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

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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

- 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

- Learning Objectives
- After this lecture, you should be able to complete the following Learning Outcomes

- 10.1

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

- Strength increases as the points more closely form an imaginary diagonal line across the center
- Correlations can be described as either positive or negative
- Positive – both variables move in the same direction
- Negative – the variables move in opposite directions

- 10.1

Figure 10.1

- 10.1

Figure 10.2

- Learning Objectives
- After this lecture, you should be able to complete the following Learning Outcomes

- 10.2

10.2

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

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

Figure 10.3

- Learning Objectives
- After this lecture, you should be able to complete the following Learning Outcomes

- 10.3

10.3

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

- Learning Objectives
- After this lecture, you should be able to complete the following Learning Outcomes

- 10.4

10.4

Focuses on the product of the X and Y deviations from their respective means

- Deviations Formula:
- Computational Formula:

10.4

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

Problem 6, 19, 21

10.4

- A Straight-Line Relationship

- Interval Data

- Random Sampling

- Normally Distributed Characteristics

- Learning Objectives
- After this lecture, you should be able to complete the following Learning Outcomes

- 10.5

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

Problem 30

Problems 18, 22 and 31

Add interpretation

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