Correlation Association between 2 variables 1 2

Suppose we wished to graph the relationship between foot length Height Foot Length and height In order to create the graph, which is called a scatterplot or scattergram, we need the foot length and height for each of our subjects. of 20 subjects. 1

1. Find 12 inches on the x-axis. 2. Find 70 inches on the y-axis. 3. Locate the intersection of 12 and Place a dot at the intersection of 12 and 70. Foot Length Assume our first subject had a 12 inch foot and was 70 inches tall. 1

5. Find 8 inches on the x-axis. 6. Find 62 inches on the y-axis. 7. Locate the intersection of 8 and Place a dot at the intersection of 8 and Continue to plot points for each pair of scores. Assume that our second subject had an 8 inch foot and was 62 inches tall. 1 2

Notice how the scores cluster to form a pattern. The more closely they cluster to a line that is drawn through them, the stronger the linear relationship between the two variables is (in this case foot length and height). 1 2

If the points on the scatterplot have an upward movement from left to right, we say the relationship between the variables is positive. 1 If the points on the scatterplot have a downward movement from left to right, we say the relationship between the variables is negative. 2

A positive relationship means that high scores on one variable are associated with high scores on the other variable are associated with low scores on the other variable. It also indicates that low scores on one variable 1

A negative relationship means that high scores on one variable are associated with low scores on the other variable. are associated with high scores on the other variable. It also indicates that low scores on one variable 1

Not only do relationships have direction (positive and negative), they also have strength (from 0.00 to 1.00 and from 0.00 to –1.00). The more closely the points cluster toward a straight line, the stronger the relationship is

A set of scores with r= –0.60 has the same strength as a set of scores with r= 0.60 because both sets cluster similarly. 1 2

For this procedure, we use Pearson’s r (also known as a Pearson Product Moment Correlation Coefficient). This statistical procedure can only be used when BOTH variables are measured on a continuous scale and you wish to measure a linear relationship. Linear Relationship Curvilinear Relationship NO Pearson r 1

Formula for correlations a 6 5 7

Assumptions of the PMCC 1.The measures are approximately normally distributed 2.The variance of the two measures is similar (homoscedasticity) -- check with scatterplot 3.The relationship is linear -- check with scatterplot 4.The sample represents the population 5.The variables are measured on a interval or ratio scale 1 2

Example We’ll use data from the class questionnaire in 2005 to see if a relationship exists between the number of times per week respondents eat fast food and their weight What’s your guess (hypothesis) about how the results of this test will turn out?.5?.8? ??? 1

Example To get a correlation coefficient: Slide the variables over

Example SPSS output The red is our correlation coefficient. The blue is our level of significance resulting from the test…what does that mean? 1 2 3

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