Is there an association?

Students need to develop their intuitions about the strength of associations between two variables.

The following three scatter plots (representing a random sample from a population) show different degrees of association for two variables. Each is accompanied by an intuitive comment on the degree of association.

Association of weight and leg length for a group of136 nine-year-olds.

There is a strong positive association between the weight and length of leg for nine-year-old children.

Association of height and leg length for a second group of 136 nine-year-olds.

There is a moderate association between the height and length of leg for nine-year-old children.

Association of height and leg length for 136 eighteen-year-olds.

There is a weak positive correlation between the height and leg length of eighteen-year-olds.

The spread of the data is seen to increase as the association becomes weaker.

Some teaching advice on strength of associations and an activity on judging associations are provided.