Correlation and Causality Unit 5E Correlation and Causality Ms. Young

Definitions A correlation exists between two variables when higher values of one variable consistently go with higher values of another or when higher values of one variable consistently go with lower values of another. A scatter diagram is a graph in which each point represents the values of two variables. Ms. Young

Relationships Between Two Data Variables No correlation: There is no apparent relationship between the two variables. Positive correlation: Both variables tend to increase (or decrease) together. Negative correlation: One variable increases while the other decreases. Strength of a correlation: The more closely two variables follow the general trend, the stronger the correlation. In a perfect correlation, all data points lie on a straight line. Ms. Young

Positive Correlation A scatter diagram shows that higher diamond weight generally goes with higher price. Ms. Young

Negative Correlation Present students with various scatter plots of data and have them discuss the type and strength of correlation as well as possible explanations for the correlation. This may be an excellent opportunity to touch on the difference between correlation and causation. A scatter diagram shows that higher life expectancy generally goes with lower infant mortality. Ms. Young

Possible Explanations for a Correlation 1. The correlation may be a coincidence. 2. Both variables might be directly influenced by some common underlying cause. 3. One variable may be a cause of the other. Ms. Young

Explain a Correlation Consider the negative correlation between infant mortality and life expectancy. Which of the three explanations for correlation applies? The negative correlation is probably due to a common underlying cause – the quality of health care. In countries where health care is better in general, infant mortality is lower and life expectancy is higher. Ms. Young

Guidelines for Establishing Causality To investigate whether a suspected cause actually causes an effect, follow these guidelines. Look for situations where the effect is correlated with the suspected cause. Check that the effect is present or absent among groups that differ only in the presence or absence of the suspected cause. Look for evidence that larger amounts of the suspected cause produce larger effects. Account for other potential causes. Test the suspected cause with an experiment. Try to determine how the suspected cause produces the effect. Have students, in small groups, read a statistical study and evaluate it using the six guidelines. Ms. Young