Chi square and Fisher's Exact Test

[preet]

Hi everyone,

Question 1
I have a sample of 40 and have run a chi square using SPSS.  I have a 2x2 table which is telling me that I have violated the assumption of the test as:

 "2 cells (50%) have expected count less than 5. The minimum expected count is .94)"

This is labelled foot note b, and the b refers to the value which is stated next to the Pearson Chi Square value.  Is this value SPSS's automatically produced Fisher's Exact Test Value?

Question 2
Also my stats book is telling me that if I have a 2x2 table then it is best to look at the Yates' Correction for Continuity value. But if I have violated the assumptions of the test because I have 2 cells (50%) with an expected count less than 5 then would I need to look at the Fisher Value.  I am confused about which value to use.  Should I use the Continuity Correction value or the Fisher's Exact Test value (in this case both are significant)?

Question 3
If the assumptions have been violated as you have a low cell count but none of the values are significant then which value should you report in your write up.  For example for a 2x2 table would I report the continuity correction or the automatically corrected Fisher value?

I hope this makes some sense!

Parneet

[statisticsdoc]

Parneet,

Yates' correction applies to 2 by 2 tables in which one or more cells have
observed frequencies less than 5. However, if I understand your note
correctly, you are concerned about a table in which the ___expected___
frequencies are less than 5.  When you have one or more cells with expected
values less than 5, use Fisher's exact test rather than Chi Square (in fact,
some sources indicate that Fisher's exact test be used when the expected
frequencies for one or more cells is less than 10).  For a 2 by 2 cell where
the expected values (not the observed count but the expected count) for one
or more cells are less than 5, use Fisher's test, and report Fisher's test.

Returning for a moment to Yates' correction, while some sources suggest
using it in all 2 X 2 tables, it provides a much more conservative test of
the null hypothesis.  Similarly, there has been concern that Yates'
correction "overcorrects" when used to adjust for small observed cell
counts.

HTH,

Steve

P.S.  By way of a digression fron this topic, please note that Fisher's
exact test, strictly speaking, assumes that the row and columns totals are
fixed.  In practice, this assumption is not met in many experimental designs
and almost all non-experimental ones.  An alternative exact test, Barnard's
test, has been developed and is discussed in the following paper:
http://www.cytel.com/Papers/twobinomials.pdf  Proponents of Barnard's exact
test suggest that this method is more powerful, particularly in 2 by 2
tables.  However, many authorities suggest that Fisher's exact test can
nonetheless be safely used.


For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
parneet
Sent: Saturday, May 19, 2007 5:46 PM
To: [hidden email]
Subject: Chi square and Fisher's Exact Test


Hi everyone,

Question 1
I have a sample of 40 and have run a chi square using SPSS.  I have a 2x2
table which is telling me that I have violated the assumption of the test
as:

 "2 cells (50%) have expected count less than 5. The minimum expected count
is .94)"

This is labelled foot note b, and the b refers to the value which is stated
next to the Pearson Chi Square value.  Is this value SPSS's automatically
produced Fisher's Exact Test Value?

Question 2
Also my stats book is telling me that if I have a 2x2 table then it is best
to look at the Yates' Correction for Continuity value. But if I have
violated the assumptions of the test because I have 2 cells (50%) with an
expected count less than 5 then would I need to look at the Fisher Value.  I
am confused about which value to use.  Should I use the Continuity
Correction value or the Fisher's Exact Test value (in this case both are
significant)?

Question 3
If the assumptions have been violated as you have a low cell count but none
of the values are significant then which value should you report in your
write up.  For example for a 2x2 table would I report the continuity
correction or the automatically corrected Fisher value?

I hope this makes some sense!

Parneet


--
View this message in context:
http://www.nabble.com/Chi-square-and-Fisher%27s-Exact-Test-tf3783821.html#a1
0700775
Sent from the SPSSX Discussion mailing list archive at Nabble.com.

[preet]

Hi Steve,

Thanks for your response, it is very helpful.  

With the 2X2 table that I have, both the expected and observed count are less than 5 in 2 cells (50% of the cells).  In this case would I need to use Yates correction?  

Also when the Fisher value is generated is it automatically reported instead of the Pearson Chi square value?  

Thanks for your help

Parneet

statisticsdoc wrote

Parneet,

Yates' correction applies to 2 by 2 tables in which one or more cells have
observed frequencies less than 5. However, if I understand your note
correctly, you are concerned about a table in which the ___expected___
frequencies are less than 5.  When you have one or more cells with expected
values less than 5, use Fisher's exact test rather than Chi Square (in fact,
some sources indicate that Fisher's exact test be used when the expected
frequencies for one or more cells is less than 10).  For a 2 by 2 cell where
the expected values (not the observed count but the expected count) for one
or more cells are less than 5, use Fisher's test, and report Fisher's test.

Returning for a moment to Yates' correction, while some sources suggest
using it in all 2 X 2 tables, it provides a much more conservative test of
the null hypothesis.  Similarly, there has been concern that Yates'
correction "overcorrects" when used to adjust for small observed cell
counts.

