Example: Analysis of Associations 1

Exercise 1: Are divorce and number of golf courses related?

1. Download the file "Golf.txt". Save the content of the file as a TEXT file and you will be able to view and edit it with any text editor, such as BBEdit. Note that there are 20 pairs of measures representing the number of golf courses and the mean divorce rate / 100 marriages / year for different regions of the US. The first line contains the names of the two variables, "Golf Courses" and "Divorce Rate".
2. Prepare a scatter plot of the data
3. Calculate the product-moment correlation coefficient (Pearson's r) and determine its level of significance. Based on this analysis what do you conclude about the association between the two variables?
4. Calculate the rank-order corrrelation coefficient (Spearman's ρ) and determine its level of significance. Based on this analysis what do you conclude about the association between the two variables?
5. Only if you consider it appropriate, calculate the Coefficient of Determination for this relationship. In either case explain your reasoning

Exercise 2: Parametric vs. non-parametric methods

1. Use the file "Golf.txt" from exercise 1. Recode the values in both variables with their respective ranks.
2. Calculate the product-moment correlation coefficient (Pearson's r) for the recoded variables and determine its level of significance. Based on this analysis what do you conclude about the association between the two variables?
3. How does the result in 2.2 compare with the result in 1.4? What do you make of this?

Exercise 3: Discuss results of correlation matrix worksheet

1. Worksheet for Calculating Correlation
2. Confirm results running this analysis in R

Competences earned this week:

1. understand how causality relates to the analysis of associations
2. measure associations using a parametric technique
3. measure associations using a non-parametric technique