Introduction to Behavioral Statistics

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Introduction to Behavioral Statistics

• Correlation Regression

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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.

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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?

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Correlation
How might we measure relationship between two
sets of scores?
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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?

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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.

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Correlation
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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

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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

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Pearson Product Moment Correlation Coefficient
Calculating Pearsons Product Moment r
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Pearson Product Moment Correlation Coefficient
Example Illustrating Computation of Pearsons r
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Pearson Product Moment Correlation Coefficient
Calculating Pearsons Product Moment r
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Pearson Product Moment r
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Pearson Product Moment r

• Computation of r from raw scores

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Pearson Product Moment r
Computation of r from raw scores
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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.

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Spearman Rank Difference Correlation (Rho)(D)
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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.

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Spearman Rank Difference Correlation (Rho)

• Next We will focus on interpreting a correlation
  coefficient and regression.

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