Correlation Flashcards
Correlation
A specific measure of how two variables are related to each other linearly
Correlation use 1
Describe pattern of change in values of two factors
correlation use 2
determine whether the pattern observed in a sample is also present in the population of the sample
Correlation coefficient (R)
Measures strength and direction of the linear relationship
Correlation values
between -1.0 and 1.0, the sign indicating only direction or slope
R formula
r=SSxy/sqrt(SSx)(SSy)
Step 1 in finding correlation
obtain mean of x and mean of y
step 2 in finding correlation
obtain deviation of x and deviation of y using means and each x (sum should equal 0)
step 3 in finding correlation
multiply the deviation scores (x-Mx)(y-My)
Step 4 in finding correlation
Square each individual variation score, both x and y separately
Step 5 in finding correlation
SSxy=the sum of the multiplied variation scores from step 3
step 6 in finding correlation
SSx/SSy=the sum of each squared variation score, both x and y.
Coefficient of Determination (eta^2 for correlations)
Measure of proportion of variance of one factor (Y) that can be explained by a second factor (X)
Covariance
The extent to which X and Y vary together, represented by the data points proximity to a regression line.
Positive Correlation
As values of one factor increase, the values of the second factor also increase (r greater than zero, less than/equal to 1)
negative correlation
As values of one factor increase, the values of the other factor decrease (r is less than zero but greater than/equal to -1)
Pearson Product-moment correlation coefficient
a way to measure the direction and strength of a linear relationship between two interval/ratio factors)
Pearson correlation coefficient (r) formula
r=sum of (Zx*Zy)/n-1
Raw Score Pearson Correlation formula
r=SSxy/sqrt(SSx*SSy) (Covariance divide by the total variance)
Restriction of Range
When we only look at one “section” of an entire sample, that particular section might actually have a different relationship to itself than it does to the rest of the entire sample/population; a correlation does not necessarily represent the entire population, and should only be compared within that context.
Third Variable
A variable that is not X or Y but is also related to the correlation between X and Y (Summer is related to Ice Cream and Crime, though it does not cause the relationship)
Reverse Causality
In correlation, the causes go both directions: worse mood may be caused by more eating, or more eating can be caused by worse mood.
Systematic Causality
A feedback loop: the more we eat, the worse we feel, and thus the more we eat.
Confound Variable
Changes in factors caused by a third variable not measured
