Data analytics, statistics, and more

Statistical Power of Two-Sample Central Tendency Tests with Unequal Sample Size

Two-sample hypothesis tests are used to compare the means, medians, or other percentiles of two populations to determine if there is a significant difference between the groups. For a given total sample size, statistical power is maximized if the sample sizes for each group are equal. With highly unequal group sizes, each additional observation adds little additional resolution. This simulation study focuses on determining the effect of unequal sample sizes on the statistical power of two-sample hypothesis tests, assuming independent samples with equal variance.

January 3, 2023

Two-Sample Permutation Test of Difference in Means

Permutation tests are designed to be robust against departures from normality. Permutation tests compute p-values by randomly selecting several thousand outcomes from the many larger number of outcomes possible that represent the null hypothesis. This post demonstrates how to perform a two-sample permutation test using various R packages.

December 22, 2022

Calculation of 95% Upper Confidence Limit for Data With No Censored Values

This post presents methods that can be used to calculate a 95% upper confidence limit on the mean of an unknown population, where all measurements are detections. The estimation methods described in this post are applicable to a random sample coming from a single statistical population.

November 1, 2022

Trend Analysis for Censored Environmental Data

This post examines several methods for conducting temporal trend analysis using censored data that do not substitute artificial values for non-detects. Parametric methods are based on censored regression using maximum likelihood estimation. Nonparametric methods are based on Kendall’s tau and the Akritas-Theil-Sen line.

October 7, 2022