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Topics: Correlation

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- The road map
- Examining “bi-variate” relationships through pictures
- Examining “bi-variate” relationships through numbers

- Exploration of relationships between variables for better understanding
- Exploration of relationships between variables as a means of predicting future behavior.

- 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?

- 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

- 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

- 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”

- 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

- 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.

- 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).

- Restriction of range
- Use of extreme groups
- Combining groups
- Outliers (extreme scores)
- Curvilinear relationships
- Sample size
- Reliability of measures

- 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

- 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