Data analytics, statistics, and more
This post presents methods that can be used to calculate a 95% upper confidence limit on the mean of an unknown population for left-censored data sets (i.e., containing a mixture of detects and non-detects). The preferred approach depends on many factors, including the number of samples and the distributional shape of the data.
Determination of an appropriate sample size when performing a correlation sudy is usually based on achieving sufficient power that the test can reject the null hypothesis that the correlation is zero. Sample sizes found using this method can yield confidence intervals that are so wide that they provide very little useful information about the magnitude of the correlation. An alternative approach is to choose a sample size that achieves a sufficiently narrow confidence interval for measuring the smallest correlation of potential interest.
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.
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.
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.