Introduction to Behavioral Statistics Correlation & Regression

Correlation Introduction to Correlation & Regression We often see things that are related to one another. height/weight IQ/Performance in School Age/Income We call this relationship Correlation Pearson r is the most common method of measuring relationship. W

Correlation Formula for calculating Pearson’s r Let x and y be two sets of paired observations with standard deviations = sx and sy How might we measure relationship between two sets of scores?

Correlation How might we measure relationship between two sets of scores?

Correlation Is this a good measure of relationship? It does give different values for different degrees of relationship. It does not provide consistency which allows it to be interpreted. Every set of scores will yield a different score The result will vary with the size of the scores. How can we equalize these scores so they will give consistent and meaningful results every time?

Correlation How can we equalize these scores so they will give consistent and meaningful results every time? We can change the scores to standard scores and take the average product of the standard scores for the X and Y variables.

Correlation

Correlation This is called the standard score formula. It is a defining formula It is not a formula that you would use to actually calculate the correlation coefficient. We call this the Pearson Product Moment r

Pearson Product Moment Correlation Coefficient The most widely used method of measuring correlation is the Pearson Product Moment Correlation. We will also consider a Rank Order Correlation Coefficient It is an Ordinal Level Correlation Method Spearman Rank Order Correlation Limits for Correlation are -1 0 +1

Pearson Product Moment Correlation Coefficient Calculating Pearson’s Product Moment r

Pearson Product Moment Correlation Coefficient Example Illustrating Computation of Pearson’s r

Pearson Product Moment Correlation Coefficient Calculating Pearson’s Product Moment r

Pearson Product Moment r

Pearson Product Moment r Computation of r from raw scores

Pearson Product Moment r Computation of r from raw scores

Spearman Rank Difference Correlation (Rho)(D) We sometimes have data we want to correlate which doesn’t meet the requirements for a Pearson r. Not at Interval Level Rho is a correlation technique that requires only ordinal level of measurement.

Spearman Rank Difference Correlation (Rho)(D)

Spearman Rank Difference Correlation (Rho) Advantages and Disadvantages of Rho Advantages: Ease of Computation Skewness influences r but not Rho Disadvantages: It is somewhat less consistent from sample to sample.

Spearman Rank Difference Correlation (Rho) Next We will focus on interpreting a correlation coefficient and regression. Press Here to Return to CLASS PAGE