Nonparametric methods are often referred to as distribution-free methods.
Nonparametric statistical methods are not applicable to ordinal data.
The sign test can be used to test whether individuals prefer one item over another.
A municipal transit system has collected data on which of two seating configurations is preferred by the passengers on its buses. In a sign test to determine whether one seating arrangement is significantly preferred. The null hypothesis would be
With the sign test, if the null hypothesis is true, the number of successes follows the
With the sign test, if the null hypothesis is true and the sample size is large, the number of successes may be approximated by the
With the Wilcoxon signed-rank test, we must assume the populations sampled from are normally distributed.
The Wilcoxon signed-rank test uses paired differences to test whether two populations are identical.
With the Wilcoxon signed-rank test, the expected value of the sum of signed ranks is equal to the sample size.
In a Wilcoxon signed-rank test, the two samples each have n=17. The expected value of T is
With the Mann-Whitney-Wilcoxon test, we need to know only the two sample sizes to compute the standard deviation of the rank sum.
With the Mann-Whitney-Wilcoxon test, we need to know only the two sample sizes to compute the expected value of the rank sum.
. For a Mann-Whitney-Wilcoxon test, the first and second samples have sizes 15 and 24, respectively. The expected value of T is
The Kruskal-Wallis test cannot be used unless the populations sampled from are approximately normal.
The Spearman rank-correlation coefficient can be computed only if quantitative data are available for the variables.