Which test is non-parametric for a single sample?

Which test is non-parametric for a single sample?

• A. Wilcoxon
• B. Mann-Whitney U
• C. Kruskal-Wallis
• D. Friedman

Answer: (A)

Non-parametric tests rely on the ranks of data rather than assuming a normal distribution. For a single sample, the Wilcoxon signed-rank test is used to determine whether the population median equals a specified value. It works by calculating the difference between each observation and the hypothesized value, ignoring zero differences, ranking the absolute differences, and then applying the signs to those ranks; the test statistic is based on the sum of signed ranks. If the observed sum is unlikely under the null hypothesis that the median matches the specified value, you conclude a difference in central tendency. This test is the non-parametric counterpart to the one-sample t-test and is appropriate when data are skewed or sample sizes are small. The other listed tests serve different designs: Mann-Whitney U compares two independent samples, Kruskal-Wallis compares more than two independent samples, and Friedman handles more than two related samples (repeated measures).

Non-parametric tests rely on the ranks of data rather than assuming a normal distribution. For a single sample, the Wilcoxon signed-rank test is used to determine whether the population median equals a specified value. It works by calculating the difference between each observation and the hypothesized value, ignoring zero differences, ranking the absolute differences, and then applying the signs to those ranks; the test statistic is based on the sum of signed ranks. If the observed sum is unlikely under the null hypothesis that the median matches the specified value, you conclude a difference in central tendency. This test is the non-parametric counterpart to the one-sample t-test and is appropriate when data are skewed or sample sizes are small. The other listed tests serve different designs: Mann-Whitney U compares two independent samples, Kruskal-Wallis compares more than two independent samples, and Friedman handles more than two related samples (repeated measures).