Statistical Reasoning 1 web 39. Weather Maps 40. Cancer Cure 1 world 41. News Graphics 42. Geographical Data 43. Three-Dimensional Effects 44. Graphic Confusion 45. Outstanding News Graph Copyright © 2011 Pearson Education, Inc.

Correlation and Causality Unit 5E Correlation and Causality A major goal of many statistical studies is to determine whether one factor causes another. In this unit we will discuss how stats can be used to search for correlations that might suggest a cause and effect relationship. Then we will discuss the more difficult task of establishing causality. Copyright © 2011 Pearson Education, Inc.

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. Here are a few examples of correlations Correlation between the variables height and weight for people. Correlation between the variables demand for apples and price of apples. Correlation between practice time and skill among piano players. A scatter diagram is a graph in which each point represents the values of two variables. Copyright © 2011 Pearson Education, Inc.

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. Copyright © 2011 Pearson Education, Inc.

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

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. Copyright © 2011 Pearson Education, Inc.

Inflation and Unemployment CN (1a-b) Prior to the 1990s, most economists assumed that the unemployment rate and the inflation rate were negatively correlated. That is when unemployment goes down, inflation goes up, and vice versa. Table 5.7 shows unemployment and inflation data for the period 1990-2006. 1a. Make a scatter diagram for these data. 1b. Does it appear that the data support the historical claim of a link between the unemployment and inflation rates? Copyright © 2011 Pearson Education, Inc.

Accuracy of Weather Forecasts CN (2) The scatter diagrams in figure 5.48 show two weeks of data comparing the actual high temperature for the day with the same-day forecast (left) and the three-day forecast (right). 2. Discuss the types of correlation on each diagram. Copyright © 2011 Pearson Education, Inc.

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. Copyright © 2011 Pearson Education, Inc.

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. Copyright © 2011 Pearson Education, Inc.

Explanation for a Correlation CN (3) Consider the correlation between infant mortality and life expectancy in Figure 5.46. 3. Which of the three possible explanations for a correlation applies? Explain. Copyright © 2011 Pearson Education, Inc.

How to Get Rich in the Stock Market CN (4) Every financial advisor has a strategy for predicting the direction of the stock market. Most focus on fundamental economic data. An alternative strategy relies on a remarkable correlation between the Super Bowl winner in January and the direction of the stock market for the rest of the year: The stock market tends to rise when a team for the old, pre-1970 NFL wins the Super Bowl. This correlation successfully matched 28 of the first 32 Super Bowls to the stock market. 4. Suppose that the Super Bowl just ended and the winner was the Detroit Lions, and old NFL team. Should you invest all your spare cash (and maybe even some that you borrow) in the stock market? Copyright © 2011 Pearson Education, Inc.

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. Copyright © 2011 Pearson Education, Inc.

Air Bags and Children – Case Study CN (5) 5. After reading through the case study Air Bags and Children, give a brief summary of this case. Copyright © 2011 Pearson Education, Inc.

What is Causing Global Warming – Case Study CN (6) 6. After reading through the case study What is Causing Global Warming, give a brief summary of this case. Copyright © 2011 Pearson Education, Inc.

Quick Quiz CN (7) 7. Answer the 10 multiple choice questions on the 5E Quick Quiz. Copyright © 2011 Pearson Education, Inc.

5E Homework Discussion Paragraph (5D) p.363:1-12 1 web 1 world 42. Success in the NFL 43. Statistical Abstract 44. Air Bags and Children 45. Global Warming 46. Tobacco Lawsuits. 1 world 47. Correlations in the News 48. Causation in the News 49. Legal Causation Class Notes 1-7 Copyright © 2011 Pearson Education, Inc.

Study for Chapter 5 Test p.363 Study the key terms and key ideas and skills for chapter 5. 5A 5B 5C 5D 5E Test next time. No homework. Copyright © 2011 Pearson Education, Inc.