In Statistics, occasionally one may have to find out the connection between two quantities. These types of studies are called paired data. A unique feature of paired data is that as you have to measure two quantities, each specific data point is related with two numbers. This is not the case with other quantitative data sets where one number is normally associated with a data point. While founding out paired data, you need to pay attention to the pairings order. This is because the both the numbers at each point of the paired data may be used to measure different things.
Analyzing a paired data
In order to analyze paired data, the statistical methods of regression and correlation are used. These methods try to find out if the quantities which are being measured influence each other in a way or not. You can show paired data in a graph with the help of a scatterplot. In such a graph, one coordinate axis signifies one quantity of a paired data, while the other coordinate axis signifies the other quantity of the paired data.
An example of a paired data
In order to explain an example of a paired data, lets assume that a lecturer calculates the number of practical assignments that each student completes for a particular unit. He then pairs this number with the respective percentage of each student. The pairs are mentioned below:-
(10, 90%) (5, 80)(8, 85%) (3, 55%) (6, 65%), (4, 70%)
Though there is logic behind counting the average number of practical assignments completed or the average test score of each student, a number of other questions might arise from the data. For e.g., is there any relationship between the number of practical assignments done and performance in the exam? The lecturer will need to keep the data paired so as to answer the question. During analysis, a scatterplot for the above mentioned data will have x-axis to indicate the number of assignments done and the y-axis will indicate the percentage acquired in the exam.
Significance of a paired data
Paired data is widely used with an intention to control or reduce the effects of puzzling variables. Often during experiments, researchers have to take measurement of something before and after a treatment have been already done. Paired data is very useful in these types of circumstances. It enables researchers to test hypothesis that the treatment bring about the intended change. This method is able to test the hypothesis in a controlled manner as researchers measure the change that has been produced on individuals.
Paired data has been widely used in different areas of statistics like twin studies and matched pairs because of its unique feature in comparison to other types of quantitative data sets.