Non-parametric tests in biostatistics are crucial when data do not meet the assumptions required for parametric tests, such as normality or homogeneity of variances.
These tests are often referred to as distribution-free tests because they don't assume a specific underlying statistical distribution.
Characteristics of Non-Parametric Tests
1. Distribution-Free:
They don't require the assumption that the data follows any particular distribution, such as the normal distribution.
2. Robust to Outliers:
Non-parametric methods are less sensitive to outliers compared to parametric tests, which can be heavily influenced by extreme values.
3. Applicable to Various Data Types:
These tests can be applied to ordinal, nominal, and interval data, particularly when such data are not normally distributed.
4. Use of Ranks:
Instead of actual data values, many non-parametric tests use the ranks of the data. This ranking reduces the effect of non-normality and outliers.
5. Handling Small Sample Sizes:
Non-parametric tests are especially useful for small sample sizes, where the central limit theorem does not ensure normality.
Advantages of Non-Parametric Tests
1. Flexibility:
They can be used with skewed data, ordinal data, and nominal data, providing a wide application range in biostatistics.
2. Minimal Assumptions:
By not requiring normal distribution or equal variances, non-parametric tests can be applied in a broader array of scenarios.
3. Useful for Small Samples:
They are ideal for analyzing data from small studies, which is common in early phases of clinical research or studies involving rare conditions.
Disadvantages of Non-Parametric Tests
1. Less Powerful than Parametric Tests:
When data actually do meet the assumptions of parametric tests, non-parametric tests are generally less powerful (i.e., they have a lower probability of detecting a true effect).
2. Limited Interpretation:
The results from non-parametric tests often pertain to medians or general distributions rather than means, which can limit their interpretability in some contexts.
3. Complexity in Multivariable Situations:
While there are non-parametric methods for multivariable analysis, they are often less straightforward than their parametric counterparts.
Common Non-Parametric Tests and Their Procedures
1. Mann-Whitney U Test:
Purpose: To compare two independent groups.
Procedure: Rank all the observations from both groups together. Compute the U statistic based on the ranks and use it to determine if there's a significant difference between the groups.
2. Wilcoxon Signed-Rank Test:
Purpose: To compare two related samples.
Procedure: For each pair, calculate the difference, rank these differences ignoring signs, then apply signs to ranks and compute the sum of positive and negative ranks to test if there's a significant median difference.
3. Kruskal-Wallis Test:
Purpose: To compare more than two independent groups.
Procedure: Rank all observations from all groups, then compute the H statistic based on these ranks to test for differences among the groups.
4. Friedman Test:
Purpose: To compare more than two related groups.
Procedure: Rank each block (where a block consists of all treatments for a subject) and compute the Friedman statistic to determine differences among groups.
5. Spearman’s Rank Correlation:
Purpose: To measure the strength and direction of association between two ranked variables.
Procedure: Rank both variables and compute the correlation coefficient between these ranks.
Usage in Biostatistical Research
Non-parametric tests are particularly useful in biostatistics for several reasons:
Dealing with Skewed Data: Biological data often have non-normal distributions due to natural biological variability and constraints (e.g., concentrations of substances often cannot be negative).
Ordinal Data: Many biostatistical measures (e.g., pain scores, stage of disease) are ordinal.
Small Sample Sizes: Early-stage clinical trials or rare disease studies often work with small sample sizes that preclude the robust application of parametric tests.
