I'd suppose that length and weight have a symmetric distribution, so using a standard Anova (assuming normal errors) is possibly ok. If the coefficients of variation are large (large SD compared to mean values), the distributions are likely right-skewed. Using the log-transformed responses might be an applicable work-around (just keep in mind that then you are not fitting additive but multiplicative effects).

The number of vertebrae is a count value, so a Poisson model (or quasi-Poisson or negative binomial, or zero-inflated models) should be used.

In both cases, "site" and "sex" should be used as predictors, so you will have a two-factorial model. The differences of the sex-effect between sites is modelled as interaction of "site"x"sex". If you want the "overall-effect" of "sex" (for instance) then you should omit the interaction. However, if there is a strong interaction, the question for an overall-effect is not very sensible.

logistic regression. you can use both continuous variables, count variables and those measured at rank order (sex). You can check the effect of each predictor separately and their combinations. it's a good old type of analysis, just google it and you find thousands of publications

I'd suppose that length and weight have a symmetric distribution, so using a standard Anova (assuming normal errors) is possibly ok. If the coefficients of variation are large (large SD compared to mean values), the distributions are likely right-skewed. Using the log-transformed responses might be an applicable work-around (just keep in mind that then you are not fitting additive but multiplicative effects).

The number of vertebrae is a count value, so a Poisson model (or quasi-Poisson or negative binomial, or zero-inflated models) should be used.

In both cases, "site" and "sex" should be used as predictors, so you will have a two-factorial model. The differences of the sex-effect between sites is modelled as interaction of "site"x"sex". If you want the "overall-effect" of "sex" (for instance) then you should omit the interaction. However, if there is a strong interaction, the question for an overall-effect is not very sensible.

One question to Nickolay: why logistic regression? This kind of regression models a binary response - I do not see what it should have to do with Brent's problem.

Jochen's explanation would solve your problem. However, if you would like to go one step further, you can perform MANOVA (by fitting site and sex as class effect again) since weight, length and number of vertebrae of fishes caught would be correlated (and assuming number of vertebrae of fishes is normally distributed).

Jochen, logistic regression models rather multinomial, than binomial response.

I tried to answer the question how to incorporate "site" and "sex" in the analysis, but you are right, if continuous variables are normally distributed the ANOVA seems to be ok to test the effect.

Well, I just thought that Brent already rejected ANOVA because of some reasons, since he was asking about "ANOVA-like" tests.

So, it is still possible to use logistic regression if one didive, for example the spectrum of values of "weight", into several categories, say from 0 to 0.2g, 2.1-5.5 g., 5.5 - 10.3 g. Biologically it is quite reasonable, because the interpretation would be easier - small, medium-sized and big animals. Same with length, and the number of vertebrae.

well, it just the point of view... ANOVA probably will fit good

First check for correlation between weight, length and # vertebrae. It's very likely, they highly correlate well. Then make a choice between either weight or length (but not both as a response variable). E.g. if you choose to use weight, then just run an ANOVA with sex and site as your factors (remember to also check for the effect of interaction between these factors). Now reduce or maintainyou model complexity basing on what you find ssignificant (recall law of parsimony?). If you chose to use # vertebrae as a response, then you want to consider a logit or probit model instead

Check for normal distribution of variables (Kolmogorov-Smirnov statistic) and/or log-transform to ensure normality.

Test each variable separately whether they are correlated or not (checking for correlation is ok and good to know but I'd prefer to perform the three analyses).

Use univariate two-way general linear models (GLMs) to evaluate differences in continuous variables. Introduce sex and site as independent factors. This test evaluates both the effect of each independent factor but also their interaction.