All About Relationship

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All About Relationship

• Minjuan Wang
• ED 690

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Whats Pearson R? (Karl Pearson)

• One type of correlation coefficient
• The relationship between two variables
• Interval or ratio
• Indicates a linear relationship
• Plotting for the data result in a straight line
• If the Scattergram shows curvilinear, then use
  other correlation coefficient

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How to Interpret Pearson R?

• Eyeballing Estimates, and generally,
• -1.00 (negatively)-gt-0.35-gt-0.65-gt0
  (none)-gt0.35-gt0.65-gt1.00 (positively)
  (approximation)
• To be more accurate, need to consider what r is
  used for and the sample size
• Prediction
• Group prediction r gt0.6 or rlt-0.6
• Individual prediction rgt0.8 or rlt-0.8
• The larger the sample size, the smaller the r

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So How to Determine r from a more accurate
Perspective?

• The concept of statistically significant
• Statistical test compares chance with systematic
  influence
• Bush/Gore 300 differences.
• Class 1 Mean 80 class 2 85, statistically
  different?
• Significance level
• The risk associated with not being 100 confident
  that results are due to the systematic influence
• A 5/ Confidence interval (95)

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To be Statistically significant (the
probability of chance)

• The difference is due to ??? and not due to ???.
• Significance level the risk associated with not
  being 100 confident about ???
• Significance level alpha 0.1, 0.05, 0.01, 0.001
• Normally, a0.05
• P lt 0.05 -gt1 chance in ?? (difference found not
  due to treatment)

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Correlation Coefficient Table

• Does r0.5 indicates a statistically significant
  relationship?
• Use Table A.2 (p. 610)
• Or Use software
• Hypothesis testing
• P value
• The p value indicates if a r is significantly
  different from 0

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Summary

• Pearson r
• Indicate the degree of linear relationship
  between two variables
• Examine a scattergram of two variables before
  using it
• Singular matrix an exact linear relationship
  among variables

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Relationship Data Type (measurement scales) and
Analysis
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Prediction Study

• Single Prediction Study
• Ya bX (p. 333)
• Y criterion score/ X score,predictor
• a constant b coefficient
• College GPA and high-school GPA
• Multiple prediction study (multiple regression
  equation)
• College GPA-gthigh-school GPA, SAT, IQ
• Y a b1x1b2X2b3X3