chi square goodness of fit assumptions

#1
Hello,

To be able to have meaningful results from a chi square goodness of fit test I should have, among other assumptions, expected frequencies for each category at least 1.


If I have expected frequencies <1, does it make sense to excude those categories from the test? Example:

Population frequencies:
2
100
150
80
(total = 332)

Sample frequencies:
1
15
20
10
(total = 46)

Therefore I get:

Expected ferquencies:
0.28 (=2*46/332)
13.86 (=100*46/332)
20.78 (=150*46/332)
11.08 (=80*46/332)
(total = 46)

Since 0.28<1, does it make sense to do the test on:

Population frequencies:
100
150
80
(total = 330)

Sample frequencies:
15
20
10
(total = 45)

Expected ferquencies:
13.64 (=100*45/330)
20.45 (=150*45/330)
10.91 (=80*45/330)
(total = 45)

? Is there a standard way to deal with low expected frequencies? Maybe a different test?

Thanks,
Diodoo
 
#2
Try a Fisher's Exact Test...it was created to work with small expected frequencies; however, I believe that it cannot be done in SPSS without a fairly expensive add-on...HTH...
 
#3
Try a Fisher's Exact Test...it was created to work with small expected frequencies
Thanks for the tip. All the examples I found of Fisher-Freeman-Halton test (the extension of Fisher's Exact Test for n x 2 tables) use "real" frequencies, i.e. natural number. Do you know if this test can also be applied to "expected" frequencies, like in my case?