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Nonparametric statistics is a branch of statistics that focuses on statistical methods that do not rely on a specified probability distribution of the data. Unlike parametric statistics, which assumes a known distribution of the data and investigates the properties of the distribution, nonparametric statistics avoids making assumptions about the distribution and focuses on the properties of the data itself.

Nonparametric statistics are often used when the data does not fit a known distribution, or when the sample size is too small to justify the use of parametric methods. Nonparametric tests are also useful when the data does not meet the assumptions of parametric tests, such as normality or equal variances.

Some common nonparametric statistical tests include the Wilcoxon signed-rank test, the Kruskal-Wallis H-test, and the Spearman rank-correlation coefficient. These tests are designed to be robust and flexible, making them well-suited for a wide range of data types and distributions.

Nonparametric statistics can be further categorized into two subfields: exploratory data analysis and inference. Exploratory data analysis involves using nonparametric methods to summarize and visualize the data, while inference involves using nonparametric tests to make conclusions about the population based on a sample of data.

Nonparametric statistics has a wide range of applications in various fields, including medicine, social sciences, and engineering. It provides an alternative to parametric statistics and can be a useful tool for data analysis when the data does not fit into a specific distribution.

Overall, nonparametric statistics offers a flexible and robust approach to statistical analysis, and is an important tool in the data analyst's toolkit.