HTH,

Steve

P.S.  By way of a digression fron this topic, please note that Fisher's
exact test, strictly speaking, assumes that the row and columns totals are
fixed.  In practice, this assumption is not met in many experimental designs
and almost all non-experimental ones.  An alternative exact test, Barnard's
test, has been developed and is discussed in the following paper:
http://www.cytel.com/Papers/twobinomials.pdf  Proponents of Barnard's exact
test suggest that this method is more powerful, particularly in 2 by 2
tables.  However, many authorities suggest that Fisher's exact test can
nonetheless be safely used.


For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[e-mail]]On Behalf Of
parneet
Sent: Saturday, May 19, 2007 5:46 PM
To: [e-mail]
Subject: Chi square and Fisher's Exact Test


Hi everyone,

Question 1
I have a sample of 40 and have run a chi square using SPSS.  I have a 2x2
table which is telling me that I have violated the assumption of the test
as:

 "2 cells (50%) have expected count less than 5. The minimum expected count
is .94)"

This is labelled foot note b, and the b refers to the value which is stated
next to the Pearson Chi Square value.  Is this value SPSS's automatically
produced Fisher's Exact Test Value?

Question 2
Also my stats book is telling me that if I have a 2x2 table then it is best
to look at the Yates' Correction for Continuity value. But if I have
violated the assumptions of the test because I have 2 cells (50%) with an
expected count less than 5 then would I need to look at the Fisher Value.  I
am confused about which value to use.  Should I use the Continuity
Correction value or the Fisher's Exact Test value (in this case both are
significant)?

Question 3
If the assumptions have been violated as you have a low cell count but none
of the values are significant then which value should you report in your
write up.  For example for a 2x2 table would I report the continuity
correction or the automatically corrected Fisher value?

I hope this makes some sense!

Parneet


--
View this message in context:
http://www.nabble.com/Chi-square-and-Fisher%27s-Exact-Test-tf3783821.html#a1
0700775
Sent from the SPSSX Discussion mailing list archive at Nabble.com.

[Marta García-Granero]

Hi Parneet

Sunday, May 20, 2007, 5:39:38 PM, You wrote:

p> With the 2X2 table that I have, both the expected and observed count are
p> less than 5 in 2 cells (50% of the cells).  In this case would I need to use
p> Yates correction?

I had never heard that Yates correction was related to OBSERVED counts
but to EXPECTED counts. My general idea (I got it time ago from one of
those old fashioned statistics books, I think it was Daniel's, but I
don't have the exact reference here right now, I can check that later):

 - Total sample size (Nt from now on) below 40&Exp<5: Fisher's exact test
 - Exp<1 (with any Nt): Fisher's exact test
 - Nt>40& Exp<5: Yates' correction CAN be used (this is not the same as
   MUST be used)
 - Exp>=5: Chi-square without continuity correction is OK (time ago
   the rule said Exp>10, but now I think it is generally accepted that
   Exp>5 is more than enough for asymptotic p-values to be correct).

Using Yates' continuity correction prevented having to compute (old
times) Fisher's exact test by hand (have you ever tried? kind of
boring, with all those a! b!...), that's why it was very used in the
past. Now, since SPSS (and other statistical programs) will compute
the "difficult" Fisher's exact test authomatically, with no pain for
the user, Yates' continuity correction is not very used (although
there is people who insist it should be always used, Montercarlo
simulations have shown that it tends to be overconservative, failing
to reject the null hypothesis). As a matter of fact, Fisher's tests is
also a bit on the conservative side, that's why Chi-square
(uncorrected) should be used when possible (Exp >5).

p> Also when the Fisher value is generated is it automatically reported instead
p> of the Pearson Chi square value?

As the saying goes "the taste of the pudding is in the eating". Try to
run CROSSTABS on a 2x2 data layout and see what happens: you will find
a row labelled "Fisher's exact test" inside the Chi-square tests pivot
table (I've always found that detail a bit misguiding, BTW, SPSS-dot-
com people, calling chi-square test Fisher's exact test...)

p> statisticsdoc wrote:

>>
>> Yates' correction applies to 2 by 2 tables in which one or more
>> cells have observed frequencies less than 5. However, if I
>> understand your note correctly, you are concerned about a table in
>> which the ___expected___ frequencies are less than 5.  When you
>> have one or more cells with expected values less than 5, use
>> Fisher's exact test rather than Chi Square (in fact, some sources
>> indicate that Fisher's exact test be used when the expected
>> frequencies for one or more cells is less than 10).  For a 2 by 2
>> cell where the expected values (not the observed count but the
>> expected count) for one or more cells are less than 5, use Fisher's
>> test, and report Fisher's test.
>>
>> Returning for a moment to Yates' correction, while some sources suggest
>> using it in all 2 X 2 tables, it provides a much more conservative test of
>> the null hypothesis.  Similarly, there has been concern that Yates'
>> correction "overcorrects" when used to adjust for small observed cell
>> counts.

--
Regards,
Dr. Marta García-Granero,PhD           mailto:[hidden email]
Statistician

---
"It is unwise to use a statistical procedure whose use one does
not understand. SPSS syntax guide cannot supply this knowledge, and it
is certainly no substitute for the basic understanding of statistics
and statistical thinking that is essential for the wise choice of
methods and the correct interpretation of their results".

(Adapted from WinPepi manual - I'm sure Joe Abrahmson will not mind)