Flashcards in Ch23Research Deck (18):
What is correlation?
the value an individual exhibits on one variable is related to the value he or she exhibits on another variable; CORRELATION IS NOT CAUSATION
What is the most frequently used correlation coefficient?
the Pearson product moment correlation
What are the other correlation coefficients?
Spearman's rho and Kendall's tau used with ranked or ordinal #s; phi, Cramer's V, and kappa used for nominal data
What are the major assumptions of correlation coefficients?
1 relationships between variables are assumed to be linear, 2 homoscedasticity, 3 both variables have enough variability to demonstrate a relationship
How are correlation coefficients interpreted?
1 the strength of the coefficient itself, 2 the variance shared by the two variables, 3 the statistical significance of the correlation coefficient, 4 the confidence intervals about the correlation coefficient
What is correlation coefficient?
Magnitude and direction of the relationship between variables expressed mathematically
What is the Pearson product moment correlation?
(r) The average of the cross-products of the z scores for the X and Y variables, ex: relationship between functional variable such as gait velocity and physical impairment variable such as knew flexion ROM in patients with TKA
range for correlation coefficient
-1 (inversely negative) to +1 (directly positive)
When do you use Spearmans's Rho and Kendall's tau correlations?
when both variables are ranked or ordinal
When do you use point-biserial correlation?
with one continuous and one dichotomous variable
What correlation coefficients are used with nominal data?
phi, Cramer's V and kappa
Strength of coefficient
Assumes that the meaningfulness of a correlation is the same regardless of context
.00 - .25 Little of any correlation
.26 - .49 Low correlation
.50 - .69 Moderate correlation
.70 - .89 High correlation
.90 – 1.00 Very high correlation
What is the coefficient of determination?
square of the correlation coefficient, (r^2)
The coefficient of determination is an indication of the percentage of variance that is shared by the two variables
What is the statistical significance of the coefficient?
The probability that the calculated correlation coefficient would have occurred by chance if there was no relationship between the variables
How do you calculate the confidence interval around the coefficient?
Converts the r values into z scores, calculates confidence intervals with the z scores, and transforms the z score intervals back into a range of r scores
Limits of interpretation
Interpretation of correlation coefficients should not extend beyond the range of the original data
What is linear regression?
Prediction of future characteristics from previously collected data; a line showing best fit between variables; variables must be defined as IV or DV