Parametric and non-parametric tests are statistical methods used to analyze data, but they differ in their assumptions and the types of data they are suitable for. Here are the key differences between parametric and non-parametric tests:
Parametric Tests:
Assumptions:
Parametric Tests: Make specific assumptions about the underlying population distribution, typically assuming that the data follows a specific probability distribution (often the normal distribution).
Data Type:
Parametric Tests: Typically applied to interval or ratio data. They are more powerful when data meet the assumptions.
Parameter Estimation:
Parametric Tests: Involve estimating parameters (e.g., mean, variance) of the population distribution.
Examples:
Parametric Tests: t-tests, analysis of variance (ANOVA), regression analysis, and correlation analysis.
Sensitivity:
Parametric Tests: More sensitive to outliers and deviations from assumptions. They may provide more precise estimates when assumptions are met.
Use Cases:
Parametric Tests: Suitable when assumptions are met, and the data distribution is known or assumed to be normal.
Non-Parametric Tests:
Assumptions:
Non-Parametric Tests: Have fewer assumptions about the underlying population distribution. They are often used when data do not meet the normality assumption.
Data Type:
Non-Parametric Tests: Can be applied to nominal, ordinal, interval, or ratio data. They are more robust in the presence of outliers or non-normality.
Parameter Estimation:
Non-Parametric Tests: Do not involve estimating parameters of the population distribution. They are distribution-free tests.
Examples:
Non-Parametric Tests: Mann-Whitney U test, Wilcoxon signed-rank test, Kruskal-Wallis test, and Spearman’s rank correlation.
Sensitivity:
Non-Parametric Tests: Less sensitive to outliers and deviations from assumptions. They may be preferred when data do not meet parametric assumptions.
Use Cases:
Non-Parametric Tests: Suitable when data distribution is unknown or not assumed to be normal, or when dealing with ordinal or categorical data.
When to Choose:
Parametric Tests: Should be chosen when the data meet the assumptions of normality and homogeneity of variances. They are generally more powerful when assumptions are satisfied.
Non-Parametric Tests: Should be chosen when the assumptions of parametric tests are violated or when dealing with non-normally distributed data. They are more robust in such situations.
Summary:
Parametric Tests: Assume a specific population distribution, are sensitive to deviations from assumptions, and are suitable for interval or ratio data.
Non-Parametric Tests: Have fewer distributional assumptions, are less sensitive to outliers, and can be applied to a wider range of data types, including nominal and ordinal data.
The choice between parametric and non-parametric tests depends on the characteristics of the data and the assumptions that can be reasonably met. Researchers should carefully consider the nature of their data before selecting a statistical test.