9.
Non-parametric tests are hypothesis tests carried out when the underlying distribution of the population is unknown. These tests are particularly useful when:
In non-parametric tests, the measure of centrality is usually the median rather than the mean, since the median does not depend on knowing the underlying distribution.
The following table summarizes the main non-parametric tests covered in this subtopic, along with their assumptions:
| Type of test | Test | Assumptions |
|---|---|---|
| Single sample | Sign test | The underlying data are continuous; The data are independent |
| Single sample | Wilcoxon signed-rank test | The underlying data are symmetric; The underlying data are continuous; The data are independent |
| Two sample | Paired sign test | The data are in matched pairs; The differences between matched pairs are continuous; The data are independent |
| Two sample | Wilcoxon matched-pairs signed-rank test | The data are in matched pairs; The differences between matched pairs are symmetric; The differences between matched pairs are continuous; The data are independent |
| Two sample | Wilcoxon rank-sum test | The two samples are independent; The underlying data are symmetric; The underlying data are continuous |
Important: Wilcoxon tests are valid only for symmetrical distributions.
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