Chapter 4: Analysing the Data Part II : Descriptive Statistics

# Scatterplots

PearsonÕs r is an elegant and fairly simple numerical concept to understand. Still, it is important not to distance yourself too much from your data by relying on simple numerical descriptions. It is often desirable to get a "feel for" your data by other means (sometimes called "eye-balling"). One way of representing association between variables is the scatterplot. The scattering of plots in the scatterplot give a visual representation of the association between the variables. In Figure 4.9 you will find the scatterplot of the creativity and reasoning data.

The dots depict the X and Y data for that particular applicant. The numbers next to the dots refer to which applicant the point corresponds to. For example, applicant #9 is found in the lower right. The reasoning test score for #9 can be found by projecting the point location down to the X-axisÑ15. Similarly, the creativity test score for applicant #9 corresponds to the height of that point on the Y-axisÑhere, at 10. The applicant numbers wouldnÕt typically be displayed in a scatterplot and are presented here only to aid you in seeing how each applicantÕs data are represented in this scatterplot.

Figure 4.9 Scatterplot of creativity and logical reasoning data.

Positive relationships show up on a scatterplot as a clustering or pattern of dots that appear to move from the lower left to the upper right, as here. Negative relationships show up as a pattern moving from the upper left to the lower right. The stronger the association, meaning the closer the correlation is to -1 or 1, the more "line-like" the scattering of dots will appear. Finally, a zero relationship will look like a random dispersion of dots in the scatterplot (see Ray and Howell for examples).