Copyright © 2011 Pearson Education, Inc. Statistical Reasoning

Copyright © 2011 Pearson Education, Inc. Slide 5-3 Unit 5E Correlation and Causality

5-E Copyright © 2011 Pearson Education, Inc. Slide 5-4 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.

5-E Copyright © 2011 Pearson Education, Inc. Slide 5-5 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. Relationships Between Two Data Variables

5-E 4-6 Slide 5-6 Correlation - Visually

5-E Copyright © 2011 Pearson Education, Inc. Slide 5-7 Positive Correlation A scatter diagram shows that higher diamond weight generally goes with higher price.

5-E Copyright © 2011 Pearson Education, Inc. Slide 5-8 Negative Correlation A scatter diagram shows that higher life expectancy generally goes with lower infant mortality.

5-E Copyright © 2011 Pearson Education, Inc. Slide 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. Possible Explanations for a Correlation

5-E Copyright © 2011 Pearson Education, Inc. Slide 5-10 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.

5-E A way that two variables can be related even though there is not a causal relation is through a lurking variable. A lurking variable is related to both the explanatory and response variable. For example, ice cream sales and crime rates have a very high correlation. Does this mean that local governments should shut down all ice cream shops? No! The lurking variable is temperature. As air temperatures rise, both ice cream sales and crime rates rise Slide 5-11 Lurking Variables

5-E Copyright © 2011 Pearson Education, Inc. Slide 5-12 In Nenno, WI, it is found that 90% of all citizens of the village drive Fords. Can we conclude that the citizens of Nenno believe that Fords are superior to all other car brands? What are some possible lurking variables in this situation? How could we design an experiment to test the situation? Example

5-E Copyright © 2011 Pearson Education, Inc. Slide Look for situations where the effect is correlated with the suspected cause. 2.Check that the effect is present or absent among groups that differ only in the presence or absence of the suspected cause. 3.Look for evidence that larger amounts of the suspected cause produce larger effects. 4.Account for other potential causes. 5.Test the suspected cause with an experiment. 6.Try to determine how the suspected cause produces the effect. To investigate whether a suspected cause actually causes an effect, follow these guidelines. Guidelines for Establishing Causality

5-E Assignment Read Case Study Air Bags and Children p Read Case Study What is Causing Global Warming? P P Copyright © 2011 Pearson Education, Inc. Slide 5-14