## Question 806:

Asked on September 7, 2009

Tags:
Pearson r ,
Spearman Correlation

1

## Answer:

No answer provided yet.One often wants to know if two variables are associated with each other (correlated). For example, is there an association between years of experience and salary (in a job setting). We could set this question up in a hypothesis test by framing it this way:

- The null hypothesis is that there is no association between years of experience and salary.
- The alternative hypothesis is that there is an association (more experience = more pay).
- To test the hypothesis we correlate the two variables and obtain a Pearson correlation coefficient r. Let's suppose from a sample of 30 worker's experience and salary we obtain the r of .50. We want to know if an r of .50 is significantly different than 0 (that's the Null hypothesis = no association = r of 0).

- To test the r, we would use this formula
**r / ****sqrt[**(1—**r**^{2})/(**N**—2)**] **and evaluate it using the t-distribution to get a p-value. - If the p-value was below .05 we'd reject the Null Hypothesis and conclude there is an association between salary and experience.

The Spearman correlation (rho) is like the Pearson r except it used the ranks of the data. For example, if you wanted to know if there was a correlation in the ranks of the top 20 most desirable cities and the top 20 most expensive cities to live you'd use the Spearman correlation. It turns out the best way to compute Spearman's rho is to just use the Pearson formula and use the ranks instead of the raw data.