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

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Correlations and non-linear relations
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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.

* 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?

  1. X1 by Y1
    • r = .82 is appropriate - a strong, linear relationship
  2. X1 by Y2
    • r = .82 is somewhat accurate, but really the relationship is curvilinear
  3. X1 by Y3
    • r = .82 is not appropriate - really there is a perfect linear relationship plus an outlier
  4. 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