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honesty
Re: Can we use Chi-square ?
I must agree to the most of Anwer's views on the use of these two statisical methods. I think there is no definite criterion not to consider Pearson's chi-square test, if the number of subjects is less than 30. The basic rule or criterion to consider Fischer's exact test is a small value (less than five) in one of the cells in a two by two crosstable. The Fisher's Exact test procedure calculates an exact probability value for the relationship between two dichotomous variables, as found in a two by two crosstable. The program calculates the difference between the data observed and the data expected, considering the given marginal and the assumptions of the model of independence. It works in exactly the same way as the Chi-square test for independence; however, the Chi-square gives only an estimate of the true probability value, an estimate which might not be very accurate if the marginal is very uneven or if there is a small value (less than five) in one of the cells (please note, it is not the total number of subjects/cases/obserations that determines the selction of particular type of statistical method/s). In such cases the Fisher exact test is a better choice than the Chi-square. However, in many cases the Chi-square is preferred because the Fisher exact test is difficult to calculate. I hope the above explanation may have resolved the confusion.
[Edited by honesty on 15-08-2005 at 09:08 AM GMT]
anwer_khur
Re: Re: Can we use Chi-square ?
quote:
ROMI wrote:
quote:
docosama wrote:
Can we use Chi-square if the sample size is less than 30 ? If not, then which test would be appropriate ?
There seems to be some confusion about the use of chi-square:
First note that Chi-square test based on chi-square distribution is used in many situations (For details see Sahai, H. and Khurshid, A. Pocket Dictionary of Statistics). Here it looks that originator of this discussion wants to know its use in contingency tables (i.e two variables are divided in rows an columns). In that case, it is generally assumed that expected frequencies (which you will find with the help of observed frequencies) of all the cells in contingencty table be greater than 1 and atleast 80% of the cells have expected frequencies greater than 5. When these assumptions are not met, other tests, such as Fisher's exact test, are more appropriate.
Fisher's Exact test is a procedure that you can use for data in a two by two contingency table.
A two by two contingency table arises in a variety of contexts, most often when a new therapy is compared to a standard therapy (or a control group) and the outcome measure is binary (live/dead, diseased/healthy, infected/uninfected, etc.).
Fisher's Exact Test is based on exact probabilities from a specific distribution known as the exact HYPERGEOMETRIC distribution (Please note this as somebody suggested here that it does not follow any distribution). The Chi-square test relies on a large sample approximation. Therefore, you may prefer to use Fishers Exact test in situations where a large sample approximation is inappropriate.
There's really no lower bound on the amount of data that is needed for Fisher's Exact Test. You do have to have at least one data value in each row and one data value in each column. If an entire row or column is zero, then you don't really have a 2 by 2 table. But you can use Fisher's Exact Test when one of the cells in your table has a zero in it. Fisher's Exact Test is also very useful for highly imbalanced tables. If one or two of the cells in a two by two table have numbers in the thousands and one or two of the other cells has numbers less than 5, you can still use Fisher's Exact Test.
As usual this test has been the subject of controversy among statisticians.
Anwer
rqayyum
Re: Can we use Chi-square ?
Although this thread is quite old , I am writing this response to keep the record straight.
First, although it is generally recommended that one should not use chi-square test if 'expected' frequency in any cell is less than 5, many statisticians consider this too restrictive. Generally, if relatively few expected values are less than 5, a minimum expectation of 1 is allowable in computing chi-square, provided contingency tables are with more than one degree of freedom. (Ref: Cochran. Biometrics 10 (1954) 417-51).
Second, a commonly used method for circumventing thinly populated cells is to combine these thinly populated cells provided they have related treatments or outcomes.
Third, Fisher Exact Test is NOT a derivative of chi-square test and DOES NOT follow chi-square distribution. It is called an 'exact' test because it calculates the exact probability of the outcomes without using any distribution.
[Edited by rqayyum on 02-27-2005 at 05:29 AM GMT]
nrehan
Re: Can we use Chi-square ?
Chi Square test can be applied if the sample size is smaller than 30. Chi Square is used for qualitative data.
Chameed is right in advising that when the number od observations in any cell are less than 5, we should use Fisher Exact test. Basically Fisher Exact Test also follows Chi Square Distribution and is considered a derivative of Chi Square.
chameed
Re: Can we use Chi-square ?
quote:
docosama wrote:
Can we use Chi-square if the sample size is less than 30 ? If not, then which test would be appropriate ?
Although there is no absolute rule, most statisticians agree that an expected frequency of 2 or less means that the chi-square test should not be used; and many argue that chi-square should not be used if an expected frequency is less than 5.
I suggest to you that if any expected frequency is less than 2 or if more than half the expected frequencies are less than 5, then you should use Fisher's exact test. I also emphasize that it is the expected frequency values and not the observed values.
