# Hypothesis Testing Matched Pairs

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• 0:01 Hypothesis Testing…
• 0:41 What Is Paired Data?
• 1:40 The Important Equation
• 2:18 Example
• 4:52 Lesson Summary

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Lesson Transcript
Instructor: Artem Cheprasov
Sometimes, data sets come paired. What does this actually mean, though? This lesson explains what matched pairs are and goes over an example of how hypothesis testing applies to them.

## Hypothesis Testing Matched Pairs

What's a pair? It's a couple of things that are in some way associated: a pair of socks, a pair of kids, a pair of apples. What's a match? It's something that resembles something else in one way or another. A key matches a lock. A pair of pants matches some shoes.

In statistics, paired or matched samples are synonymous terms for two dependent samples, those where each sample's data value is collected from the same source. Meaning, they depend on one another somehow. This lesson goes over an example of hypothesis testing matched pairs.

## What Is Paired Data?

Before going further. Let me give you a real clear example of paired data, or matched samples, and dependency in the world of statistics.

Let's say we want to learn about the mean heart rate of 20 patients after they have gone through a treatment protocol consisting of taking medication. These 20 patients have their heart rate recorded prior to (sample one) and after (sample two) they complete the therapy. While we get two samples in such a scenario, the data value in each sample has a corresponding data value belonging to the same person in the other sample. This is why they are dependent or matched samples.

In other words, if both corresponding data values come from the same source, the samples are considered to be paired or matched. In our example, each person has two data values, and since they come from the same source, they are paired data.

## The Important Equation

To figure out if there is a significant difference between the matched pairs, we need to know the following equation.

Since it's really a mash of weird symbols, let's define what all of them mean prior to using an example to further understand them.

Our test statistic is t. d is the mean of the paired differences in our sample. mud is the mean of the paired differences for the entire population. sd is the standard deviation of the paired differences in the sample, and n refers to the total number of paired sample differences.

## Example

Now we're ready to rock and roll! Let's use the following example: A company sends its employees to a psychologist to see if he can increase their sales numbers. The following table shows the sales figures (in thousands of dollars) for the employees over a period of a month before and after the sessions with the psychologist.

Employee 1 Employee 2 Employee 3 Employee 4 Employee 5 Employee 6
Before 10 8 15 38 60 90
After 14 9 16 42 80 83
d -4 -1 -1 -4 -20 7

Although you may have to calculate this out on your own on a test using your knowledge from other lessons, to speed things up, I'll calculate the following values for you:

• d = -3.833
• sd = 8.886
• n = 6 (since we have six employees)

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