The assumptions of the Pearson product moment correlation
can be easily overlooked. The assumptions are as follows: level of measurement,
related pairs, absence of outliers, normality of variables, linearity, and
homoskedasticity.
Level of measurement refers to each variable. For a Pearson correlation, each variable should be continuous. If one or both of the variables are ordinal
in measurement, then a Spearman correlation could be conducted instead.
Related pairs refers to the pairs of variables. Each
participant or observation should have a pair of values. So if the correlation
was between weight and height, then each observation used should have both a
weight and a height value.
Absence of outliers refers to not having outliers in either
variable. Having an outlier can skew the results of the correlation by pulling
the line of best fit formed by the correlation too far in one direction or
another. Typically, an outlier is
defined as a value that is 3.29 standard deviations from the mean, or a
standardized value of less than ±3.29.
Linearity and homoskedasticity refer to the shape of the
values formed by the scatterplot. For linearity, a “straight line” relationship
between the variable should be formed.
If a line were to be drawn between all the dots going from left to
right, the line should be straight and not curved. Homoskedasticity refers to the distance
between the points to that straight line. The shape of the scatterplot should
be tube-like in shape. If the shape is cone-like, then homoskedasticity would
not be met.
