Chapter 14
Monotonic relationship
A consistently ONE-DIRECTIONAL relationship between two variables.
Restricted range
A narrow range of performance scores that makes it difficult to obtain a significant validity coefficient.
Sum of products (SP)
Measures the amount of covariability between two variables
Regression equation for Y
Ŷ= bx+a
Standardized form of the regression equation
ˆzY =(beta)zX
Perfect correlation
-1.00 or +1.00 indicates a perfectly consistent relationship. each change in X is accompanied by a perfectly predictable change in Y.
Outliers
One or two extreme data points, can have a dramatic effect on the value of a correlation
1. Convert each dichotomous variable into numerical values (1 and 0) 2. Use regular Pearsons formula with converted scores
Phi
Slope
Rise over run
r^2SSy
SSregression (predicted variability)
(1-r^2)SSy
SSresidual (unpredicted variability)
Correlation
Statistical technique used to measure and describe the relationship between two variables
Coefficient of determination (r^2)
The percent of changes in y that are explained by changes in x
Negative correlation
The two variables go in opposite directions. As the X variable increases, the Y variable decreases. AKA: inverse relationship.
Positive correlation
The two variables tend to change in the same direction: As the value of X increases, the Y variable also tends to increase; when the X decreases, the Y variable also decreases.
Point-biserial correlation
used when only one of the variables is dichotomous
Linear equation
Y = bx+a (graph is a line)
Regression
a statistical technique for finding the best-fitting straight line for a set of data
dichotomous/binomial variable
a variable with only two values
Phi-coefficient (φ)
correlation between 2 variables when BOTH are dichotomous
Ex: if we are looking at gender, male and female are _____
dichotomous variables
Standard error of estimate
distance between the predicted Y values on regression line and the actual Y values in the data
Pearson correlation
measures the degree and the direction of the linear relationship between two variables
"As one variable increases, the other variable also tends to increase or decrease." is an example of a....
monotonic relationship
a correlation of 0 indicates...
no consistency at all. For a correlation of 0, the data points are scattered randomly with no clear trend
Regression line
resulting "best-fitting" straight line
Correlation matrix
table of the correlation coefficients the variables are named on the top and along the side and the correlations among them are displayed
Analysis of regression
the process of testing the significance of a regression equation
Least-squared-error solution
the regression line that has the smallest total squared error
Y-intercept
the y-coordinate of a point where a graph crosses the y-axis
