correlation
association between scores on two variables
scatter diagram
graph showing the relationship between two variables: the values of one variable are along the horizontal axis and the values of the other variable are along the vertical axis; each score is shown as a dot in this two-dimensional space
htm a scatter diagram
1) draw the axes and decide which variable goes on which axis 2) determine the range of values to use for each variable and mark them on the axes 3) mark a dot for each pair of scores
linear correlation
relationship between two variable that shows up on a scatter diagram as athe dots roughly following a straight line
curvilinear correlation
relationship between two variables that shows up on a scatter diagram as dots following a systematic pattern that is not a straight line; any association between two variables other than a linear correlation
no correlation
no systematic relationship between two variables
positive correlation
relationship between two variables in which high scores on one go with high scores on the other, mediums with mediums, and lows with lows; on a scatter diagram, the dots roughly follow a straight line sloping up and to the right
negative correlation
relationship between two variables in which high scores on one go with low scores on the other, mediums with mediums, and lows with highs; on a scatter diagram, the dots roughly follow a straight line sloping down and to the right
cross-product of Z scores
the result of multiplying a person's Z score on one variable by the person's Z score on another variable
perfect correlation
relationship between two variables that shows up on a scatter diagram as the dots exactly following a straight line; correlation of r=1 or r=-1; situation in which each person's Z score on one variable is exactly the same as that person's Z score on the o
correlation coefficient (r)
measure of the degree of linear correlation between two variables, ranging from -1 through 0 to +1; average of the cross-products of Z scores of two variables
r
correlation coefficient
Z(x)
Z score for variable x
Z(y)
Z score for variable y
r=EZ(x)Z(y)/N
formula for correlation coefficient
htf correlation coefficient
1) change all score to Z scores 2) figure the cross-product of the Z scores for each person 3) add up the cross products of the Z scores 4) divide by the number of people in the study
direction of causality
path of causal effect; if X is thought to cause Y, then the direction of causality is from X to Y
longitudinal study
study where people are measured at two or more points in time
true experiment
a study in which participants are randomly assigned to a particular level of a variable and then measured on another variable
statistically significant
conclusion that the results of a study would be unlikely if in fact there were no association in the larger group you want to know about
predictor variable (usually X)
in prediction, variable that is used to predict scores of individuals on another variable
criterion variable (usually Y)
in prediction, a variable that is predicted
prediction model
formula or rule for making predictions; formula for predicting a person's score on a criterion variable based on the person's score on one or more predictor variables
(B)
regression coefficient ina prediction model using Z scores
B
standardized regression coefficient
htf raw score prediction
1) change the person's raw score on the predictor variable to a Z score 2) multiply the standardized regression coefficient by the person's Z score on the predictor variable 3) change the person's predicted Z score on the criterion variable to a raw score
proportion of variance accounted for (r^2)
measure of association between variables used when comparing associations found in different studies or with different variables; correlation coefficient squares; the proportion of the total variance in one variable that can be explained by the other vari
correlation matrix
common way of reporting the correlation coefficients among several variables in a research article; table in which the variables are named on the top and along the side and the correlations among them are all shown
multiple correlation
correlation of a criterion variable with two or more predictor variables
multiple regression
procedure for predicting scores on a criterion variable from scores on two or more predictor variables
multiple correlation coefficient (R)
measure of degree of multiple correlation; positive square root of the proportion of variance accounted for in a multiple regression analysis