Correlations Exercises

Correlations are used to describe the strength and direction of a relationship between two variables. A correlation between two variables is known as a bivariate correlation. In this module, the Pearson Product-Moment Correlation will be used when running a correlation matrix. The Pearson correlation coefficient ranges from a value of –1.0 to 1.0. A correlation coefficient is never above 1.0 or below –1.0. A perfect positive correlation is 1.0, and a perfect negative correlation is –1.0. The size of the coefficient determines the strength of the relationship and the sign (i.e., + or –) determines the direction of the relationship. The closer the value is to zero, the weaker the relationship, and the closer the value is to 1.0 or –1.0, the stronger the relationship. A correlation coefficient of zero indicates no relationship between the variables.

A scatterplot is used to depict the relationship between two variables. The general shape of the collection of points indicates whether the correlation is positive or negative. A positive relationship will have the data points group into a cluster from the lower left-hand corner to the upper right-hand corner of the graph. A negative relationship will be depicted by points clustering in the lower right-hand corner to the upper left-hand corner of the graph. When the two variables are not related, the points on the scatterplot will be scattered in a random fashion.

Part I

Using Polit2SetB dataset, create a correlation matrix using the following variables: Number of visits to the doctor in the past 12 months (docvisit), body mass index (bmi), Physical Health component subscale (sf12phys), and Mental Health component subscale (sf12ment). Run means and descriptives for each variable, as well as the correlation matrix.

Follow these steps using SPSS:

1. Click on Analyze, then correlate, then bivariate.

2. Select each variable and move them into the box labeled “Variables.”

3. Be sure the “Pearson and two-tailed” box is checked.

4. Click on the Options tab (upper-right corner) and check “means and standard deviations.” The “Exclude cases pairwise” box should also be checked. Click on Continue.

5. Click on OK.

To run descriptives for docvisit, bmi, sf12phys, and sf12ment, do the following in SPSS:

1. Click on Analyze,then click on Descriptives Statistics, then Descriptives.

2. Click on the first continuous variable you wish to obtain descriptives for (docvisit) and then click on the arrow button and move it into the Variables box. Then click on bmi,and then click on the arrow button and move it into the Variables box. Then click on sf12phys, and then click on the arrow button and move it into the Variables box. Then click on sf12ment,and then click on the arrow button and move it into the Variables box.

3. Click on the Options button in the upper right corner. Click on mean and standard deviation.

4. Click on Continue and then click on OK.

Assignment: Answer the following questions about the correlation matrix.

1. What is the strongest correlation in the matrix? (Provide correlation value and names of variables)

2. What is the weakest correlation in the matrix? (Provide correlation value and names of variables)

3. How many original correlations are present on the matrix?

4. What does the entry of 1.00 indicate on the diagonal of the matrix?

5. Indicate the strength and direction of the relationship between body mass index and physical health component subscale.

6. Which variable is most strongly correlated with body mass index? What is the correlational coefficient? What is the sample size for this relationship?

7. What is the mean and standard deviation for BMI and doctor visits?

Part II

Using Polit2SetB dataset, create a scatterplot using the following variables: x-axis = body mass index (bmi) and the y-axis = weight-pounds (weight).

Follow these steps in SPSS:

1. Click on Graphs, then click on Legacy Dialogs, then click onScatter/Dot.

2. Click on Simple Scatter and then click on Define.

3. Click on weight-pounds and move it to the y-axis box and then click on body mass index and move it to the x-axis box.

4. Click on OK.

To run descriptives for bmi and weight, do the following in SPSS:

5. Click on Analyze,then click on Descriptives Statistics, then Descriptives.

6. Click on the first continuous variable you wish to obtain descriptives for (body mass index), and then click on the arrow button and move it into the Variables box. Then click on weight-pounds,and then click on the arrow button and move it into the Variables box.

7. Click on the Options button in the upper-right corner. Click on mean and standard deviation.

8. Click on Continue and then click on OK.

Assignment:

1. What is the mean and standard deviation for weight and bmi?

2. Describe the strength and direction of the relationship between weight and bmi.

3. Describe the scatterplot. What information does it provide to a researcher?