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Chapter 15: Correlation - Coggle Diagram
Chapter 15: Correlation
The relationship obtained in a correlational study is typically described and evaluated with a statistical measure known as correlation.
Usually the 2 variables are observed as they exist naturally in the environment ---no attempt to control or manipulate the variables.
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- Direction of the Relationship - the sign of the correlation, positive or negative, describes the direction of the relationship.
Positive correlation - 2 variables tend to change in the same direction: as the value of X increases, the Y variable tends to increase.
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- The Form of the Relationship - straight-line relationships; however there are other forms of relationships & special correlations used to measure them.
- The Strength or Consistency of the Relationship - correlation measures the consistency of the relationship. Linear: data fits on a straight line.
Perfect Correlation - always identified by a correlation of 1.00 and indicates a perfectly consistent relationship.
Pearson Correlation - measures the degree & the direction of the linear relationship b/w 2 variables. Sample is identified by "r". Population is identified by "p".
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Sum of Products of Deviations (SP) = sum of (X-Mx)(Y-My). Mx is the mean for the X scores and My is the mean for the Y scores.
- Find the X deviation and the Y deviation for each individual.
- Find the product of the deviations for each individual.
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each x & y values can be transformed into a z-score using the mean and standard deviation for the set of Xs & Ys.
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Positive sign for correlation indicates that points are clustered around a line that slopes up to the right.
High value for correlation (near 1.00) indicates that the points are very tightly clustered to the line.
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- Prediction - if 2 variables are known to be related in some systemic way, it is possible to use one of the variables to make accurate predictions about the other.
Validity - measure the correlation b/w the new test and other measures to demonstrate if new test is valid.
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Correlation & Causation - necessary to conduct a true experiment in which one variable is manipulated. Correlation does not always establish causation.
Correlation & Restricted Range - if correlation is computed from scores that do not represent the full range of possible values, be cautious in interpreting correlation.
Outliers - Individual with an X or Y that is substantially different from the values obtained for other individuals in data set.
Correlation & Strength of Relationship - Coefficient of determination (r^2) because it measures the proportion of variability in one variable that can be determined from the relationship with the other variable.
Partial Correlations - measure relationship between 2 variables while eliminating or holding constant the influence of the third variable.
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Point-Biserial Correlation - measure the strength of the relationship when one of the 2 variables is dichotomous.
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