Psychological Statistics Final Study Guide

CHAPTER 13:
 Correlation: association (or relationship) between two scale/quantitative variables (not an IV
and DV)
o Can display this relationship visually in a scatterplot
o Not really about causality
o Line of best fit or “regression line” to make predictions about values not measured
 Bivariate distribution: Joint distribution of two variables
o scores are paired
o Typically the same person provides 2 scores: one for each variable
 Types of correlation: Correlation just detects linear relationships and depends on how you
operationalize the variable
o Positive correlation: high score on one variable and high score on the other OR low
score on one and low on the other (they vary together)
o Negative correlation: scores vary in a way that is opposite, low score on one variable
comes with high score on the other
o Zero correlation: the null hypothesis, no association between variables (cloud of
points or a straight line parallel to the x-axis)
o Perfect correlation: all points fall in a straight line, perfect prediction
 Correlation coefficient: “r” - statistic that quantifies the relation between two variables
o Measure of tendency for paired scores to vary systematically
 High-high; low-low
 High-low; low-high
o Variance: tendency of sample scores to depart from sample mean
o Covariance: tendency of scores to fall on same side of the mean or opposite sides of the
mean
 If scores tend to fall on same side of mean  product of paired deviation
scores will be positive
 If scores tend to fall on opposite sides of the mean  product of paired
deviation scores will be negative
 If scores tend to fall far from the mean  product of paired deviation scores
will be large
 If scores tend to fall close to the mean  product of paired deviation scores
will be small

,  What about units of measurement? We need to standardize
X−M
o Z= - reflects standard deviation from the mean
SD
o “Pearson’s Product Moment Correlation Coefficient” aka R =
Σ ( X−M variable 1 ) ( X −M variable 2 )
SD × SD
 positive or negative, ranges from -1 to +1
 0 means no relationship (dot cloud or straight horizontal line)
 It’s strength (magnitude) of coefficient, not sign, that indicates how large it is
 Correlation ≠ Causation:
o Causality requires manipulation of a variable to test its impact
o At least three possible causal explanations for a correlation
 AB
 BA
 C  A and B
o So typically with research designs that use correlation analyses, we are not inferring
causality, just an association
 Correlations can be used to test:
o Reliability: consistency of its measurement (test and retest reliability – score from
time #1 and score from time #2)
o Validity: accuracy of measurement – does it measure what we want to measure
(correlation between two measures which should be correlated and measure the same
thing)
 Calculating R:
o Start with a scatterplot


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