What type of statistical test to use when comparing two groups?

As a statistical expert with extensive experience in analyzing and interpreting data, I often encounter the question of which statistical test to use when comparing two groups. The choice of the test depends on several factors, including the type of data, the research hypothesis, and the assumptions underlying each test. Here's a comprehensive guide to help you make an informed decision:

Step 1: Determine the Type of Data

The first step in choosing a statistical test is to understand the nature of your data. Data can be classified into three main types: nominal, ordinal, and interval/ratio.

- Nominal data represents categories without any intrinsic order (e.g., gender, race).
- Ordinal data has a natural order but the differences between values are not necessarily equal (e.g., satisfaction levels: very satisfied, satisfied, neutral, dissatisfied, very dissatisfied).
- Interval/Ratio data has equal intervals between values and a true zero point (e.g., temperature in Celsius or Fahrenheit, income).

Step 2: Define the Research Hypothesis

Your hypothesis will guide you in selecting the appropriate test. Are you comparing one group to a hypothetical value, two unpaired groups, two paired groups, or more than two groups?

Step 3: Check the Assumptions

Each test has certain assumptions that must be met for the results to be valid. For example, parametric tests like the t-test assume that the data is normally distributed and has equal variances.

Step 4: Choose the Appropriate Test

Based on the type of data and the hypothesis, here are some common tests used for different scenarios:

- One-sample t-test: Compares the mean of a single group to a known value when the data is interval/ratio and normally distributed.
- Wilcoxon test: Used for nominal or ordinal data or when the normality assumption is violated.
- Unpaired (Independent) t-test: Compares the means of two unpaired groups with interval/ratio data that is normally distributed.
- Mann-Whitney test: The non-parametric alternative to the unpaired t-test, used when the normality assumption is not met.
- Paired (Dependent) t-test: Compares the means of two related groups (e.g., before and after treatment) with interval/ratio data that is normally distributed.
- Wilcoxon test: The non-parametric alternative to the paired t-test for related groups.
- One-way ANOVA: Compares the means of three or more unrelated groups with interval/ratio data that is normally distributed and has equal variances.
- Kruskal-Wallis test: The non-parametric alternative to one-way ANOVA for unrelated groups when the normality assumption is not met.

**Step 5: Analyze and Interpret the Results**

Once you've chosen the test, perform the analysis and interpret the results in the context of your research question. Consider the p-value, effect size, and confidence intervals.

Step 6: Report Your Findings

When reporting your findings, be sure to include the test used, the data assumptions, the results of the test, and a discussion of the implications.

In conclusion, the choice of a statistical test is crucial for the validity of your research findings. By carefully considering the type of data, the research hypothesis, and the assumptions of each test, you can select the most appropriate test for your analysis.

Choosing a statistical testType of DataCompare one group to a hypothetical valueOne-sample ttestWilcoxon testCompare two unpaired groupsUnpaired t testMann-Whitney testCompare two paired groupsPaired t testWilcoxon testCompare three or more unmatched groupsOne-way ANOVAKruskal-Wallis test6 more rows