R help - Dec 2010 - Problem applying Chi-square in R and Cochran's Recommendations

Sir,

I have a problem here while applying chisquare test to the following Data (
below the subject of this mail) ...when I wanted to test the significance
using three different free statistical packages, here R, EpiInfo and
OpenEpi.

*Only OpenEpi accepts the test based on Cochran's Recommendations. *
R says " chi squared approximation may be incorrect."
Does it mean the same as what EpInfo saying " Chi square is not valid"

Regards,
Dr. B. Manoj Aravind.

*Table for analysis*

                                  Number of STDs Identified
Type of Health worker     <2                    2 or >

ASHA                             39                    5
AWW                              22                    1
ANM                               1                     12

......................................
*In R the ouput was like this....*
> std<- cbind(c(39,22,1),c(5,1,12))
> std
     [,1] [,2]
[1,]   39    5
[2,]   22    1
[3,]    1   12
> chisq.test(std)
Pearson's Chi-squared test

data:  std
X-squared = 43.8055, df = 2, p-value = 3.074e-10

Warning message:
In chisq.test(std) : *Chi-squared approximation may be incorrect*

In EpInfo the output was this

            Analysis of Single Table
An expected cell is <5.  *Chi square is not valid.*
              Chi square = 43.81
              2 degrees of freedom
              P<0.00000000 <--
.....................................
In OpenEpi the output was like this

Single Table AnalysisVar 2 39 544Var 1221 2311213 621880   Chi Square for R
by C Table
------------------------------
  Chi Square=43.81Degrees of Freedom=2p-value= <0.0000001 Cochran recommends
accepting the chi square if: 1. No more than 20% of cells have expected <
5.2.
No cell has an expected value < 1. In this table: 17% of 6 cells have
expected values < 5.No cells have expected values < 1.  *Using these
criteria, this chi square can be accepted.*  Expected value = row
total*column total/grand total Rosner, B. Fundamentals of Biostatistics. 5th
ed. Duxbury Thompson Learning. 2000; p. 395

	[[alternative HTML version deleted]]

Manoj Aravind <aravindbm at gmail.com> [Wed, Dec 29, 2010 at 03:59:16PM
CET]:
> Sir,
> 
> I have a problem here while applying chisquare test to the following Data (
> below the subject of this mail) ...when I wanted to test the significance
> using three different free statistical packages, here R, EpiInfo and
> OpenEpi.
> 
> *Only OpenEpi accepts the test based on Cochran's Recommendations. *
> R says " chi squared approximation may be incorrect."
> Does it mean the same as what EpInfo saying " Chi square is not
valid"
Yes. Take confidence from the fact that arithmetically all three
programs arrive at the same result (anything but surprising).
The recommendations when to trust Chi-Square are similar. R lets
you look at the source though, so if you type
> chisq.test
you get a result containing the following lines:

        sr <- rowSums(x)
        sc <- colSums(x)
        E <- outer(sr, sc, "*")/n

(so E contains the expected values for the cell entries)

and

	names(PARAMETER) <- "df"
    	if (any(E < 5) && is.finite(PARAMETER)) 
            warning("Chi-squared approximation may be incorrect")

so it seems that R is fussier about the quality of the approximation
than EpiInfo: 

[...]
> ------------------------------
>   Chi Square=43.81Degrees of Freedom=2p-value= <0.0000001 Cochran
recommends
> accepting the chi square if: 1. No more than 20% of cells have expected
< 5.2.
> No cell has an expected value < 1. In this table: 17% of 6 cells have
> expected values < 5.No cells have expected values < 1.  *Using these
> criteria, this chi square can be accepted.*  Expected value = row
> total*column total/grand total Rosner, B. Fundamentals of Biostatistics.
5th
> ed. Duxbury Thompson Learning. 2000; p. 395
> 
Note that these are recommendations which you are free to heed or ignore.

-- 
Johannes H?sing               There is something fascinating about science. 
                              One gets such wholesale returns of conjecture 
mailto:johannes at huesing.name  from such a trifling investment of fact.
http://derwisch.wikidot.com         (Mark Twain, "Life on the
Mississippi")