Data analytics, statistics, and more
The issue of uncertainty in estimating population parameters from data samples is often addressed using statistical intervals. The three types of statistical interval differ in their definitions as well as their typical applications. It is important to fully understand the assumptions and limitations underlying the use, interpretation, and calculation of statistical intervals before applying them.
An important objective of many environmental monitoring programs is to detect changes or trends in constituent concentrations over time. The Mann-Kendell test is one of the most popular nonparametric tests for determining temporal trend. This post evaluates the power of the Mann-Kendall test to identify a trend for various sample sizes and variability in the data using Monte Carlo simulation.
Many statistical analyses depend on the type of data distribution. This post explores methods gooness-of-fit tests for the lognormal distribution, the gamma distribution, and normal distribution when data contain censored (non-detect) values.
Regression performed using censored data can be challenging. Common practices for handling censored data include deletion of the censored observations or substituting nondetects with arbitrary constants, generally based on some fraction of the detection limit. These approaches tend to be biased and cause a loss of information. Censored regression methods produce more accurate and robust estimates than these bias-prone methods.
Ordinary least squares regression is optimal when all regression assumptions are valid. When some of these assumptions are invalid, least squares regression can perform poorly. Robust regression is an alternative to least squares regression when data contain outliers or influential observations.