Sometimes statistical studies want to determine the relationship between two quantities. These types of studies have what is known as paired data. The characteristic that distinguishes paired data is that since there are two quantities to measure, each individual data point is associated to two numbers. This is in contrast to the usual association of one number to each data point as in other quantitative data sets.
When looking at paired data, the order of the pairing is important. This is because the first number of each point of paired data is a measure of one thing while the second number could be a measure of something quite different.
An Example of Paired Data
To see an example of paired data, suppose a teacher counts the number of homework assignments each student turned in for a particular unit, and then pairs this number with each student’s percentage on the unit test. The pairs are as follows:
(10, 95%) (5, 80%) (9, 85%) (2, 50%) (5, 60%) (3, 70%)
While it would make sense to calculate the average number of homework assignments turned in or the average test score, there may be other questions to ask about the data. For instance, is there any connection between the number of homework assignments turned in and performance on the test? The teacher would need to keep the data paired in order to answer this question.
Analyzing Paired Data
The statistical techniques of correlation and regression are used to analyzed paired data. These techniques attempt to determine if the quantities being measured have any influence on each other.
Paired data can be graphed by means of a scatterplot. In this type of graph, one coordinate axis represents one quantity of the paired data while the other coordinate axis represents the other quantity of the paired data. A scatterplot for the above data would have the x-axis denote the number of assignments turned in and the y-axis denote the percentage on the unit test.