hlth 300 biostatistics for public health practice, raul cruz-cano, ph.d
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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 - PowerPoint PPT PresentationTRANSCRIPT
© 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
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
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
4
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
10.1
Figure 10.1
10.1
Figure 10.2
Identify a curvilinear correlation
Learning ObjectivesAfter this lecture, you should be able to complete the following Learning Outcomes
10.2
8
10.2
A relationship between X and Y that begins as positive and becomes negative, or begins as negative and becomes positive
Curvilinear Correlation
Figure 10.3A non-linear transformation, e.g. square root, might take care of this
Discuss the characteristics of correlation coefficients
Learning ObjectivesAfter this lecture, you should be able to complete the following Learning Outcomes
10.3
11
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
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
13
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
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 ObjectivesAfter this lecture, you should be able to complete the following Learning Outcomes
10.5
18
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
19
Exercise
Problem 30
20
Homework
Problems 18, 22 and 31Add interpretation
© 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