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)