# Chi square test, expected frequency less than 5

#### sammy0131

##### New Member
Please someone help me out.

I have three independent group data (Group A, B, and C), which sample size is 128, 100, and 31. Among those, the numbers of sample that showed the type I reaction were 67 for Group A, 40 for Group B, and 18 for Group C, and the numbers of sample that showed the type II reaction were 26 for Group A, 18 for Group B, and 4 for Group C. The sample showed both reactions were independent. I wanted to know the ratio of the sample showed the type I reaction over the type II reaction were significantly different from the expected frequency.

I first calculated its ratio for each group, which is 67/26 = 2.58 for Group A, 40/18 = 2.22 for Group B, and 18/4 = 4.50 for Group C. And the assume the expected frequency would be the total number of the sample showed the type I reaction (67+40+18 = 125) over the total number of the sample showed the type II reaction (26+18+4 = 48) , thus 125/48 = 2.6. And then I was trying to calculate the chi-square but realized the expected frequency was too small less than 5.

I'd very very much appreciate what type of test I can use in this case. Fisher's test doesn't work either because the data is not nominal?

Sam

#### Masteras

##### TS Contributor
so you want to see whether there adifferences between reposnce 1 and responce 2? perform log-linear analysis with dep the frequencies of each cell and 2 indep: the type of responce and the group. if the type is significant then there is difference

#### sammy0131

##### New Member

>"if the type is significant then there is difference"
I don't understand this part yet...., but I've been trying to find out a way after my first post.

I wonder if I use the chi-square test for three groups X two reactions, does this mean that I am comparing the ratio of the number of each group (e.g., as for the Group A, 67 vs 26, type I vs type II, respectively)?

Can I use the expected frequency for Group A&Type I as 128/259*125(total of Group A/total of ALL*total of Type I)?

Thanks! I'd truly appreciate for your reply as I really need to figure out this soon!!

Sam

#### Masteras

##### TS Contributor
i sai use log-linear models in spss for instance. two indep variables, the the type and the group. if the type is significant this means that the frequencies in type I are significantly more than the frequencies in type 2. so that asks your question. i cannot think of a better way now.