I have a table with four groups (4 BMI groups) as the independent variable (factor). I have a dependent variable that is “percent mother smoking in pregnancy”.
Is it permissible to use ANOVA for this or do I have to use chisquare or some other test?
Answer
There is a difference between having a binary variable as your dependent variable and having a proportion as your dependent variable.

Binary dependent variable:
 This sounds like what you have. (i.e., each mother either smoked or she did not smoke)
 In this case I would not use ANOVA. Logistic regression with some form of coding (perhaps dummy coding) for the categorical predictor variable is the obvious choice if you are conceptualising the binary variable as the dependent variable (otherwise you could do chisquare).

Proportion as dependent variable:
 This does not sound like what you have. (i.e., you don’t have data on the proportion of total waking time that a mother was smoking during pregnancy in a sample of smoking pregnant women).
 In this case, ANOVA and standard linear model approaches in general may or may not be reasonable for your purposes. See @Ben Bolker’s answer for a discussion of the issues.
Attribution
Source : Link , Question Author : drew , Answer Author : Jeromy Anglim