Classify the strength of a linear association from r

Classify Pearson's r

For these exercises, |r|<0.25 is reported as little or no linear association; 0.25≤|r|<0.50 is weak, 0.50≤|r|<0.75 is moderate, and 0.75≤|r|≤1 is strong. These are reporting conventions, not universal boundaries. At |r|=1, also state perfect linear association. A small r does not establish independence or rule out a curved relationship

1. Check the possible range Pearson's correlation coefficient must be between -1 and 1 inclusive \(\displaystyle -1\le r\le1\)
2. Use magnitude for strength Compare the magnitude of r with the strength bands, ignoring its sign while deciding strength \(\displaystyle |r|\ge0.75\Rightarrow\text{strong},\quad0.5\le|r|<0.75\Rightarrow\text{moderate}\)
3. Use sign for direction A positive sign gives a positive direction and a negative sign gives a negative direction \(\displaystyle r<0\Rightarrow\text{negative direction},\quad r>0\Rightarrow\text{positive direction}\)
4. Give edges to the stronger band The boundaries 0.25, 0.50 and 0.75 in magnitude belong to the stronger neighbouring band \(\displaystyle |r|=0.75\Rightarrow\text{strong},\quad |r|=0.50\Rightarrow\text{moderate}\)
5. State the exercise convention For these exercises, |r|<0.25 is reported as little or no linear association; 0.25≤|r|<0.50 is weak, 0.50≤|r|<0.75 is moderate, and 0.75≤|r|≤1 is strong. These are reporting conventions, not universal boundaries. At |r|=1, also state perfect linear association. A small r does not establish independence or rule out a curved relationship
6. Scope of labels The cutoffs are a stated exercise convention. A category label does not establish causation, independence or absence of nonlinear association

Worked example

Classify the stated correlation using the taught strength and direction bands

1. \(\displaystyle |r|=|-0.62|=0.62\)Take the absolute value to decide the strength
2. \(\displaystyle 0.50\le0.62<0.75\)The magnitude lies in the moderate band
3. \(\displaystyle r<0\Rightarrow\text{negative direction}\)The negative sign gives the direction
4. \(\displaystyle r=-0.62\Rightarrow\text{moderate negative association}\)Combining the strength and direction gives the classification

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