how to test most frequent variable between groups? I have different groups of dolphins, some with offspring, some without. I'll count how many types of vocalizations were emitted by each group, and want to find out if there is a statistical difference between groups with and without offspring.
My dataset is something like:
Group_number    Vocal1  Vocal2  Offspring
Gr01    5   3   0
Gr02    7   3   0
Gr03    4   4   0
Gr04    1   6   0
Gr05    7   9   0
Gr06    6   2   1
Gr07    2   4   1
Gr08    2   6   1
Gr09    9   7   1
Gr10    8   8   1

I have to do this one vocalization type at a time (I have some tens of types)? Or can I do it all in a single run (like a multiple linear regression)? Someone told me to do a chi-square, but am not sure how to do it, or if it's appropriate. T-student, ANOVA, MANOVA, GLM, what's the pros and cons of each method, supposing my data is normally distributed? And what if it's not? Sorry if it seems a silly and vague question, but maybe someone could point me to a simple tutorial or something.
Thanks in advance!
 A: First of all, your data is not normally distributed because it takes discrete values. But, if there is enough range in the data, you may say it approximates a normal distribution. It's an assumption you need to verify.
The question is vague because this is a data mining/data analysis question, and many methods will provide you with many (similar but different) results. There are no pros/cons here, since they all test for different things. For the methods you mentioned, here's a brief description:


*

*Chi-squared. This will tell you if there is a relation between your groups. I assume the test will be offspring versus all the vocalizations. You may find signficance but not be certain where it comes from. If you find a relation, you have to dig deeper to find the source. Avoid having groups with few observations otherwise this test will not be valid.

*(Student) T-test, or a test of equivalence in means. You compare the mean value of two populations, versus the alternative hypothesis that they are not equal. You will need to test each vocalization individually.

*ANOVA. You are testing if the variance is explained across different factors (offspring). This needs to be done for each different variable.  The idea is to look at the variance of the continuous variable within each class $s_i$ and compare it to the total variance st. The correlation coefficient for one class compared to the total is then $\nu_i=s_i/s_t$. This test also assumes normality.

*MANOVA. This is testing if your qualitative factor (offspring) has an effect on ALL of the other variables. It is a generalization of ANOVA to multiple variables, which sounds appropriate for your study. We still have the normality assumption.

*GLM. Modeling can show you the relationships in your data as well, but you need to have a predictor variable defined in advance. (Offspring?)


Other ideas: If you are looking to see how your vocalizations are related only to offspring, then try perhaps a discriminant analysis (normality assumption again) or a logistic regression (no normality assumption).
