**Serial Measurements
Gerard E. Dallal, Ph.D. **

When the same quantity is measured repeatedly over time on the same
individuals, the resulting values are called **serial measurements**.

Standard repeated measures analyses are almost always inappropriate for serial measurements. When a repeated measures analysis is applied to serial data, the result is invariably one of two types--either the mean response is not the same at all time points or the way the mean value changes over time depends on the level of some between subjects factor, that is, there is an interaction between time and the between subjects factor.

These analyses typically raise more questions than they answer. For example, a treatment-by-time interaction will be observed unless the mean response over time is the same for all treatments. However, it rarely is, and many of these interaction will be of questionable biological importance and difficult to interpret. It is common to see reports with a significant treatment-by-time interaction, in which investigators use Student's t test to compare two treatments at every time point and declare the two treatments to be the same at the 1st, 3rd, 4th, 5th, 6th, 8th, 9th, and 10th measurements but different at the 2nd and 7th measurements, without any sense of what this might mean biologically. For this reason, it is usually better to construct a simple summary of the repeated measurements for each subject based on biological considerations and analyze the summary by using familiar univariate statistical techniques, that is, techniques that are appropriate when there is a single measurement per subject. Typical summaries include mean response, difference between first and last measurement, area under the curve as determined by trapezoidal rule, maximum response, linear regression coefficient, and time of maximum response. See Matthews JNS, Altman DG, Campbell MJ, and Royston PG (1990), "Analysis of Serial Measurements In Medical Research," British Medical Journal, 300, 230-5.