Psychology2016

A-12 APPENDIX A

If you do take a statistics course, you will find out that most analyses are done by

computers, and you don’t have to manually go through the long formulas.

We’ve already talked about the correlation coefficient. Let’s see how psychologists

can predict one variable from another by using it. to Learning Objective 1.9.

THE CORRELATION COEFFICIENT

A.6 Explain how statistics are used to predict one score from another.

A correlation is a measure of the relationship between two or more variables. For exam-

ple, if you wanted to know if scores on the SAT are related to grade point average, you

could get SAT scores and GPAs from a group of people and enter those numbers into a

mathematical formula, which will produce a number called the correlation coefficient.

The correlation coefficient represents the direction of the relationship and its strength.

Chapter One discusses correlation in more detail and also emphasizes that correlation

does not allow the assumption that one variable causes the other.

Is the formula for the correlation coefficient really complicated?

Actually, the definitional formula for finding a correlation coefficient is not very

complicated. Here it is:

r =

SZxZy

n

The r is the correlation coefficient, the number representing the strength and direc-

tion of the relationship between the two variables. Zx and Zy are the z scores for each

score. If you remember, the z score tells you how many standard deviations a score is

away from the mean. You would calculate the Zx and Zy for each subject, multiply, and

add them up. Then divide by the number of subjects. There is a very complicated- looking

formula based on the raw scores.

r =

SXY −

SX SY

N

Ñ

qSX^2 −

(SX)^2

rqSY^2 −

(SY)^2

r

N N

Don’t worry. You can do all this work on inexpensive calculators or on comput-

ers using common statistical programs or spreadsheets. Let’s take the following exam-

ple of two sets of scores, one on a test of drawing ability with scores from 1 (poor) to

5  ( excellent) and the other on a test of writing ability using the same scale (see Table A.4).

If we plugged our data set into our calculator or spreadsheet, we would find that

r (the correlation coefficient) equals 0.86. That would indicate a fairly strong correlation.

If you continue studies in statistics, you will find out how to see if the correlation coeffi-

cient we calculated is statistically significant or, if you recall, not due to just dumb luck

when we picked our subjects. In our case, the r is very significant and would happen by

chance only 1 in 100 times!

Remember that the correlation coefficient has values that range between +1.0 and

−1.0. The closer the r is to these values, the stronger the relationship. A positive r means

a positive relationship, whereas a negative r means a negative relationship. to

Learning Objective 1.9; see Figure 1.3.

Our example had us trying to see if two scores were related. It is also possible to

see if three or more scores are related with various techniques. The most common one is

called multiple regression.

correlation coefficient

a number that represents the strength

and direction of a relationship

existing between two variables;

number derived from the formula for

measuring a correlation.

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