.-
help for ^iov^                                                     (STB-33: sg59)
.-

Index of ordinal variation
--------------------------

    ^iov^ varlist [^if^ exp] [^in^ exp] [, ^r^ows(#) ^a^ctual ]


Description
-----------

Provides a measure of variability (and its complement) for ordinal variables.
The complement measures lack of variability.  Each variable can either have
the same, fixed, number of categories, by using the option ^actual^, you can
use the actually existing number of categories.  If you don't use either
option, the default number is 5.

The ^iov^ is 0 (and ^ioc^ is 1) when all values fall into one category; the
^iov^ is 1 (and the ^ioc^ is 0) when extreme polarization is present.  The
p-value for a goodness-of-fit test (where the uniform distribution is the null
hypothesis; see @nbgof@) is also presented.  The Berry-Mielke article gives an
algorithm for an exact test and they also make fortran code for this test
available.  The test I used is not exact.

Note that the program expects data in the form of individual observations; if
data are grouped they should be expanded prior to using this program.


Options
-------

Two options, in addition to ^if^ and ^in^ are allowed: ^rows(^#^)^ and
^actual^.  If you use neither, the program assumes that every variable called
should be treated as though it has five categories.  If you use both options,
only the ^actual^ option will be used.

The default value for ^rows^ is 5, chosen simply because the most usual use
for this in my own work is with 5-point Likert scales.  Note that if your
variable has other than 5 possible values you should definitely use this
option as these calculations will be wrong if you have the wrong number of
categories.

The use of ^actual^ tells the program to use the actually existing number of
categories.  Each user must decide whether to use the possible number of
categories or the actual number in every case, but in my experience it is the
possible number that usually, but not always, of interest.  Note further that
using this program with the possible number of rows given eases use on new
data sets that are based on the same data collection form

If you use the ^actual^ option then the output tells you how many rows there
are for each variable; if you use no option, or use the ^rows^ option, then
this information is not supplied.


Examples
--------

The first example is from the originators of this statistic (Berry and Mielke,
1994):

     . ^iov likert^

     Variable   IOV          IOC            p-value
     ---------+------------------------------------
     likert   | 0.6976       0.3024         0.0440

Next we use the same data, except that we have duplicated the above variable
and then set all cases with a value of 5 to missing:

     . ^replace lik2=. if lik2==5^
     (4 real changes made, 4 to missing)

     . ^iov lik*, ac^

     Variable   IOV          IOC            p-value        rows
     ---------+------------------------------------------------
     likert   | 0.6976       0.3024         0.0440            5
     lik2     | 0.8116       0.1884         0.0000            4

Next is a made-up example.  There are two variables and 40 observations in the
data set.  Variable "x" is just the numbers 1-40, while variable "y" has 10
each of the values 1, 2, 3, and 4; I start with a brief description of the two
variables:

     . ^su x y^

     Variable |     Obs        Mean   Std. Dev.       Min        Max
     ---------+-----------------------------------------------------
            x |      40        20.5   11.69045          1         40
            y |      40         2.5   1.132277          1          4

     . ^iov x, r(40)^

     Variable   IOV          IOC            p-value
     ---------+------------------------------------
     x        | 0.6833       0.3167         0.9364


     . ^iov y, r(4)^

     Variable   IOV          IOC            p-value
     ---------+------------------------------------
     y        | 0.8333       0.1667         0.0000

Note the odd result for these two variables when I don't use the ^rows^
option; the p-value is not affected, but the values of the statistics are:

     . ^iov x y^

     Variable   IOV          IOC            p-value
     ---------+------------------------------------
     x        | 0.0250       0.9750         0.9364
     y        | 0.6250       0.3750         0.0000


Reference
----------

Berry, KJ and Mielke, PW, Jr. (1994), "A Test of Significance for the Index of
Ordinal Variation," _Perceptual and Motor Skills_, 79, pp. 1291-1295.


Author
-------

    Richard Goldstein
    Qualitas, Inc.
    richgold@@netcom.com