An Introduction to the Permutation Test:
The Permutation Test, also known as a re-randomization test or exact test, is a non-parametric method for testing the null hypothesis that two different groups come from the same distribution. Instead of relying on a theoretical distribution (like the t-test which relies on the normal distribution), the permutation test creates its distribution from the data by calculating all possible outcomes from rearrangements (permutations) of the data.
- Basic Steps:
- Combine all data from both groups into a single dataset.
- Repeatedly shuffle (permute) the combined data and then allocate the first ‘n’ items to the first group and the rest to the second group.
- For each shuffle, calculate the test statistic (e.g., difference in means).
- The p-value is then calculated as the proportion of shuffled permutations where the test statistic is more extreme than the observed test statistic from the original groups.
- Advantages:
- No assumptions about the underlying distribution of the data.
- Can be applied to a wide range of test statistics and sample sizes.
- Limitations:
- Computationally intensive for datasets with large sample sizes since it requires evaluating all possible permutations.
Formulation of Initial Questions about the Data:
Before diving deep into any data analysis project, it’s imperative to formulate questions that guide the research and analysis process. These questions ensure the analysis remains focused and purposeful.
- Purpose and Goals: Understanding the objectives of the analysis. What do we hope to achieve or conclude at the end of the process?
- Data Understanding: What kind of data do we have? How is the data structured? What are the primary features and potential target variables?
- Potential Patterns: Are there specific patterns, correlations, or trends we anticipate or are particularly interested in uncovering?
- Challenges and Constraints: Are there limitations in the data? Do we anticipate any biases, missing values, or anomalies?
- Stakeholder Considerations: Who is the target audience for the results? Are there specific questions or concerns from stakeholders that the analysis should address?
- Potential Impact: How might the results of the analysis affect decision-making processes or future actions?