Correlation is often the first step in what?
identifying potential causal relationships
What does correlation express
quantitatively the size and direction of relationship between variables
Correlation coefficient
statistic which expresses numerically the magnitude and direction of association between two variables
3 types of different relationships
positive linear correlation
negative linear correlation
non-linear correlation
Correlation coefficient characteristics: calculated from
pairs of measurements on variables x and y for the same group of individuals
Correlation coefficient characteristics: values range from
+1 to -1
Correlation coefficient characteristics: +1 means what, 0 means what, and -1 means what?
+1 = perfect positive correlation
-1 = perfect negative correlation
0 = no correlation
Correlation coefficient characteristics: square of the correlation coefficient is
coefficient of determination
The type of correlation coefficient expressed depends on
scale of measurements
Condition where phi is appropriate
both x and y measure on a nominal scale
Conditions where rho is appropriate
both x and y measure on, or transformed to, ordinal scales
Conditions where r is appropriate
both x and y measure on an interval ratio scale
Pearson’s r is for when
both x and y measured on interval or ratio scale
r assumes what?
both variables x and y are normally distributed, and have linear relationship
Pearson’s r is a measure of
the extent to which paired scores are correlated
To calculate r, we need to represent the
position of each paired score within its own distribution
To calculate r, we need to represent the position of each paired score within its own distribution: convert each
raw score to z or standard score
To calculate r, we need to represent the position of each paired score within its own distribution: corrects for
x and y having different means and standard deviations
The closer the relationship between two variables approximates a _________ the more r approaches _______
straight line
1.0
In biological/social sciences, r is not usually _______
1.0
r > 0.7 =
quite high
r = 0.3 - 0.7 =
moderate
r < 0.3 =
weak
Spearman’s p
when at least one of x or y measured on ordinal scale