2-Sample Median Bootstrap Test Calculator

Use this 2-sample median bootstrap test calculator to determine whether the difference between two medians is statistically significant. This calculator requires two independent samples and can use continuous or ordinal data. It calculates the p-value and constructs a confidence interval for the difference. Because this calculator evaluates medians, it is a solid choice for skewed data, outliers, and ordinal scales (e.g., Likert items). You can copy and paste your data or type it in, up to 2000 rows. The editable headers are used in the results.

The default settings are good for most cases. However you can change them as needed. Below the 2-sample median bootstrap calculator, I provide more details about how to choose these options and output interpretations. See all my Statistical Calculators!

If you’re new to bootstrap tests, read about them in my Introduction to Bootstrapping. While the mechanics of bootstrap tests differ from traditional hypothesis tests, their interpretations are very similar. Analysts will frequently use nonparametric tests, such as Mann Whitney U Test, to assess medians. However, those nonparametric tests have very stringent assumptions for testing medians specifically. Frequently, the data don’t satisfy these assumptions and the nonparametric tests cannot assess the medians. This bootstrap test doesn’t have that assumption.

In the Median Test Calculator you can change the significance level. This setting affects the width of your confidence intervals. While the default of 0.05 is a good, standard choice, you can change it. Learn why in Significance Levels.

You’ll also need to choose either a one- or two-tailed test in the calculator. The default two-tailed test is the best for most situations. However, learn about why you’d change this setting in my article, One-Tailed and Two-Tailed Tests Explained.

Choosing the Test Type in the Median Bootstrap Test Calculator

In this calculator, the Test Type option affects only the P-value calculations.

Use Shift Bootstrap in most cases. It’s a good default when data are skewed, have outliers, sample sizes are unequal, or the two groups clearly differ in spread/shape.

Choose Permutation when the two groups have a similar shape and spread and sample sizes are reasonably balanced.

As a practical check, you can run both types of tests. If they agree, confidence goes up. If they differ and the distribution shapes look different or sample sizes are unbalanced, prefer the Shift Bootstrap method.

Choosing the Confidence Interval Method in the Calculator

In this median bootstrap calculator, the Confidence Interval Method choice affects only how it constructs the CI.

Use BCa (bias-corrected & accelerated) in most cases. Pick BCa when the bootstrap histogram of the median difference looks skewed, when samples are small to moderate, when there are outliers, or when your data are discrete/with ties (e.g., Likert). BCa adjusts for bias and skew in the bootstrap distribution, so it tends to give better-calibrated coverage.

Choose Percentile when you have a large sample and want something simple and fast. This approach is acceptable when your bootstrap histogram looks roughly symmetric and centered around the observed difference.

Practical tip: if the two methods are similar, you’re fine. If they differ, prefer BCa unless you have very heavily tied, very small samples—in that edge case, show both.

Interpreting the Results of the 2-Sample Median Bootstrap Test Calculator

The 2-sample median bootstrap test results are very similar in nature to 2-sample t-test results. Simply compare the p-value to your significance level. If the p-value is less than or equal to the significance level, your results are statistically significant. You can reject the null hypothesis and conclude that the population medians are different. Learn more about Interpreting P-values.

Similarly, you can be confident that the correct value of the population median difference falls within the confidence interval. The precise confidence level depends on the significance level you chose. Learn more about Interpreting Confidence Intervals.

Monte Carlo standard error of p-hat

While you’re probably familiar with most of the statistics in this median bootstrap test calculator, the Monte Carlo standard error of p-hat might be new to you!

MC SE (p̂) is the “wiggle room” in the p-value caused by using a random resampling procedure. If you ran the same analysis again on the same data with a different random seed, p̂ would jiggle by about this amount. It relates to simulation noise—and it gets smaller when you use more resamples (B).

In short, MC SE (p̂) tells you how precise the p-value is for your analysis in this bootstrap test calculator. Your statistical significance decision hinges on the significance level (like 0.05). Check p̂ ± 2×MC SE. If that interval crosses the cutoff, bump B until it doesn’t. To hit a desired precision, use the rule of thumb: B ≈ 0.25 / (target SE)². For example, if you want MC SE ≈ 0.001, choose about B = 250,000 resamples.