Using the Raw Score Method to Compute the Correlation Coefficient

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  • 0:07 Correlation
  • 2:17 Computation
  • 5:15 Lesson Summary
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Lesson Transcript
Instructor: Devin Kowalczyk

Devin has taught psychology and has a master's degree in clinical forensic psychology. He is working on his PhD.

This lesson looks at the mathematical steps involved in computing a correlation coefficient by using raw scores. We will walk through the process with easy to follow numbers.

Correlation

Your brain is kind of awesome. You learn to associate things. Like the smell of chocolate in the house usually means that there is chocolate cake. Why do you know this? You haven't seen the chocolate cake. Yet, you smell it.

This is an example of your brain correlating the smell of chocolate to the presence of chocolate cake. A correlation is simply defined as a relationship between two variables. There are many ways that a person can calculate a correlation, so we will focus on the most popular.

A Pearson correlation is a statistical procedure for determining the correlation of normally distributed, interval or ratio data. What the heck does that mean? Statistical procedure simply means a statistical formula that you'll work with. We'll get to it in a moment. Normally distributed is a way to describe the spread of the data. We need a picture for this.

Normally distributed data in a bell curve
example of bell curve

Boom! There is the bell-shaped curve. Along the Y axis (the tall one), we see how often something occurs. The more often it occurs, the higher the line goes. On the X axis, we have the responses that are possible. So, in a normally distributed set of data, most of our responses will be in the middle, which gives it the height, and few responses will be on the extreme high or low, which makes those spots shorter.

Interval and ratio describe the quantitative measurement of data. This is explored in more detail in other lessons. All you need to know is that you need well-written questions to use a correlation, questions that give you a range of possible responses.

There are ways around some of the interval and ratio concerns. If you have a large number of participants, then you can still run your correlation because the large sample size will compensate. For example, if you have a bunch of questions like, 'Rate this lesson, 1 being bad and 5 being great,' then you will need over 100 participants. Now, we will move on to the actual computing of a Pearson correlation using raw data.

Computation

Let's say we are trying to correlate something like 'number of hours sitting each day' and 'weight in pounds.' Since we'll be dealing with a formula, I have designated the hours as X and the weight as Y. This will help ease our computation later.

I list out each subject's number, so that subject one is in the first slot and subject two in the second slot.

Data for example problem
example data table

The order of the subjects doesn't matter, but you need to keep each subject's results together. Meaning, my first slot of 4 hours and 160 pounds. needs to stay linked, otherwise our math is useless. Does it matter which is X and which is Y? No. You could switch the hours to Y and the weight to X, and you'll get the same results.

Next, we will look at three columns below: XY, X^2 and Y^2. If you hadn't guessed it, we will be doing some math. In the XY column, you will multiply the one labeled X by the Y column. In the next column, you will square each X. So, 4 is squared to 16. The same is done with the Y squared column, 160 squared is 25,600. See what I did there?

Table after performing calculations
example of data table

Next, we're going to look at the formula below, and unless you're familiar with statistics, it will be terrifying.

Pearson correlation formula
handwritten formula

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