![]() Note that we will never see a duplicate permutation - permutation tests sample an array of all possible permutations without replacement. Those draws are then combined to estimate the population distribution. At the end of this step, we’ll have a large number of theoretical draws from our population. Image by author.įirst, we develop many permutations of our variable of interest, labeled P1, P2, …, P120. ![]() There are 5 observations, represented by each row, and two columns of interest, Risk and Deaths.įigure 2: framework for a permutation test. In figure 2, we see a graphical representation of a permutation test. From there, we can determine how rare our observed values are relative to the population. The purpose of a permutation test is to estimate the population distribution, the distribution where our observations came from. Permutation tests are very simple, but surprisingly powerful. Let’s slow down a bit and really understand permutation tests… Permutation Tests 101 But, how does permutation testing actually work? This “studentization” process allows us to run autocorrelation tests on non-exchangeable data. To account for the lack of exchangeability, we divide our test statistic by an estimate of the standard error, thereby converting out test statistic to a t-statistic. The p-value is the proportion of samples that have a test statistic larger than that of our observed data. To get a p-value, we randomly sample (without replacement) possible permutations of our variable of interest. Permutation tests are non-parametric tests that solely rely on the assumption of exchangeability. In this post we will discuss the basics of permutation tests and briefly outline the time series method. However, it’s pretty efficient and can be implemented at scale. The method is very mathy and brand new, so there’s little support and no python/R libraries. Image by author.Ī recent paper published by researchers at Stanford extends the permutation testing framework to time series data, an area where permutation tests are often invalid. Here, 98.2% of our permutation distribution is below our red line, indicating a p-value of 0.018. The red vertical line is our observed data test statistic. Figure 1: example of a permutation test distribution.
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