# Weighted Chi Square?

#### kowalsks

##### New Member
I'm probably using the wrong terminology but here goes! I am trying to analyse categorical data- student grades. The students can earn: Merit, Satisfactory, Borderline or Unsatisfactory. I want to use a chi square to see if there are any differences between two groups of students: One would be my "control variable" (large group of students who should represent a normal cohort of grades), the other is a test variable (smaller group of students who have had slightly different teaching).

I performed a chi square test, but then realised that the distribution of the control group wouldn't have equal numbers of Merits, Satisfactorys and Borderlines (basically, we would expect only about 20% Merit, 75% Satisfactory, and only about 5% Borderline, for this particular test Unsatisfactorys are rare).

How do I tell SPSS that I expect only 20% M, 75% S, and 5% B?

Thanks!

#### BioStatMatt

##### TS Contributor
Hmm. Its not clear what type of test you have used. However, it appears that you would want to use a chi-square test for homogeneity with a 4x2 contingency table. Where the rows correspond to the grade categories and the columns correspond to the groups. This type of analysis will indeed allow you to determine whether the grade categories are distributed similarly between these two groups. If this is the type of analysis you have already performed, then you shouldn't need to do any additional work.

I've never used SPSS, so I'm no help there though.

~Matt

#### kowalsks

##### New Member
Thanks for your reply. I'll try to explain this better. . .

I have done a chi square test for homogeneity, but the issue I was having is that this test calculates the expected values of each cell as if they all had equal probabilities of being populated (i.e. it assumes the distribution of grades is 25%, 25%, 25%, and 25%). This is not the case, as the majority of students receive a grade of S, with fewer students getting each of the other grades). So, I want observed to = expected for the control group. That way I can see how the experimental group varies from the distribution of the control (not how both groups vary from all probabilities being equal).

Does anyone know how to do that in SPSS? Or by hand?

Thanks!