13, October, 2023

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:
    1. Combine all data from both groups into a single dataset.
    2. Repeatedly shuffle (permute) the combined data and then allocate the first ‘n’ items to the first group and the rest to the second group.
    3. For each shuffle, calculate the test statistic (e.g., difference in means).
    4. 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?

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