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TRANSCRIPT
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© 2014 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • 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
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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
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Differentiate between the strength and direction of a correlation
Learning ObjectivesAfter this lecture, you should be able to complete the following Learning Outcomes
10.1
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10.1
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
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10.1
Figure 10.1
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10.1
Figure 10.2
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Identify a curvilinear correlation
Learning ObjectivesAfter this lecture, you should be able to complete the following Learning Outcomes
10.2
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10.2
A relationship between X and Y that begins as positive and becomes negative, or begins as negative and becomes positive
Curvilinear Correlation
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Figure 10.3A non-linear transformation, e.g. square root, might take care of this
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Discuss the characteristics of correlation coefficients
Learning ObjectivesAfter this lecture, you should be able to complete the following Learning Outcomes
10.3
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The Correlation Coefficient10.3
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
Numerically expresses both the direction and strength of a relationship between two variables
• Ranges between -1.0 and + 1.0
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Calculate and test the significance of Pearson’s correlation coefficient (r)
Learning ObjectivesAfter this lecture, you should be able to complete the following Learning Outcomes
10.4
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10.4
Focuses on the product of the X and Y deviations from their respective means
– Deviations Formula:
– Computational Formula:
Pearson’s Correlation Coefficient (r)
2 2
SP
SS SSX Y
X X Y Yr
X X Y Y
2 2 2 2
XY NXYr
X NX Y NY
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10.4
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
2
2
1
r Nt
r
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Exercises
Problem 6, 19, 21
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Requirements for the Use of Pearson’s r Correlation Coefficient
10.4
A Straight-Line Relationship
Interval Data
Random Sampling
Normally Distributed Characteristics
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Calculate the partial correlation coefficient
Learning ObjectivesAfter this lecture, you should be able to complete the following Learning Outcomes
10.5
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10.5
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
. 2 21 1XY XZ YZ
XY Z
XZ YZ
r r rr
r r
.
2.
3
1XY Z
XY Z
r Nt
r
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19
Exercise
Problem 30
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Homework
Problems 18, 22 and 31Add interpretation
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© 2014 by Pearson Higher Education, IncUpper Saddle River, New Jersey 07458 • 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
10.1
10.2
10.3
10.4
10.5