Covariance, correlation, scatterplots

Scatterplots can be used to visualize the relationship between two variables (X & Y) and can be helpful in detecting potential bivariate outliers in one's data. The covariance is an index of the relationship between two variables (X & Y) in their original scales of measurement. This index can range from negative to positive infinity, with a value of 0 indicating no relationship between X & Y.

Pearson's correlation provides an index of the relationship between two standardized variables (M=0, SD=1) and ranges between -1 (signifying a perfect negative association) to +1 (signifying a perfect positive association. A value of 0 indicates no relationship between the two variables. Pearson's r assumes that the relationship between X & Y is linear (as opposed to curvilinear). It does not require one's variables be normally distributed. Nevertheless, the magnitude of correlation coefficients may be attenuated when the distributions of X & Y exhibit different shapes (see e.g., Schumacker & Lomax, 2010). Other factors that may impact correlations are the presence of outliers and range restriction on one or both variables.

Cohen (1988) suggested the following rules of thumb for judging the magnitude of a correlation coefficient within the social and behavioral sciences: |r|=.10 (small relationship); |r|=.30 (medium relationship; |r|=.50 (large relationship.

--------------------------------------------------------------------------------------------------------------------------------------------------------------------

General introduction to scatterplots and Pearson's r correlation coefficient (June 2020): video, Excel file

Basic introduction to scatterplots, correlation, and covariance using SPSS (June 2020): Powerpoint, SPSS data file, video demonstration (accompanying Powerpoint)

Short demonstration on point-biserial correlation using SPSS (June 2020): video, SPSS data

Computing the sample covariance and Pearson's r (July, 2019): video, Excel sheet used in demo

--------------------------------------------------------------------------------------------------------------------------------------------------------------------

Older presentations (not as high quality but you might find useful):

Powerpoint presentation

Introduction to correlation, covariance, and scatterplots in SPSS (video) SPSS data file

Review of correlation, covariance, and scatterplots in Excel (video), Excel data file

Another correlation coefficient: Point-biserial correlation, SPSS data file

Video of scatterplots and correlation, Powerpoint, SPSS file 1, SPSS file 2, SPSS file 3