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Introduction to Behavioral Statistics

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Title: Introduction to Behavioral Statistics


1
Introduction to Behavioral Statistics
  • Correlation Regression

2
Correlation
  • Introduction to Correlation Regression
  • We often see things that are related to one
    another.
  • height/weight
  • IQ/Performance in School
  • Age/Income
  • We call this relationship Correlation
  • Pearson r is the most common method of measuring
    relationship.

3
Correlation
  • Formula for calculating Pearsons r
  • Let x and y be two sets of paired observations
    with standard deviations sx and sy
  • How might we measure relationship between two
    sets of scores?

4
Correlation
How might we measure relationship between two
sets of scores?
5
Correlation
  • Is this a good measure of relationship?
  • It does give different values for different
    degrees of relationship.
  • It does not provide consistency which allows it
    to be interpreted.
  • Every set of scores will yield a different score
  • The result will vary with the size of the scores.
  • How can we equalize these scores so they will
    give consistent and meaningful results every time?

6
Correlation
  • How can we equalize these scores so they will
    give consistent and meaningful results every
    time?
  • We can change the scores to standard scores and
    take the average product of the standard scores
    for the X and Y variables.

7
Correlation
8
Correlation
  • This is called the standard score formula.
  • It is a defining formula
  • It is not a formula that you would use to
    actually calculate the correlation coefficient.
  • We call this the Pearson Product Moment r

9
Pearson Product Moment Correlation Coefficient
  • The most widely used method of measuring
    correlation is the Pearson Product Moment
    Correlation.
  • We will also consider a Rank Order Correlation
    Coefficient
  • It is an Ordinal Level Correlation Method
  • Spearman Rank Order Correlation
  • Limits for Correlation are -1 0 1

10
Pearson Product Moment Correlation Coefficient
Calculating Pearsons Product Moment r
11
Pearson Product Moment Correlation Coefficient
Example Illustrating Computation of Pearsons r
12
Pearson Product Moment Correlation Coefficient
Calculating Pearsons Product Moment r
13
Pearson Product Moment r
14
Pearson Product Moment r
  • Computation of r from raw scores

15
Pearson Product Moment r
Computation of r from raw scores
16
Spearman Rank Difference Correlation (Rho)(D)
  • Rho
  • We sometimes have data we want to correlate which
    doesnt meet the requirements for a Pearson r.
  • Not at Interval Level
  • Rho is a correlation technique that requires only
    ordinal level of measurement.

17
Spearman Rank Difference Correlation (Rho)(D)
18
Spearman Rank Difference Correlation (Rho)
  • Advantages and Disadvantages of Rho
  • Advantages
  • Ease of Computation
  • Skewness influences r but not Rho
  • Disadvantages
  • It is somewhat less consistent from sample to
    sample.

19
Spearman Rank Difference Correlation (Rho)
  • Next We will focus on interpreting a correlation
    coefficient and regression.

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