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