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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.

 

Scatterplot with weight on the horizontal axis and leg length on the vertical axis, values rise from lower left to upper right and are quite close together.

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.

 

Scatterplot with height on the horizontal axis and leg length on the vertical axis, values rise from lower left to upper right, moderately spread.

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.

 

Scatterplot with height on the horizontal axis and leg length on the vertical axis, values appear to rise from lower left to upper right but there is a high degree of spread.

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.