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Topics: Correlation

Topics: Correlation. The road map Examining “bi-variate” relationships through pictures Examining “bi-variate” relationships through numbers . Correlational Research. Exploration of relationships between variables for better understanding

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Topics: Correlation

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  1. Topics: Correlation • The road map • Examining “bi-variate” relationships through pictures • Examining “bi-variate” relationships through numbers

  2. Correlational Research • Exploration of relationships between variables for better understanding • Exploration of relationships between variables as a means of predicting future behavior.

  3. Correlation:Bi-Variate Relationships • A correlation describes a relationship between two variables • Correlation tries to answer the following questions: • What is the relationship between variable X and variable Y? • How are the scores on one measure associated with scores on another measure? • To what extent do the high scores on one variable go with the high scores on the second variable?

  4. Types of Correlation Studies • Measures of same individuals on two or more different variables • Measures of different individuals on the “same” variable • Measures of the same individuals on the “same” variable(s) measured at different times

  5. Representations of Relationships • Tabular Representation: arrangement of scores in a joint distribution table • Graphical Representation: a picture of the joint distribution • Numerical Represenation: a number summarizing the relationship

  6. Scatter Plot: SAT/GPA(Overachievement Study)

  7. Creating a Scatter Plot • Construct a joint distribution table • Draw the axis of the graph • Label the abscissa with name of units of the X variable • Label the ordinate with the name of the units of the Y variable • Plot one point for each subject representing their scores on each variable • Draw a perimeter line (“fence”) around the full set of data points trying to get as tight a fit as possible. • Examine the shape: • The “tilt” • The “thickness”

  8. Reading the Nature of Relationship • Tilt: The slope (or slant) of the scatter as represented by an imaginary line. • Positive relationship: The estimated line goes from lower-left to upper right (high-high, low-low situation) • Negative relationship: The estimated line goes from upper left to lower right (high-low, low-high situation) • No relationship: The line is horizontal or vertical because the points have no slant

  9. Examples of Various Scatter Plots Demontrating Tilt

  10. Reading the Strength of Relationship • Shape: the degree to which the points in the scatter plot cluster around the imaginary line that represents the slope. • Strong relationship: If oval is elongated and thin. • Weak relationship: If oval is not much longer than it is wide. • Moderate relationship: Somewhere in between.

  11. Examples of Various scatter plots Demontrating Shape (Strength)

  12. Numerical Representation: The Correlation Coefficient • Correlation Coefficient = numerical summary of scatter plots. A measure of the strength of association between two variables. • Correlation indicated by ‘r’ (lowercase) • Correlation range:-1.00 0.00 +1.00 • Absolute magnitude: is the indicator of the strength of relationship. Closer to value of 1.00 (+ or -) the stronger the relationship; closer to 0 the weaker the relationship. • Sign (+ or -): is the indication of the nature (direction,)tilt) of the relationship (positive,negative).

  13. Types of Correlation Coefficients

  14. Influences on Correlation Coefficients • Restriction of range • Use of extreme groups • Combining groups • Outliers (extreme scores) • Curvilinear relationships • Sample size • Reliability of measures

  15. Restriction of Range: Example

  16. Using Extreme Groups Example

  17. Combining Groups Example

  18. Outliers (Extreme Scores) Example

  19. Curvilinear Examples

  20. Coefficient of Determination • Coefficient of Determination: the squared correlation coefficient • The proportion of variability in Y that can be explained (accounted for) by knowing X • Lies between 0 and +1.00 • r2 will always be lower than r • Often converted to a percentage

  21. Coefficient of Determination:Graphical Display

  22. Some Warnings • Correlation does not address issue of cause and effect: correlation ≠ causation • Correlation is a way to establish independence of measures • No rules about what is “strong”, “moderate”, “weak” relationship

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