Chi-square or ANOVA for two groups with multiple possible categories I am working on a research project examining diagnoses in two populations, lets say A and B. Then I categorize their diagnoses: D1, D2, D3, ... (about 9 of them). (N>500 for both groups). So D1 is the number of patients with D1 as a diagnoses. (Also each of these diagnoses have subcategories, but I wont go into that). 
Originally I was going to use a Chi Square analysis with the raw numbers to determine the significance of each diagnoses... but now I'm wondering if I should do an ANOVA (which I've never done in excel).. 
Any thoughts here? 
Most of the groups should have an n>1, otherwise I will use a Fisher Exact test (using the =hypogeo.dist function in excel). 
I guess my question is how will I be able to tell if there are significantly more of one diagnoses in group A rather than group B if I get one chi square value from the entire data section.
Side note, when can I assume a normal distribution for a population and use t tests? 
*Resident doctor who was a math major, very rusty!  
 A: Chi-squared test. I think I see what you are doing with the chi-squared test.
Here are simulated data for groups A and B, with categories
labeled with numbers 1 through 6.  Using R statistical software, I have selected different
theoretical probability apportionments to categories for
the two groups.
Make category counts for A and B.
set.seed(528)
p.a = c(.1,.2,.3,.2,.1,.1)
a = sample(1:6, 500, rep=T, prob=p.a)
t.a = tabulate(a);  t.a
[1]  44 100 160  90  50  56
p.b = c(.3,.2,.2,.1,.1,.1)
b = sample(1:6, 500, rep=T, prob=p.b)
t.b = tabulate(b);  t.b
[1] 141  91 100  49  59  60

Put the counts into a table:
TBL = rbind(t.a, t.b);  TBL 
    [,1] [,2] [,3] [,4] [,5] [,6]
t.a   44  100  160   90   50   56
t.b  141   91  100   49   59   60
rowSums(TBL)  # row totals
t.a t.b 
500 500                            
colSums(TBL)  # column totals
[1] 185 191 260 139 109 116

Chi-squared test for counts in table: This is a test of
homogeneity of distributions among categories. For my data, distributions
for groups A and B are (highly) significantly different with
a P-value very near 0.
chisq.test(TBL)

        Pearson's Chi-squared test

data:  TBL
X-squared = 78.104, df = 5, p-value = 2.091e-15

Possible two-way ANOVA. However, I am not sure what you plan for an ANOVA. 
Do you
have numerical test results for each patient?


*

*These test results should not have been used to decide
how the 500 patients in each group are put into categories.

*I'm assuming assignment to categories is based on some
combination of overt characteristics, such as age, gender,
symptoms, attempted treatments.


Then you could do a two-factor ANOVA with test result data.
The ANOVA table would have rows for Group (A,B), Category(1 through 6), and Error/Residual. With 500 subjects in each group,
the degrees of freedom DF would be 1 for Group, 5 for Category,
and 993 for Error (or Residual). 
Possible two-sample t test.  If you have test results from patients in the two groups, then you could use a
Welch two-sample t test to see if population mean test
results differ between groups A and B. 
However, you should not use nominal categorical group labels as data for a two-sample t test. 
