Learning Outcomes:

After having completed this topic you should be able to:

• explain the concept of simple linear correlation
  

• identify the implications of various possible values of the correlation coefficient
  

• compute a simple linear correlation using SPSS
  

SELF-CHECK

a) Why would you be interested in the relationship between two variables?

b) What is a scatter diagram?

Introduction

Researchers are often concerned with the way two variables relate to each other for a given groups of persons such as students in schools, workers in a factory or office. For example, do students who have higher scores in mathematics also have higher scores in mathematics? Is there a relationship between a person's self-esteem and his or her personality? Is there a relationship between attitudes towards reading and the number of books read? Is there a relationship between years of experience as a teacher and attitudes towards teaching? These are some of the questions asked by educational researchers. To answer these questions, you must make observations or collect data for each variable for a group of persons.

Example:

Data was gathered for the following two variables from a sample of 12 students.

Student No.      IQ Test     Scores (Science Test)

                        (X)                   (Y)

   1                120                   31

   2                112                   25

   3                110                   19

   4                120                   24

   5                103                   17

   6                126                   28

   7                113                   18

   8                114                   20

   9                106                   16

  10               108                   15

  11               128                    27

  12               109                   19

Scatter Diagram Showing the Relationship between IQ Scores (X axis) and Science Score (Y axis) for 12 Students

• Each unit or student is represented by a point on the scatter diagram. A dot is placed for each student at the point of intersection of a straight line drawn through his IQ score perpendicular to the X axis and through his Science score perpendicular to the Y axis. For example, a student who obtained an IQ score of 120 also obtained a Science score of 24. The intersection between these lines is represented by the dot 'A'.
  

• The scatter diagram above shows a moderate positive relationship between IQ Scores and Science Scores. However, we do not have a summarised measure of this relationship. There is need for a more precise measure to describe the relationship between the two variables. You need a numerical descriptive measure of the correlation between IQ scores and Science scores which will be discussed later.
  

A

LINEAR

CORRELATION

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