Estimate r from a scatterplot

Estimate Pearson's r from a scatterplot

Estimate r in two stages. Read the sign from the left-to-right direction, then estimate the magnitude from how closely the points follow a straight path

1. Read the sign from direction A cloud that rises from left to right gives a positive r, while a cloud that falls gives a negative r \(\displaystyle \text{rising}\Rightarrow r>0,\quad\text{falling}\Rightarrow r<0\)
2. Read magnitude from clustering The magnitude of r is large when points lie close to a straight path and small when they are widely spread \(\displaystyle \text{tight clustering}\Rightarrow |r|\text{ near }1\)
3. Ignore slope size The slope depends on the scales and units on the axes, so it does not measure the magnitude of r \(\displaystyle \text{steep slope}\not\Rightarrow |r|\text{ near }1\)
4. Keep near-zero estimates small A cloud with little linear pattern has an r estimate near zero, even if it has a slight visual tilt \(\displaystyle \text{little linear pattern}\Rightarrow |r|\approx0\)

Worked example

For these six fictional card-sorting sessions, choose the closest estimate of Pearson’s r from −0.9, 0.1, 0.5 and 0.9. A visual estimate does not determine an exact two-decimal coefficient

1. \(\displaystyle \text{rising tendency}\Rightarrow r>0\)The direction rules out the negative candidate
2. \(\displaystyle \text{close to a straight path}\Rightarrow |r|\text{ near }1\)Of the positive candidates, 0.9 best matches the visible clustering. Slope size is not the strength
3. \(\displaystyle S_{xx}=S_{yy}=17.5,\quad S_{xy}=15.5,\quad r=\frac{31}{35}\approx0.886\)An independent calculation from the supplied pairs confirms that 0.9 is the closest candidate. This calculation verifies the visual choice; it is not precision inferred from the picture alone

Common mistakes

Difficulty levels

Questions about this topic

In this chapter