Lesson 22 Comparing correlations

Comparing correlations

Overview Resources
Worksheet 1
This is a follow-up to TM18: Prediction and correlation. The emphasis is on moving from the intuitive notion that a wide scatter means a poor correlation to comparing correlations quantitatively. Three different data sets are compared by reducing them to four-cell tables of confirming and disconfirming cases. Correlation is estimated as a ratio of confirming to disconfirming cases.
Correlation as the degree of fit between one variable and another.
• Data handling: median and range; estimation and precision,
• Scatter graphs and lines of best fit,
• Identifying key features present in the data.
• EPISODE 1
Intuitive comparisons of correlation
Pupils handle three different correlation scatters, comparing two grades, two marks, or two race times. They look at each in terms of the range of prediction, or how useful a ‘line of best fit’ is. They then look for a measure of the usefulness in a semi- quantitative way: the ratio of the range of one variable for each value of the second, to the full range of variation possible. Pupils try to verbalise their intuition on why one scatter graph is useful for prediction (good correlation), while another is not.
EPISODE 2
Measuring correlation using confirming and disconfirming values
Pupils go back to the same data to organise it differently, this time in relation to a hypothesis of a relationship such as ‘the better a person is in one subject, the better they are in the other’ This leads to a four cell table for each scatter graph, which is then looked at in terms of the ratio of confirming to disconfirming cases.