Appendix C Statistics
Descriptive Statistics
Mean: the arithmetic mean, commonly called the "average," is the sum of
all observations divided by the number of observations.
Median: the midpoint of a distribution of values, the value that has the
same number of observations above and below it.
Mode: the most common value observed.
Minimum: the lowest value observed.
Maximum: the highest value observed.
Standard Deviation: a measure of the dispersion of values around the mean.
The standard deviation is the square root of the arithmetic mean of
the squared deviations from the mean.
Measures of Association
Spearman's rho is a nonparametric measure of association, designed to
determine whether two variables share a common rank order, or mon-
otonic form. Spearman's rho is
+
1.0
whenever the rankings corre-
spond exactly and -
1.0
whenever they are exactly reversed. A value
of zero indicates there is no relationship between the two variables.
The formula for Spearman's rho, r" is
6 ID2
r
=
I - ----------
s
0
N(N~
- I)
where D is the difference in rank for each case, and N is the number of
cases.
Kendall's tau is a non parametric measure of association which measures
the degree of association between the rank order of two variables by
counting the number of times pairs of rankings appear in the same
order, subtracting the number which are not in order, and adjusting
so that the value of Kendall's tau is
+
1.0
whenever the rankings cor-
respond exactly and -
1.0
whenever they are exactly reversed. A value
of zero indicates there is no relationship between the two variables.
The formula for Kendall's tau,
ta
is
C-D
ta
= ---------
V2N(N- I)
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