Scientific Data Analysis

Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

Science involves collecting data. But what do you do once is collected? Learn about how to analyze data, including the difference between accuracy and precision.

Analyzing Scientific Data

Science is all about collecting data. If we look at the definition of science, we can say that science is the study of the natural world through systematic observation and experiment. That observation and experiment is where you collect the data. But what do you do with that data once you've collected it?

You can set up a robot collecting terabytes upon terabytes of data, but never have the time or resources to analyze it. Analyzing it is the hardest part. In fact, when data is sent back from rovers on Mars, it can take many months to analyze it.

In this lesson, we're going to discuss some of the basic principles of scientific data analysis.

Precision, Accuracy and Error

The first step in data analysis is to look at sources of error. Every measurement that anybody ever takes has experimental error. Experimental error is the difference between the measurements you take and a perfect set of measurements. There are two types of experimental error: precision and accuracy. People use those words interchangeably, but they're very different.

Precision describes how close together your measurements are. For example, let's say you're measuring the length of a long table. You do it five times to make your results more reliable. If your measurements were 6.00 meters, followed by 6.01, 5.98, 5.99, and 6.01 again, your results are very precise. Now it might turn out that the ruler was misprinted, and the table isn't even close to 6 meters. But your measurements were really close together, so they were still precise.

Accuracy is how correct your measurements are - how close you are to the true value. In the case of accuracy, your ruler being misprinted most certainly makes your results inaccurate. But let's say your ruler is working fine. If your measurements for the table were 3 m, 5 m, 7 m, and 5 m, and it turns out the table is really 5 m, your results are highly accurate. The average of those numbers is exactly 5 meters. Great! But those results are not very precise, because they're not close together.

Precision versus accuracy: A is accurate but not precise, B is accurate and precise, and C is precise but not accurate.
Precision versus accuracy: A is accurate but not precise, B is accurate and precise, and C is precise but not accurate

When taking measurements, you have to consider how precise the equipment you're using is. For example, if you use a ruler with millimeters on it, you might be able to measure to the nearest half millimeter at best. So your experimental equipment error is plus or minus half a millimeter. This affects the precision of your measurements, but doesn't affect their accuracy.

Another type of error is called systematic error. This is where all your measurements are shifted by a certain amount, up or down. For example, if you were weighing things on a scale, and the scale wasn't zeroed. This kind of error would affect your accuracy, but not your precision.

Averages and Trendlines

After you've collected your data, and have noted down any sources of error, it's time to analyze your data and make some conclusions. The first step is often to calculate averages. An average is a number that represents the central or typical value for a set of data. The most common average is called the mean. To find the mean, you add up all your numbers and divide the total by how many numbers there were. In some very simple experiments, this is your final value.

But usually there's more to it than that. Let's look at an experiment where you are measuring the number of cars that pass down a particular road each hour. You probably did multiple trials by taking your measurements over several days, instead of relying on one particular day. The first step would be to average your trials to get the number of cars for each hour.

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