Term

Definition
● Correlation describes the linear relationship between observed variables. 


Term

Definition
● One way to compute a correlation coefficient is to convert all the raw scores (both variables) to z scores. ● This will give us two sets of z scores. ● To calculate the correlation, crossmultiply the two sets of z scores and normalize by n. 


Term
The sign of the correlation coefficient 

Definition
● The denominator of r must be positive, so the sign of r will be determined by the numerator (the crossproduct of the z scores). 


Term
The sign and range of the correlation. 

Definition
● For a particular observation (a pair of scores), when the z score of x has the same sign as the z score of y, r will be positive. ● When the z score of x has the same sign as the z score of y, r will be positive. ● The value of r can never be greater than 1.0 nor less than 1.0. ● The sign of the correlation is given by the slope of the scatterplot. ● When the slope is positive, 0 >= r <= 1. ● When the slope is negative, 0 >= r <= 1. 


Term
The shape of the scattergram 

Definition
● When the scatterplot is elongated, the correlation will tend to be “larger” (nearer 1 or 1). ● When the scatterplot is blobby the correlation will tend to be nearer 0. 


Term
The influence of sample means and SDs 

Definition
● Because correlation is a function of the z scores of the variables, r is not affected by the mean or the standard deviation of the original observations. 


Term
The influence of variability 

Definition
● As variability decreases, the correlation increases. ● As variability increases, the correlation decreases. 


Term
The influence of the range of scores 

Definition
● All else being equal, the smaller the range of x and y scores, the lower the correlation coefficient. ● If each score reflects both the true value of the variable and additive random variability, then as the range of scores decrease the apparent influence of variability increases. 


Term
The influence of the slope 

Definition
● For the same reason, the absolute slope of the original variables is also unimportant. 


Term
The influence of linearity 

Definition
● The correlation coefficient only measures the linear relationship between the variables. ● Therefore, if the slope isn't constant throughout the range of scores, r will decline. 


Term
Factors that influence the correlation 

Definition
● The strength of the linear relationship between x and y. ● The strength of any nonlinear relationship between x and y. ● The range of the scores across the variables. ● Measurement error (and other uncontrolled sources of variability). 


Term
Potential problems with correlation 

Definition
● Nonnormally distributed variables. ● Restriction of range. ● Nonlinear relationship between variables. ● Poor measurement reliability. 


Term
Factors influencing correlation 

Definition
● The true underlying relationship between x and y. ● The range of scores in x and y. ● All else being equal, as the range of x or y becomes more restricted, the value of the correlation will decrease. ● When samples are pooled, the correlation of the aggregated data will depend on where the samples lie relative to one another on both the x and y variables. 

