Sample Size for Chi Square test

NN_STAT

New Member
Hello,

I need to calculate a minimum sample size for the chi square test.

I have two groups, sick and healthy patients, and I have a new test that should detect the sick patients. The machine tell "sick" or "healthy". I was asked to check if the results of the test (E) are independent to the status (D). This is a simple 2X2 table. What is the required sample size for the appropriate chi square test ?

Dragan

Super Moderator
Hello,

I need to calculate a minimum sample size for the chi square test.

I have two groups, sick and healthy patients, and I have a new test that should detect the sick patients. The machine tell "sick" or "healthy". I was asked to check if the results of the test (E) are independent to the status (D). This is a simple 2X2 table. What is the required sample size for the appropriate chi square test ?
Basically, just look at your expected frequencies in your 2X2 table...they shouldn't be less than 5.

NN_STAT

New Member
under H0 my expected frequencies should reflect independence.

so you are saying that I should put in every cell in the table a size of 5 patients, so I need 10 sick and 10 healthy ?

Dragan

Super Moderator
under H0 my expected frequencies should reflect independence.

so you are saying that I should put in every cell in the table a size of 5 patients, so I need 10 sick and 10 healthy ?
Essentially, what you need is an expected frequency of at least 5 in each of the 4 cells of a 2x2 chi-square design to justify the use of an (asymptotic) approximation of a chi-square statistic under a true null hypothesiss that the two variables are independent...Let your software package compute the expected frequencies.

gianmarco

TS Contributor
Hi!
May be Dragan was warning you about the fact that in order for chi-square test to be reliable none of the expected frequencies should be smaller that 5. I have made some search in the web, and I have realized that this is a rather controversial topic....but this is another story...
As for your question, provided that I do not know the size of your sample, you could use Fisher test instead, since you have a 2x2 table. For further info, you could jump to this link.

Hope this helps,
Regards
Gm

NN_STAT

New Member
thank you to both of you !

ginamarco said: "I do not know the size of your sample". Well, this is the problem, I do not have one, I need to decide how many to sample....

NN_STAT

New Member
thanks, I found another software (PS), and now I understand the rationale behind the calculations.