Imagine a city introduces a new, lower speed limit to reduce traffic accidents. A year later, the mayor proudly announces that accidents are down 15%. But is the new speed limit the reason? Maybe accidents were already on a downward trend. Or perhaps the weather was unusually mild that year, leading to fewer incidents. How can we isolate the effect of the policy itself?

This is where Interrupted Time Series (ITS) analysis comes in. It's a powerful quasi-experimental method used to evaluate the impact of an intervention on data collected over time. A quasi-experiment is a study that looks like a true experiment but lacks random assignment.

The logic is straightforward. You start with a time series, which is just a sequence of data points measured at consistent intervals, like monthly accident reports or quarterly sales figures. Then, you identify a specific point in time when an intervention occurred. This is the "interruption."

The analysis compares the trend in the data before the interruption to the trend after it. By establishing the pre-intervention trend, we can forecast what would likely have happened if the intervention had never occurred. The difference between this forecast and what actually happened is our estimated impact.

The graph above shows the two key effects ITS can measure:

1. Level change: An immediate jump or drop in the outcome right after the intervention. In our example, the post-intervention trend starts at a lower point than where the pre-intervention trend left off.
2. Slope change: A change in the rate of increase or decrease over time. The post-intervention trend might be flatter or steeper than the pre-intervention trend.

A simple pre-post comparison—looking at one data point before the intervention and one after—is often misleading. It completely ignores the underlying trend.

For instance, if traffic accidents were already decreasing by 5% each year, a simple pre-post analysis might wrongly attribute that ongoing decrease to the new speed limit policy. ITS is superior because it accounts for that pre-existing trend. It essentially uses the past to create its own control group, answering the question: "What would have happened if everything had continued as it was?"

While randomized controlled trials (RCTs) are often considered the gold standard in research, they aren't always practical or ethical. You can't randomly assign a new law to half a country. ITS provides a robust alternative for evaluating large-scale policies and events in their natural settings.

Like any statistical method, ITS relies on a few key assumptions to produce valid results.

If our city lowered the speed limit and, in the very same month, launched a major road safety advertising campaign, ITS alone couldn't separate the effects of the two initiatives. The analysis assumes the interruption is the only relevant change happening at that specific time.

Another key assumption is that the data collection process remained consistent over the entire period. If the city changed how it defined or reported an "accident" halfway through the study, any observed change could be an artifact of the new measurement, not the policy.

Finally, a major limitation is the need for a sufficient number of data points. A general rule of thumb is to have at least 8-10 observations both before and after the intervention to reliably model the trends. With too little data, it's hard to be confident that you've captured the true underlying pattern.

Ready to test your understanding?

ITS is a valuable tool for anyone looking to measure the real-world impact of policies, events, or programs when a traditional experiment isn't feasible.