## PhD Statistics Help - Interrupted Time Series

This design is similar to the pretest-posttest except that there are more than two measurements. Ideally, there are an equal number of measurement periods before and after treatment, and the period between measurements is constant. These designs can range from several To hundreds of measurements, with the number determining what types of analyses can be conducted.

This design is found in two applications. First, it is a direct extension of the pretest-posttest with more than two measurements. The second use in when periodic data exist over a considerable length of time and the purpose of the investigation is to determine whether the variables of interest change at a specified point in series. This second use is generally considered to be a time series, although a broader use of the term is taken here.

The multiple pretest-posttest designs are an improvement over the single pretest-posttest. The advantage of this design is that it allows the determination of trends over time, that is, the slope of the graph of the dependent variable over time. The trend estimate is important because it might well be that the posttest level of the dependent variable is at exactly the place one would expect, based on previous observations over time. The dependent variable might show an increase, decrease, or cyclical change over time without treatment or intervention. This is especially true with aggregate data based on naturally social units. Traffic accident rates, crime rates, and unemployment rates all show trends over time having causes that lie outside of most studies. Techniques have developed to determine trends in data and estimate whether discontinuity occurred at a specified location in the series.

Procedures to analyze time-series data can become quite complex and most social scientists receive little exposure to them in graduate school. For long series with 50 measurements or more, complex mathematical modelling procedures have developed that can well describe the form of series and uncover any changes that may have occurred. Perhaps the most powerful techniques are the autoregressive integrated moving average (ARIMA), which indicates complex trends in a time series (see McDowall, McCleary, Meidinger and Hay,1980, for details).

For a smaller number of measurements, other less complex and powerful procedures must be used. Certainly, the analysis of variance is available when there are a few retesting. However, there would be too many groups means to compare as the number of retesting becomes large. Swaminathan and Algina (1977) have developed multiple regression procedures which allow a comparison of regression lines before and after treatment. While the multiple testing designs are certainly more powerful than the single pretest-posttest, they do suffer from most of the same shortcomings.