Fisher's test alternatives

[Nogitsune]

Good evening,

I have several variables that, when performing a chi square test, do not satisfy the expected count no less than 5 assumption. Unfortunately, the categories in these variables cannot be collapsed. As far as I could understand, instead of Chi Square Test, Fisher's exact test is advised – but it is only applicable to 2X2 table. I have several 2X8 crosstabs. Is it possible to use another test? I have tried using the "Exact" option in SPSS, but it returns error that there is insufficient memory for running Fisher's test (although my computer has absolutely no problem with memory). Is Monte Carlo an acceptable option (reading Fisher's exact test from the result)? 

Thank you!

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[Bruce Weaver]

I just want to point out that the minimum expected count of 5 rule of thumb is too severe for tables larger than 2x2.  The following is from my notes on assumptions for the Chi-square test of association.

--- beginning of excerpt ---
For tables larger than 2x2, the chi-square distribution with the appropriate degrees of freedom provides a good approximation to the sampling distribution of Pearson's chi-square when the null hypothesis is true, and the following conditions are met:

1. Each observation is independent of all the others (i.e., one observation per subject);
2. "No more than 20% of the expected counts are less than 5 and all individual expected counts are 1 or greater" (Yates, Moore & McCabe, 1999, p. 734).

Notice that it is okay to have some expected counts less than 5, provided none are less than 1, and at least 80% of the expected counts are equal to or greater than 5.
--- end of excerpt ---

If you still find yourself wanting/needing an exact test, choosing the exact option would be the way to go.  You said that your computer "has absolutely no problem with memory".  What is the basis of that statement?  Maybe some proper diagnostic tests would reveal that you actually do have a problem with memory.  I suggest that you post the observed counts for one of your tables that doesn't work and let some of us try it.  (We only need the observed counts, because we use them as weights.)  

Regarding 2x2 tables, unless you have the rare situation where all marginal totals are fixed in advance, the N-1 Chi-square is arguably a much better choice than the Fisher-Irwin test (aka., Fisher's exact test).  Ian Campbell's nice simulation study has shown that it works well provided all expected counts are equal to 1 or more.  For more details, see the link below.  And note that when you have a 2x2 table, the "linear-by-linear" Chi-square that SPSS computes is equivalent to the N-1 Chi-square.  

https://sites.google.com/a/lakeheadu.ca/bweaver/Home/statistics/notes/chisqr_assumptions

HTH.

Kseniya Katsman wrote

Good evening,

I have several variables that, when performing a chi square test, do not
satisfy the expected count no less than 5 assumption. Unfortunately, the
categories in these variables cannot be collapsed. As far as I could
understand, instead of Chi Square Test, Fisher's exact test is advised –
but it is only applicable to 2X2 table. I have several 2X8 crosstabs. Is it
possible to use another test? I have tried using the "Exact" option in
SPSS, but it returns error that there is insufficient memory for running
Fisher's test (although my computer has absolutely no problem with memory).
Is Monte Carlo an acceptable option (reading Fisher's exact test from the
result)?

Thank you!

Best,
Kseniya.

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[Rich Ulrich]

Bruce has given a fine reply.  I will add a couple of comments.

You state that "Fisher's Exact test" does refer explicitly to the 2x2 test, which is correct.

And your own table is 2x8.  But you report an error "for running Fisher's test" -- SPSS

should not be labeling a 2x8 test as "Fisher's", so I hope that this is just a think-o.

By the way, it is possible to have NxK "exact stats" based on a standard other than Fisher's,

for ranking the extremeness of the cells.  Your test should be described as the "Exact test

based on the extension of the Fisher test for 2x2 tables" or similar language.

However, from what I recall (and what I read online -- Mehta), the Exact Tests module

does switch automatically to a Monte Carlo procedure when a table has some counts

so large (millions?) that exact enumeration would take too long.  In short, you should

never get the error message that you report.  How many SPSS routines now provide

Exact Stats as an option?

It might be useful if you would cut-and-paste your syntax and error message so that

the error -- yours or SPSS's -- can be pinned down.

--

Rich Ulrich

---

From: SPSSX(r) Discussion <[hidden email]> on behalf of Kseniya Katsman <[hidden email]>
Sent: Thursday, February 23, 2017 10:31:06 PM
To: [hidden email]
Subject: Fisher's test alternatives

 

Good evening,

I have several variables that, when performing a chi square test, do not satisfy the expected count no less than 5 assumption. Unfortunately, the categories in these variables cannot be collapsed. As far as I could understand, instead of Chi Square Test, Fisher's exact test is advised – but it is only applicable to 2X2 table. I have several 2X8 crosstabs. Is it possible to use another test? I have tried using the "Exact" option in SPSS, but it returns error that there is insufficient memory for running Fisher's test (although my computer has absolutely no problem with memory). Is Monte Carlo an acceptable option (reading Fisher's exact test from the result)? 

Thank you!

===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD

===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD

[kalammar27]

Hi,

You can press on Exact, and chose Monte Carlo instead of the time limit

Good Luck

[kalammar27]

other thing if your dependent variable is scale with sub-scales , the chi square is not advised at all