predictor
1st variable
pearson’s r
correlation coefficient used for interval/ratio data in linear relationships
criterion
2nd variable
correlation coefficient range
-1 to +1 (0=none)
correlation coefficient guidelines
-.20-+.20 = weak
.20-50 = moderate
.50+ = strong
partial correlations
measure relationship between two variables while controlling a third variable by holding it constant
coefficient of determination (R^2)
measure accuracy of correlational predictions (how much variability can be explained by predictor)
R^2 guidelines
.01 = small effect
.09 = medium effect
.25 = large effect
regression
allows us to make predictions using the line of best fit
Y = bX + a
b = slope
a = y-intercept
the error of prediction
Y - Ŷ
total squared error
sum(Y − Ŷ)2
best fitting line has the smallest…
total squared error (least squared error solution)
regression test hypotheses are always
nondirectional
regression test generic hypothesis
the equation using X does/does not account for a significant proportion of variance in the Y scores
point always falling on regression line
(𝑋bar, Ybar)
multiple regression
regression with 2 or more predictor variables for the single criterion variable
beta/standardized b coefficients
can be compared, larger for one variable means it predicts more variance of criterion
spearman rho coefficient used when
both variables measured on ordinal scale
or interval/ratio nonlinear
point-biserial coefficient used when
one variable continuous (interval/ratio) and other two-level (nominal)
phi coefficient Φ used when
association between 2 dichotomous variables (nominal)
chi square x^2 used when
two nominal variables but with dichotomous or multiple group variables
can determine if one variable is independent of other categorical variable
determines if random or by chance
contingency table
chi square table for frequency in each category
NOIR
nominal - categories
ordinal - categorize + rank, distance between each is different
interval - rank + equal distances between scores
ratio - rank, equal distance, + true zero