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# HLTH 300 Biostatistics for Public Health Practice, Raul Cruz-Cano, Ph.D. - PowerPoint PPT Presentation

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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• Chapter 10: Correlation

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

5/5/2014, Spring 2014

Final Exam 12e

• 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 12e

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

• 10.1

Differentiate between the strengthand direction of a correlation

10.1 12e

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

Figure 10.1

Figure 10.2

• Learning Objectives 12e

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

• 10.2

Identify a curvilinear correlation

10.2 12e

Curvilinear Correlation

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

Figure 10.3

• Learning Objectives care of this

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

• 10.3

Discuss the characteristics of correlation coefficients

10.3 care of this

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

• Learning Objectives care of this

• 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)

10.4 care of this

Pearson’s Correlation Coefficient (r)

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

• Deviations Formula:

• Computational Formula:

10.4 care of this

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

Exercises care of this

Problem 6, 19, 21

10 care of this.4

Requirements for the Use of Pearson’s r Correlation Coefficient

• A Straight-Line Relationship

• Interval Data

• Random Sampling

• Normally Distributed Characteristics

• Learning Objectives care of this

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

• 10.5

Calculate the partial correlation coefficient

10.5 care of this

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

Exercise care of this

Problem 30

Homework care of this

Problems 18, 22 and 31

CHAPTER SUMMARY care of this

• 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