Trendtests

Trendtests are statistical procedures designed to detect a monotone trend between an ordered explanatory variable and a response variable. They are used when the groups or exposure levels have a natural order and the research question is whether the response tends to increase or decrease with the order.

Several trend tests exist, depending on the data type and assumptions. The Cochran-Armitage test for trend assesses a linear trend in proportions across ordered categories of a predictor in a binary outcome setting. The Jonckheere-Terpstra test is a nonparametric test for ordered alternatives across k independent samples when the response is ordinal or continuous. Spearman's rank correlation and Kendall's tau quantify monotone association and can serve as trend assessments when one variable is ordinal/continuous and the other is monotone. Cuzick's test for trend extends Wilcoxon-type tests to detect a trend across multiple ordered groups. The Mantel-Haenszel test for trend (or linear-by-linear association) is used in stratified tables to assess a linear trend across ordered exposure levels while controlling for strata.

Assumptions typically include independence of observations and an a priori ordered structure. The alternative hypothesis concerns a monotone increase or decrease with the order. A significant result indicates evidence of a trend, not necessarily a specific linear slope, and power depends on the degree of trend, sample size, and variance.

Trend tests are implemented in standard statistical packages and are commonly reported in dose–response and epidemiologic studies. When the trend is non-monotone or the order is uncertain, alternative analyses may be more appropriate.