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S1 Revision Notes: Correlation

Section 1: Productmoment correlation coefficient

Recap:
The productmoment correlation coefficient, r, measures how close the points on a scatter graph lie to a
straight line (or more mathematically it measures the strength of the linear relationship between two
variables).

The key points:
r always lies between…

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c) Student I was absent from school for most of the year owing to illness. With reference to this and
to your scatter diagram, discuss briefly whether your interpretation in a) should be amended.
Solution
a) If you use the formulae:
















So,

This indicates a strong positive correlation suggesting that…

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Note 2: You can check you have correctly entered the data into some makes of calculator by using the

memories labelled A, B, C, ..., F (in red). For example if you press RCL A you get the value for ,

RCL B gives , etc.
b) A scatter graph…

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,
where d is the difference in the ranks.

Note: This formula is in the formula book.





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Created on 13/05/2005 10:18 AM by A. Duncombe

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Example:
The table shows the hardness of the water supply (measured in units of parts per million of calcium) and the
cardiovascular disease death rate (in units of deaths per 10000 population) in a random sample of ten
English towns.

Town A B C D E F G H I…

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Often the explanation is that both variables are related to a 3rd variable not being measured. In the example
above for instance both life expectancy and the number of TVs in the population will both be related to the
country's wealth.




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Created on 13/05/2005 10:18 AM by A. Duncombe

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