Survey research and design in psychology/Tutorials/Correlation/Correlations and non-linear relations

Correlations and non-linear relations

View the accompanying screencast: [1] The purpose of this exercise is to emphasise the importance of visualising bivariate relationships to check whether a linear correlation best represents the patterns in the data. Data file: xy.sav Syntax: * Correlations between 4 pairs of variables. CORRELATIONS /VARIABLES = x1 y1. CORRELATIONS /VARIABLES = x1 y2. CORRELATIONS /VARIABLES = x1 y3. CORRELATIONS /VARIABLES = x2 y4. * Scatterplots between 4 pairs of variables. GRAPH /SCATTERPLOT(BIVAR)=x1 WITH y1. GRAPH /SCATTERPLOT(BIVAR)=x1 WITH y2. GRAPH /SCATTERPLOT(BIVAR)=x1 WITH y3. GRAPH /SCATTERPLOT(BIVAR)=x2 WITH y4. What do the linear correlations and bivariate scatterplots indicate about the relationship between the following pairs? X1 by Y1 r = .82 is appropriate - a strong, linear relationship X1 by Y2 r = .82 is somewhat accurate, but really the relationship is curvilinear X1 by Y3 r = .82 is not appropriate - really there is a perfect linear relationship plus an outlier X2 by Y4 r = .82 is not appropriate - there is a restricted range for x2 and an outlier

Four sets of data with the same correlation of 0.816