Section 15 - Statistics: An Introduction Fifth Edition...

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1 Statistics: An Introduction Fifth Edition 562 Section 15: Correlational Inferential Techniques A. Introduction Example: For adults, does intelligence decline as people get older? Take random sample of adults, find age and intelligence. (Ignore pp. 315-316 in text). r is sample correlation (“rho”) is population correlation. Want to test 0 : 0 : 1 0 H H Hypothesis Testing for the Population Correlation Coefficient ( ρ ) 563
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2 564 565 Section 15: Correlational Inferential Techniques B. Sampling Distribution for r Not normal. Skewed negatively for positive . Skewed positively for negative . However, a logrithmic transformation of “ r ” is normal: This is called the Fisher log transformation of the correlation. r r Z 1 1 log 2 1 ' 566 Section 15: Correlational Inferential Techniques C. Fisher’s Z ’ Transformation Table D. 7 (p. 619) gives transformation. Resulting values are referred to as Z ’. For r = 0, Z ’ = 0 For r = .1, Z ’ = .1 So, for small r , r and Z ’ are nearly same. For r = .2, Z ’ = .203 For r = .5, Z ’ = .549 For r = .7, Z ’ = .867 For r = .9, Z ’ = 1.472 As r increases, Z ’ increases more.
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3 567 Section 15: Correlational Inferential Techniques D. Sampling Distribution for Z Z ’ stretches the ends of the scale. Leads to approximately normal sampling distribution if is not too close to 1 or -1, population is bivariate normal, and n 10. Standard Error of Z Depends only on sample size. Z 1 n 3 Procedure: Same as before except use transformed values for r and ρ . Test Statistic: General Form: Logical Idea (but will not work): Actual Computation: 568 569 Section 15: Correlational Inferential Techniques Example: Age and Intelligence Collect data for n = 28 people Step 1: Step 2. 0
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Section 15 - Statistics: An Introduction Fifth Edition...

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