Nonparametric Statistics:
Advantages:
* Less restrictive assumptions: This is the biggest advantage. Nonparametric methods don't assume the data follows a specific distribution (like the normal distribution). This makes them robust to outliers and violations of assumptions like normality, homogeneity of variance, and linearity. They can handle ordinal data (ranked data) easily.
* Easier to understand and apply: The calculations and interpretations are often simpler and more intuitive than their parametric counterparts.
* Can be used with small sample sizes: While parametric tests often require larger sample sizes for accurate results, nonparametric tests can be effective even with small samples.
* Can analyze data from various measurement scales: They accommodate nominal, ordinal, and interval/ratio data, offering flexibility.
Disadvantages:
* Less powerful: When the assumptions of parametric tests are met, parametric tests are generally more powerful (meaning they are more likely to detect a true effect if one exists). Nonparametric tests lose some power because they don't use all the information in the data.
* Can be less efficient: They may require larger sample sizes to achieve the same level of precision as parametric tests.
* Limited range of tests: There aren't nonparametric equivalents for all parametric tests. Some sophisticated analyses are only possible using parametric methods.
Parametric Statistics:
Advantages:
* More powerful: When assumptions are met, they offer greater statistical power and are more sensitive to detecting real effects.
* More precise estimates: They generally provide more precise estimates of population parameters.
* Wider range of tests: A greater variety of statistical tests and models are available.
* Can handle more complex designs: They are better suited for complex experimental designs and analyses.
Disadvantages:
* Strong assumptions: They require the data to meet certain assumptions (e.g., normality, homogeneity of variance, independence of observations). Violation of these assumptions can lead to inaccurate or misleading results.
* Sensitive to outliers: Outliers can disproportionately influence the results of parametric tests.
* May not be appropriate for all data types: They are typically not suitable for ordinal data or data that are heavily skewed or have a limited range.
* Can be more complex to understand and apply: The underlying mathematical principles can be more challenging.
In Summary:
Choose nonparametric methods when:
* Your data severely violates the assumptions of parametric tests.
* You have a small sample size.
* Your data is ordinal.
* Simplicity and ease of interpretation are prioritized.
Choose parametric methods when:
* Your data meets the assumptions of the test.
* You have a sufficiently large sample size.
* You need higher statistical power.
* You require more sophisticated analyses.
It's crucial to carefully examine your data and consider the nature of your research question before selecting the appropriate statistical approach. If you're unsure, consulting a statistician is always a good idea.