Non-parametric statistics are used when determining the statistical measure of some types of completed research for several reasons:

1. No assumptions about data distribution: Non-parametric statistics do not assume a specific distribution of the population from which the data is sampled. This makes them suitable for situations where the data violates the assumptions of parametric tests (which assume a specific distribution, like normal distribution). Non-parametric tests are particularly useful when the data is skewed, has outliers, or has an unknown distribution.

2. Ordinal or categorical data: Non-parametric statistics are appropriate for analyzing ordinal or categorical data, where the variables do not have a numerical scale or any meaningful order. Since parametric tests rely on numerical values and their magnitude, they would not be appropriate for such data.

Two examples where non-parametric statistics would be used are:

1. Mann-Whitney U test: This non-parametric test is used to determine if there is a significant difference between two independent groups for a variable that is measured on an ordinal or continuous scale. For instance, if researchers wanted to compare the median income of two different cities, they could use the Mann-Whitney U test if the income data does not follow a normal distribution.

2. Wilcoxon signed-rank test: This non-parametric test is used to assess whether there is a significant difference between two related groups for a variable measured on an ordinal or continuous scale. For example, if researchers want to determine if there is a significant difference in the pain levels of patients before and after a certain treatment, they would use the Wilcoxon signed-rank test if the pain data is not normally distributed.

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