Performing T-tests to Compare Autocorrelated Time Series Data Collected from Direct-Reading Instruments

Abstract

Industrial hygienists now commonly use direct-reading instruments to evaluate hazards in the workplace. The stored values over time from these instruments constitute a time series of measurements that are often autocorrelated. Given the need to statistically compare two occupational scenarios using values from a direct-reading instrument, a t-test must consider measurement autocorrelation or the resulting test will have a largely inflated type-1 error probability (false rejection of the null hypothesis). A method is described for both the one-sample and two-sample cases which properly adjusts for autocorrelation. This method involves the computation of an “equivalent sample size” that effectively decreases the actual sample size when determining the standard error of the mean for the time series. An example is provided for the one-sample case, and an example is given where a two-sample t-test is conducted for two autocorrelated time series comprised of lognormally distributed measurements.

Keywords:

• autocorrelation
• direct-reading
• t test
• time series

ACKNOWLEDGMENT

We would like to thank the anonymous reviewer for his/her thorough review of this article which resulted in many meaningful changes to enhance the clarity of our explanations. That reviewer was also responsible for determining the closed form expression of Eq. (7)(7) that we present in Eq. (9)(9) , for which we are very grateful. We would also like to thank Mr. Craig Taylor and Dr. Kim Anderson for acquiring the data displayed in Figure 5.