A data trend denotes a correlation that exists between concentration and time or spatial location. It can also refer to a variation in the characteristics of a population with another variable in a predictable fashion. Data trends can either take an increasing, decreasing, or cyclic format—this article address how to test for data trends with particular emphasis on Linear Regression and Mann-Kendall Test.
Linear Regression (Parametric Methods to Test and Model Trends)
Linear Regression is a parametric (the data that meet the assumption of normality) test that predicts the value of a variable based on the value of another variable (Chan, 2004). The variable that is predicted is called the dependent variable. The variable used to predict the other variable’s value is called the independent or predictor variable.
The type of data trend tested by linear regression is known as linear temporal trends. Ordinary least squares regression allows for the best line of fit to be fixed. When testing the data trend, the linear regression uses a linear correlation coefficient Pearson’s r. Pearson’s r demonstrates the relationship between the observed and calculated concentrations. It also illustrates the direction and “strength” of the linear trend. When Pearson’s r value is negative, it exemplifies an increasing linear trend. However, when it is negative, it characterizes a decreasing linear trend. Additionally, the absolute value of r ranges from – 1 to 1. Therefore, a trend is considered very strong (positively or negatively) if the absolute value of r is near one.
The weaknesses of this test are that (1) to use it, the normality conventions cannot be desecrated, (2) it is extremely sensitive to outliers, (3) it is very difficult for the nondetects to be readily resolved.
Mann-Kendall Test (Nonparametric Method to Test and Model Trends)
Mann-Kendall Test is a nonparametric (data that doesn’t meet the assumption of normality) test that measures the strength and direction of correlation between two variables measured on an ordinal scale. In terms of data trends, the Mann-Kendall test assesses the monotonic trends. Monotonic trends are trends whereby concentrations are either steadily increasing or decreasing over time. Mann-Kendall Test is not applicable in cases where there are cyclic trends, i.e., where there is an alternating increase followed by a decrease of concentrations.
In the nonparametric test, Mann-Kendall Test is highly recommended since it can clearly demonstrate whether a trend exists and whether the trend is positive or negative. Moreover, the value from the Kendall Tau calculation allows for a comparison of the strength of the correlation between two data series.
The strengths of the Mann-Kendall Test are that (1) it can be used in a data consisting of nondetects (2) the findings are not adversely affected by the magnitude of extreme values. However, it cannot be used for data sets comprising of mixed detection limits.