How to interpret Monte Carlo Simulation in SPSS outputs
João Maroco
If a I do a chi-square test (Analyse/crosstabs/Chi-square) and select
the option Monte Carlo in the "Exact" module, What does the obtained
p-value indicates? Is it the probability of obtaining a crosstabs
table as the one observed in a large number of Samples (10000) if H0
is true? or is it the probability of obtainig a X2 statistic as large
(or larger than?) as the one observed in the data?
Thanks and Season greetings,
Joao
Rich Ulrich
some comments that are relevant to the Monte Carlo on tables.
On 20 Dec 2002 01:32:48 -0800, jpma...@ispa.pt (João Maroco) wrote:
> This is a quite basic question, I wonder if someone could help.
>
> If a I do a chi-square test (Analyse/crosstabs/Chi-square) and select
I think this is the test that I get, from (Analyze/ Descriptive
statistics/ Chi-square); and which the online help file says is
at (Analyze/ Summaries/ Chi-square).
> the option Monte Carlo in the "Exact" module, What does the obtained
> p-value indicates? Is it the probability of obtaining a crosstabs
> table as [*] the one observed in a large number of Samples (10000) if H0
> is true? or is it the probability of obtainig a X2 statistic as large
> (or larger than?) as the one observed in the data?
... There seem to be words missing from the question, where I
placed [*]. Is this a question,
"Does the Monte Carlo answer show the *tail* probability,
like it usually shows for test statistics -- call this p -- or does it
show 1-p, which would thus be defined as the cumulative
probability?"
My guess is "p" but it should be evident from any few tables.
And, to be more complete, the online documentation for 10.1
says that it is the *Pearson chisquared* that determines the
ordering for how-extreme the tables are considered to be,
for an 'exact' determination.
You might be aware that the RxK table has at least two popular
chisquared tests reported, the Pearson and Maximum Likelihood:
The two effectively differ in how much they punish [multiple, small
deviations] versus [a single large deviation]. - You might find it
worth noting, that the Likelihood test says that the table with
[multiple, small deviations] is relatively more extreme.
These tests belong to the family of "power divergence statistics"
of Cressie and Read (1984); according to Agresti (1990).
In his Problem 3.26, Agresti gives names to 3 additional members
of the family. Any one of them is potentially the basis for
describing a table as extreme.
If the Crosstabs procedure gives several other statistics, those
will be separately tabulated -- I think that each one, separately, can
use up the time-limit that is specified, if one is specified.
--
Rich Ulrich, wpi...@pitt.edu
http://www.pitt.edu/~wpilib/index.html