© 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey All Rights Reserved HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D. 5/5/2014, Spring 2014 Fox/Levin/Forde, Elementary Statistics in Social Research, 12e Chapter 10: Correlation 1

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 2

Differentiate between the strength and direction of a correlation Learning Objectives After this lecture, you should be able to complete the following Learning Outcomes 10.1

4 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 Correlation

10.1 Figure 10.1

10.1 Figure 10.2

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

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

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

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

The Correlation Coefficient 10.3 DirectionStrength 11 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 Numerically expresses both the direction and strength of a relationship between two variables Ranges between -1.0 and + 1.0

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

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

The null hypothesis states that no correlation exists in the population (ρ = 0) To test the significance of r, a t 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 Testing the Significance of Pearson’s r

15 Exercises Problem 6, 19, 21

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

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

18 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 Partial Correlation

19 Exercise Problem 30

20 Homework Problems 18, 22 and 31 Add interpretation

© 2014 by Pearson Higher Education, Inc Upper Saddle River, New Jersey All Rights Reserved Correlation allows researchers to determine the strength and direction of the relationship between two or more variables In a curvilinear correlation, the relationship between two variables starts out positive and turns negative, or vice versa The correlation coefficient numerically expresses the direction and strength of a linear relationship between two variables Pearson’s correlation coefficient can be calculated for two interval-level variables The partial correlation coefficient can be used to examine the relationship between two variables, after removing the common effect of a third variable CHAPTER SUMMARY