Describe the assumptions, advantages and disadvantages of non-parametric statistics

Non-parametric statistics are a type of statistical analysis that does not assume a specific probability distribution for the population from which the sample is drawn.

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These methods are often used when the data does not meet the assumptions required for parametric tests or when dealing with ordinal or nominal data.

Assumptions of Non-Parametric Statistics:

1. No Assumption of Normality: Unlike parametric tests, non-parametric methods do not assume that the data follows a specific distribution, such as the normal distribution.
2. Equal Variances Not Assumed: Non-parametric tests do not require homogeneity of variances, making them robust in situations where the variances are unequal.
3. Ordinal or Nominal Data: Non-parametric tests are suitable for analyzing data that is on an ordinal or nominal scale.

Advantages of Non-Parametric Statistics:

1. Robustness: Non-parametric tests are less sensitive to outliers and do not rely on strict assumptions about the distribution of data. They can be applied to data that deviates from normality.
2. Applicability to Non-Normally Distributed Data: Non-parametric tests are particularly useful when dealing with data that does not follow a normal distribution, as they don’t require the normality assumption that many parametric tests do.
3. Simplicity: Non-parametric tests are often simpler to understand and apply, making them accessible to researchers and practitioners with less statistical expertise.
4. Wide Applicability: Non-parametric tests can be applied to a variety of data types, including ordinal, nominal, and interval data.

Disadvantages of Non-Parametric Statistics:

1. Less Power: Non-parametric tests generally have less statistical power compared to their parametric counterparts, meaning they may be less able to detect true effects when they exist.
2. Less Precise: Non-parametric tests typically provide less precise estimates of population parameters compared to parametric tests.
3. Limited Use with Continuous Data: While non-parametric tests are versatile, they may not be the best choice when dealing with continuous data that reasonably conforms to normality and other parametric assumptions.
4. Fewer Options: There are fewer non-parametric tests available compared to parametric tests, and they may not cover all the situations that parametric tests do.

Examples of common non-parametric tests include the Wilcoxon signed-rank test, Mann-Whitney U test, Kruskal-Wallis test, and Spearman’s rank correlation coefficient. Researchers should carefully consider the nature of their data and the specific research question when choosing between non-parametric and parametric statistical methods.