Charting the Non-Parametric Odyssey: Statistical Frameworks for Distribution-Free Hypothesis Testing
<p>Statistics is the corpus of instruments of knowledge that allow us to infer from data through tools including, but not limited to, estimation of parameters, construction of confidence intervals, and hypothesis testing to validate our assumptions. In this article, we will learn about frameworks that allow us to test our hypothesis about the values of different data quantiles, namely the Sign Test and the Wilcoxon Signed Rank Test. What’s unique about these frameworks is that, unlike popular hypothesis tests such as the z-test or the t-test, these tests don’t require any assumption made on the data, either through intuition or enforced via the Central Limit Theorem i.e., they are distribution-free or non-parametric. All that you need is data coming from a symmetric and continuous distribution, and you will be equipped with the tools to test claims such as:</p>
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