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HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D.

Fox/Levin/Forde, Elementary Statistics in Social Research, 12e. Chapter 10: Correlation. HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D. 5/5/2014 , Spring 2014. Final Exam. Monday 5/19/2014 Time and Place of the class Chapters 9, 10 and 11

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HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D.

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  1. Fox/Levin/Forde, Elementary Statistics in Social Research, 12e • Chapter 10: Correlation HLTH 300 Biostatistics for Public Health Practice,Raul Cruz-Cano, Ph.D. 5/5/2014, Spring 2014

  2. Final Exam • Monday 5/19/2014 • Time and Place of the class • Chapters 9, 10 and 11 • Same format as past two exams • No re-submission of homework • Summer SAS Course

  3. Learning Objectives • After this lecture, you should be able to complete the following Learning Outcomes • 10.1 Differentiate between the strengthand direction of a correlation

  4. 10.1 Correlation Until now, we’ve examined the presence or absence of a relationship between two or more variables What about the strength and direction of this relationship? • We refer to this as the correlation between variables Strength of Correlation • This can be visualized using a scatter plot • Strength increases as the points more closely form an imaginary diagonal line across the center Direction of Correlation • Correlations can be described as either positive or negative • Positive – both variables move in the same direction • Negative – the variables move in opposite directions

  5. 10.1 Figure 10.1

  6. 10.1 Figure 10.2

  7. Learning Objectives • After this lecture, you should be able to complete the following Learning Outcomes • 10.2 Identify a curvilinear correlation

  8. 10.2 Curvilinear Correlation A relationship between X and Y that begins as positive and becomes negative, or begins as negative and becomes positive

  9. A non-linear transformation, e.g. square root, might take care of this Figure 10.3

  10. Learning Objectives • After this lecture, you should be able to complete the following Learning Outcomes • 10.3 Discuss the characteristics of correlation coefficients

  11. 10.3 The Correlation Coefficient Numerically expresses both the direction and strength of a relationship between two variables • Ranges between -1.0 and + 1.0 Direction • Strength • The sign (either – or +) indicates the direction of the relationship • Values close to zero indicate little or no correlation • Values closer to -1 or +1, indicate stronger correlations

  12. Learning Objectives • After this lecture, you should be able to complete the following Learning Outcomes • 10.4 Calculate and test the significance of Pearson’s correlation coefficient (r)

  13. 10.4 Pearson’s Correlation Coefficient (r) Focuses on the product of the X and Y deviations from their respective means • Deviations Formula: • Computational Formula:

  14. 10.4 Testing the Significance of Pearson’s r The null hypothesis states that no correlation exists in the population (ρ = 0) • To test the significance of r, at ratio with degrees of freedom N – 2 must be calculated A simplified method for testing the significance of r • Compare the calculated r to a critical value found in Table H in Appendix C

  15. Exercises Problem 6, 19, 21

  16. 10.4 Requirements for the Use of Pearson’s r Correlation Coefficient • A Straight-Line Relationship • Interval Data • Random Sampling • Normally Distributed Characteristics

  17. Learning Objectives • After this lecture, you should be able to complete the following Learning Outcomes • 10.5 Calculate the partial correlation coefficient

  18. 10.5 Partial Correlation The correlation between two variables, X and Y, after removing the common effects of a third variable, Z When testing the significance of a partial correlation, a slightly different t formula is used

  19. Exercise Problem 30

  20. Homework Problems 18, 22 and 31 Add interpretation

  21. CHAPTER SUMMARY • Correlation allows researchers to determine the strength and direction of the relationship between two or more variables 10.1 • In a curvilinear correlation, the relationship between two variables starts out positive and turns negative, or vice versa 10.2 • The correlation coefficient numerically expresses the direction and strength of a linear relationship between two variables 10.3 • Pearson’s correlation coefficient can be calculated for two interval-level variables 10.4 • The partial correlation coefficient can be used to examine the relationship between two variables, after removing the common effect of a third variable 10.5

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