1. Correlational Analysis

2. What is a correlation?
A correlation measures the strength of a relationship between two variables. Correlations are plotted on scatter graphs.
Correlations can be used to compare the results of two variables that have both been measured instead of manipulated.
For example, the relationship between height and shoe size can be investigated with a correlation. Neither variable can be manipulated but both can be measured.
What relationship would you expect?
Correlations cannot be used to indicate cause and effect. It may be a coincidence that two variables are correlated, or a third variable could cause changes in both variables.

3. Correlation coefficients
Correlation coefficients are used to measure the strength and direction of correlations. They range from +1.0 to –1.0
The value of the coefficient shows the correlation’s strength. The closer the value is to 0, the less correlated the data is.
The sign of a coefficient shows the direction of a correlation. A value of 1 indicates a positive correlation, –1 is negative.
strong positive correlation
weak negative correlation
Teacher’s notes:
A correlation coefficient of 0 indicates there is no correlation at all.
Worksheet:
The worksheet 3_5_Correlations.doc accompanies this slide.
The solution can be found on the handout 3_5_Correlations_answer.doc.

4. Tasks Read through the booklet about correlations
Sketch the three types of correlation
Problems with correlational analysis…

5. More cat owners 'have degrees' than dog-lovers
People who own a cat are more likely to have a university degree than those with a pet dog, a study by Bristol University suggests. A poll of 2,524 households found that 47.2% of those with a cat had at least one person educated to degree level, compared with 38.4% of homes with dogs. The study said longer hours, possibly associated with better qualified jobs, may make owning a dog impractical. It also found that UK pet ownership was much higher than previously thought. Dr Murray, whose post is funded by the Cats Protection charity, said researchers hoped to repeat the study using the results of the 2011 census to get a clearer idea of trends in UK pet ownership.

6. Correlation coefficients
No correlation -1
perfect negative correlation +1
perfect positive correlation
Weak
Strong
We calculate a coefficient between -1 and +1
The closer to 1 (+ or -) the stronger the relationship

7. Here are some scattergrams and the correlation coefficients that correspond to them. Try matching them up.
+0.91
+0.01
-0.85
+0.22
-0.61
+0.66

8. Tasks Read the evaluation of correlational analysis in your booklet.
Complete the task in your booklet, conducting your own correlational analysis testing the hypothesis that students who do more academic subjects are harder workers.

9. One measure of the functioning of the immune system is the level of activity of white blood cells. What does the graph below tell you about the relationship between stress and the level of activity of white blood cells? (2 marks)