Hi,
didn't get your name.
For large tables (5 X 5) or bigger the dist of the log of the cross product
ratios tends to normality. there are (nC2)**2/2 of these (200 in a 5X5
table. The chi-sq test for independence fits a main effects loglinear model
to the table and this can be expressed in terms of the cross product ratios
(see Discrete Multivariate Analysis by bishop fineburg and holland 1975).
Problems only arise when there are a lot of zeros as this posits weight in
the log dist at +/- infinity.
This in turn will result in a poor chi-sq approx.
Gerard
dsimcha
<dsim...@yahoo.co
m> To
Sent by: r-help@r-project.org
r-help-boun...@r- cc
project.org
Subject
[R] Validity of Pearson's
03/06/2009 04:32 Chi-Square for Large Tables
Is Pearson's Chi-Square test for contingency tables asymptotically unbiased
for large tables (large degrees of freedom) regardless of the expected
values in each cell? The rule of thumb is that Pearson's Chi-square should
not be used when large numbers of cells have expected values < 5. However,
I compared the results on 4x4 contingency tables for R's chisq.test using
chi-square approximation vs. chisq.test using a large number of monte carlo
simulations, and the results agree within a fairly small error. This is
true even when every cell of the table has an expected value < 2. I tried
several tables, but the best example was:
4 1 1 1
1 4 1 1
1 1 4 1
1 1 1 4
As expected, the chi-square approximation appears to be very poor when both
the expected values and degrees of freedom are small. Is there a good
theoretical reason why the chi-square test seems to perform well on large
contingency tables even with small expected values? Are the standard rules
of thumb overly simplistic?
--
View this message in context:
http://www.nabble.com/Validity-of-Pearson%27s-Chi-Square-for-Large-Tables-tp23844791p23844791.html
Sent from the R help mailing list archive at Nabble.com.
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
**********************************************************************************
The information transmitted is intended only for the person or entity to which
it is addressed and may contain confidential and/or privileged material. Any
review, retransmission, dissemination or other use of, or taking of any action
in reliance upon, this information by persons or entities other than the
intended recipient is prohibited. If you received this in error, please contact
the sender and delete the material from any computer. It is the policy of the
Department of Justice, Equality and Law Reform and the Agencies and Offices
using its IT services to disallow the sending of offensive material.
Should you consider that the material contained in this message is offensive
you should contact the sender immediately and also mailminder[at]justice.ie.
Is le haghaidh an duine nó an eintitis ar a bhfuil sí dírithe, agus le haghaidh
an duine nó an eintitis sin amháin, a bheartaítear an fhaisnéis a tarchuireadh
agus féadfaidh sé go bhfuil ábhar faoi rún agus/nó faoi phribhléid inti.
Toirmisctear aon athbhreithniú, atarchur nó leathadh a dhéanamh ar an
bhfaisnéis seo, aon úsáid eile a bhaint aisti nó aon ghníomh a dhéanamh ar a
hiontaoibh, ag daoine nó ag eintitis seachas an faighteoir beartaithe. Má fuair
tú é seo trí dhearmad, téigh i dteagmháil leis an seoltóir, le do thoil, agus
scrios an t-ábhar as aon ríomhaire. Is é beartas na Roinne Dlí agus Cirt,
Comhionannais agus Athchóirithe Dlí, agus na nOifígí agus na nGníomhaireachtaí
a úsáideann seirbhísí TF na Roinne, seoladh ábhair cholúil a dhícheadú.
Más rud é go measann tú gur ábhar colúil atá san ábhar atá sa teachtaireacht
seo is ceart duit dul i dteagmháil leis an seoltóir láithreach agus le
mailminder[ag]justice.ie chomh maith.
***********************************************************************************
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
