Compare and contrast the roles of parametric and non-parametric tests in analysing data, including examples of types of data and appropriate tests.

## College Answer

Parametric tests are used to compare different groups of continuous variables when the data is normally (or near-normally) distributed. Non-parametric tests do not make any assumptions about the distribution of data. They focus on order rather than absolute values, and are used to analyse data that is abnormally distributed (eg. significantly skewed) or data which represent ordered categories but may not be linear (eg. pain scores, ASA score, NYHA score). Commonly used parametric tests include the unpaired t-test (comparing 2 different groups with continuous variables [eg. age in males/females) and variations of the ANalysis Of VAriance (ANOVA: comparing multiple groups with continuous variables [eg. PaO2:FIO2 ratio in Medical/Surgical/Trauma patients). Commonly used non-parametric

tests include the Mann-Whitney U test (comparing 2 different groups with continuous variables [eg. ICU stay in males/females]) and the Kruskal-Wallace test (comparing continuous variables in more than 2 groups [eg. pain score with PCA/epidural/s-c morphine]).

## Discussion

You use these to figure out the p-value, i.e. the chance of getting the same results if the null hypothesis were true. There are parametric and non-parametric tests.

### Parametric tests

**Description of parametric tests**

Parametric tests are more accurate, but require assumptions to be made about the data, eg. that the data is normally distributed (in a bell curve). If the data deviate strongly from the assumptions, the parametric test could lead to incorrect conclusions.

If the sample size is too small, parametric tests may lead to incorrect conclusions due to the loss of "normality" of sample distribution.

**Examples of parametric tests:**

- Normal distribution
- Students T Test
- Analysis of variance
- Pearson correlation coefficient
- Regression or multiple regression

### Non-parametric tests

**Description of non-parametric tests**

Non-parametric tests make no assumptions about the distribution of the data. If the assumptions for a parametric test are not met (eg. the distribution has a lot of skew in it), one may be able to use an analogous non-parametric tests.

Non-parametric tests are particularly good for small sample sizes (<30). However, non-parametric tests have less power.

**Examples of non-parametric tests:**

- Mann-Whitney U test
- Wilcoxon sum test
- Wilcoxon signed-rank test
- Kruskal-Wallis test
- Friedman's test
- Spearman's rank order

### References

Hoskin, Tanya. "Parametric and Nonparametric: Demystifying the Terms." *Mayo Clinic CTSA BERD Resource. Retrieved from http://www. mayo. edu/mayo-edudocs/center-for-translational-science-activities-documents/berd-5-6. pdf*(2012)