Statistical Sciences 1023A/B Chapter 11: Chapter 11

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Statistical Sciences
Statistical Sciences 1023A/B
Lori Murray

Chapter 11 Relationships Can Be Deceiving Property of Dr. Lori Murray, 2016. All rights reserved. 115 Relationships Can Be Deceiving Use the following two pictures to speculate on what influences outliers have on correlation For each picture, do you think the correlation is higher or lower than it would be without the outlier? (HINT: correlation measures how closely points fall to a straight line) If you were to draw a scatterplot of the number of women in the work force versus the number of Christmas trees sold in Canada for each year between 1930 and the present, you would find a very strong correlation. Why do you think this would be true? Does one cause the other? Problems with Correlations Outliers can substantially inflate or deflate correlations. o Especially true for small samples o An outlier that is consistent with the trend of the rest of the data will inflate the correlation o An outlier that is inconsistent will substantially decrease it Groups combined inappropriately may mask relationships. Example 1: Highway Deaths and Speed Limits Correlation between death rate and speed limit is 0.55 If Italy removed, correlation drops to 0.098 (much higher death rate than the other countries) If Britain removed, correlation jumps to 0.70
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