Introduction

When conducting statistical analysis, researchers are often faced with the decision of choosing between non-parametric and parametric tests. Both types of tests serve different purposes and are used in different scenarios. This paper will discuss the differences between non-parametric and parametric tests, provide examples of each, discuss the appropriate situations to use these tests, as well as the assumptions that need to be met by the investigator. Finally, it will outline a data analysis plan, including the test to address the study hypothesis and the measures of central tendency for demographic variables.

Differences between Non-parametric and Parametric Tests

Non-parametric tests, also known as distribution-free tests, are statistical tests that do not rely on assumptions about the population distribution. These tests are used when the data do not meet the assumptions required for parametric tests. Non-parametric tests do not make assumptions about the shape of the distribution or the underlying parameters of the data.

In contrast, parametric tests are statistical tests that assume specific properties about the data, such as normality and homogeneity of variances. Parametric tests make assumptions about the shape of the population distribution and the parameters of the population. These assumptions allow for more powerful tests and precise estimates of the population parameters, but they must be met in order for the test to be valid.

Examples and Appropriateness of Non-parametric and Parametric Tests

An example of a non-parametric test is the Wilcoxon Signed-Rank Test. This test is used to determine if the median of a paired dataset differs significantly from a hypothesized value. It is appropriate to use this test when the data are not normally distributed, and the assumption of equal variances between pairs is violated. For example, if we want to compare the heights of a group of individuals before and after an intervention, and the data are not normally distributed, the Wilcoxon Signed-Rank Test would be an appropriate choice.

On the other hand, an example of a parametric test is the t-test. The t-test is used to determine if the means of two groups differ significantly. It assumes that the data are normally distributed, and the variances of the two groups are equal. If these assumptions are met, the t-test provides greater statistical power compared to non-parametric tests. For instance, if we want to compare the average test scores of two different teaching methods, and the data are normally distributed and have equal variances, the t-test would be appropriate.

Assumptions for Running Non-parametric and Parametric Tests

Non-parametric tests do not require as many assumptions as parametric tests. However, there are still some assumptions that need to be met. For the Wilcoxon Signed-Rank Test example, the data need to be at least ordinal and independent. The assumption of independence can be violated if the paired measurements are highly correlated.

In contrast, parametric tests have more stringent assumptions. For the t-test example, the assumptions include normality, homogeneity of variances, and independence of observations. Normality assumes that the data are normally distributed, which can be assessed visually through histograms or statistically through tests like the Shapiro-Wilk test. Homogeneity of variances assumes that the variances of the two groups being compared are equal, which can be assessed through tests like Levene’s test. Independence of observations assumes that the data points being compared are independent of each other.

Data Analysis Plan

To address the study hypothesis, the appropriate test will depend on the specific research question and the type of data being analyzed.