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

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Hlth 300 biostatistics for public health practice raul cruz cano ph d

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

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 Objectives

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

  • 10.1

Differentiate between the strengthand direction of a correlation


Correlation

10.1

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


Hlth 300 biostatistics for public health practice raul cruz cano ph d

  • 10.1

Figure 10.1


Hlth 300 biostatistics for public health practice raul cruz cano ph d

  • 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

Identify a curvilinear correlation


Curvilinear correlation

10.2

Curvilinear Correlation

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


Hlth 300 biostatistics for public health practice raul cruz cano ph d

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

Figure 10.3


Discuss the characteristics of correlation coefficients

  • Learning Objectives

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

  • 10.3

Discuss the characteristics of correlation coefficients


The correlation coefficient

10.3

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


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

Calculate and test the significance of Pearson’s correlation coefficient (r)


Pearson s correlation coefficient r

10.4

Pearson’s Correlation Coefficient (r)

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

  • Deviations Formula:

  • Computational Formula:


Testing the significance of pearson s r

10.4

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

Exercises

Problem 6, 19, 21


Requirements for the use of pearson s r correlation coefficient

10.4

Requirements for the Use of Pearson’s r Correlation Coefficient

  • 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

Calculate the partial correlation coefficient


Partial correlation

10.5

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

Exercise

Problem 30


Homework

Homework

Problems 18, 22 and 31

Add interpretation


Hlth 300 biostatistics for public health practice raul cruz cano ph d

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


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