9231 · 4.4
Non-parametric tests flashcards
Revision flashcards for Cambridge 9231 Non-parametric tests (syllabus 4.4). Flip, recall, then mark a real past-paper question.
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What is a non-parametric test?
A hypothesis test that does not assume the data is drawn from a population with a specific distribution (e.g., normal). It often uses ranks or signs instead of the original data values.
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When should you use a non-parametric test?
When the population distribution is unknown (or known to be not normal), the sample size is small, or the data is ordinal (can be ranked but not measured precisely).
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What does the Sign Test investigate?
It tests the null hypothesis that the population median is equal to a specified value. It only considers the sign (+ or -) of data points relative to this median.
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What is the test statistic for a Sign Test?
The number of positive or negative signs, whichever is smaller. Under $H_0$, this statistic follows a binomial distribution $B(n, 0.5)$, where $n$ is the sample size after discarding zeros.
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What does the Wilcoxon signed-rank test investigate?
It tests the null hypothesis about a single population's median. It's more powerful than the sign test as it considers both the sign and magnitude (via ranks) of the differences from the median.
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How do you handle zero differences in a Wilcoxon signed-rank test?
Data points equal to the hypothesised median result in a zero difference. These are discarded, and the sample size, $n$, is reduced accordingly.
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How do you handle tied ranks in Wilcoxon tests?
If two or more data points have the same absolute difference (signed-rank) or value (rank-sum), they are assigned the average of the ranks they would have occupied.
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What does the Wilcoxon rank-sum test investigate?
It tests whether two independent samples come from populations with the same median. It is the non-parametric alternative to the independent two-sample t-test.
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What is the test statistic for the Wilcoxon signed-rank test?
$W = \min(W_+, W_-)$, where $W_+$ is the sum of ranks of positive differences and $W_-$ is the sum of ranks of negative differences.
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What is the test statistic for the Wilcoxon rank-sum test?
The sum of the ranks for one of the samples, typically the one with the smaller sample size. This sum is then compared to a critical range from the tables.
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When is a continuity correction needed?
When using a continuous distribution (the normal distribution) to approximate a discrete distribution (the distribution of the Wilcoxon test statistics). You add or subtract 0.5 from the value before calculating the z-score.