Question

When should nonparametric statistics be used?

Short answer

Nonparametric statistics are used when data don't fit the normal distribution, are ordinal or ranked, or in cases with small sample sizes or unknown distributions.

Step-by-step solution

Understand Nonparametric vs Parametric

Nonparametric statistics are statistical methods that don’t assume a specific distribution for the data. They are used when data don’t fit the normal distribution or when we have ordinal data or ranked data.

Identify the Distribution of Data

Determine the distribution of your data. If the data is not normally distributed or doesn’t meet the assumptions of parametric tests (like homogeneity of variances), nonparametric methods should be considered.

Consider Data Type

Check the type of data you are working with. If you have ordinal data, ranks, or non-numeric categories, nonparametric statistics are more appropriate than parametric statistics that require interval or ratio scales.

Evaluate Sample Size

For smaller sample sizes where parametric test assumptions are difficult to verify, nonparametric tests can be beneficial since they are less sensitive to sample size and distribution assumptions.

Final Step: Decide Based on Flexibility Needs

Nonparametric methods are also preferred when flexibility is required because they can be applied more generally without strict assumptions about the data’s distribution.

Key concepts

Parametric vs Nonparametric Methods

Parametric and nonparametric methods are integral to statistical analysis and differ primarily in how they handle data and underlying assumptions. Parametric methods presume that the data follows a certain distribution, typically a normal distribution. This assumption allows for more powerful statistical tests, but it also restricts the application if the assumption doesn't hold true.
In contrast, nonparametric methods do not assume a specific distribution for the data. This flexibility makes nonparametric methods suitable for a wider range of data, particularly when the normality assumption cannot be verified or when the data has a unique distribution.
Use nonparametric methods when your dataset is small, when you have ordinal data, or when the data obviously deviates from normal distribution. This choice accounts for these issues, providing a robust framework for analysis without being constrained by strict parameters.

Data Distribution

Understanding the distribution of your data is critical for choosing the right statistical methods. Data distribution refers to how data points are spread across different values. The normal distribution is a common assumption in parametric tests, characterized by its bell-shaped curve. However, when data does not follow this pattern, it is essential to consider nonparametric methods.
Several tests can help determine the distribution of your data, such as the Kolmogorov-Smirnov test or the Shapiro-Wilk test. These tests check whether your data behaves like a normal distribution. If these tests show significant deviation from normality, you should consider alternatives like nonparametric tests.
Nonparametric tests are robust to a wider range of distributions, including skewed or multi-modal data, providing valuable tools when normality is not guaranteed.

Sample Size Considerations

The size of your data sample is a key factor in deciding which statistical approach to use. Parametric methods often require larger sample sizes to reliably estimate the parameters of the distribution. This is because smaller samples can easily distort the representation of the true population parameters.
On the other hand, nonparametric methods are more flexible with sample size and tend to be more reliable even with small sample sizes. This is due to their fewer assumptions concerning data distribution.
If you don’t have access to a large data sample or the sample size is less than ideal, nonparametric tests might be advantageous as they help draw more accurate conclusions in the presence of limited data.

Ordinal Data

Ordinal data refers to a type of data that represents categories with a meaningful order but not a standard distance between them. Examples include race rankings or class grades. Because these data are ranked rather than measured on an absolute scale, they are unsuitable for parametric tests which require interval or ratio scale data.
Nonparametric methods, however, excel in analyzing ordinal data because they focus on the ranks themselves rather than the specific values. Commonly used nonparametric tests for ordinal data include the Mann-Whitney U test or the Wilcoxon rank-sum test.
Applying nonparametric methods to ordinal data ensures that the analysis respects the data's inherent structure and order, while steering clear of the misleading conclusions that misapplication of parametric tests might generate.

Statistical Assumptions

In statistical testing, assumptions are critical guidelines that dictate when a particular method is appropriate to use. Parametric tests, for example, require assumptions regarding data distribution (normality), sample representativeness, and homogeneity of variances. If any of these assumptions are violated, the test results may not be valid.
Nonparametric tests offer a solution when these assumptions are too stringent or cannot be validated, as they require fewer assumptions. This makes nonparametric methods highly attractive when working with real-world data, which rarely perfectly meets all criteria.
Using nonparametric methods can provide more reliable results in situations with high-level assumption violations. This flexibility often makes them the preferred choice in exploratory or preliminary data analysis.