Examining and Quantifying Relationships Among Variables. Contingency Tables (categorical variables) Correlations (linear relationships) Other measures of association (eta, omega) Multiple regression (more than two variables at a time). Contingency Tables
When all of your variables are categorical, you can use contingency tables to see if your variables are related.
• A contingency table is a table displaying information in cells formed by the intersection of two or more categorical variables.
• A contingency or relationship occurs when there is a pattern between the data on the rows with the data on the columns
Phi = .405
(association measure)2 X 100
PVE = (.7)2 X 100 = 49%
Four sets of data with the same correlation of 0.81, as described by F. Anscombe.
r2 = 0.0
r2 = 0.30
r2 = 0.95
Correlation, bidirectional Diagrams
Regression, X influences Y, unidirectional
• DiagramsThe 9,234.56 is the Y intercept (look at the above regression line; it crosses the Y axis a little below $10,000; specifically, it crosses the Y axis at $9,234.56).
• The 7,638.85 is the simple regression coefficient, which tells you the average amount of increase in starting salary that occurs when GPA increases by one unit. (It is also the slope or the rise over the run).
• Now, you can plug in a value for X (i.e., starting salary) and easily get the predicted starting salary.
• If you put in a 3.00 for GPA in the above equation and solve it, you will see that the predicted starting salary is $32,151.11
• Now plug in another number within the range of the data (how about a 3.5) and see what the predicted starting salary is. (Check on your work: it is $35,970.54)
Shared Variance in Multiple Regression, the same time
all overlap = R2
Unique overlap of an individual predictor (x the same time2) is standardized beta
All overlap of an individual predictor (x2) is Pearson’s r2
Y the same time
Multicollinearity is the area the two predictors have in common, the extent to which the two predictors correlate with each other