F-Test on comparisons of several variables

I am supposed to do an analysis of data in a study of zinc levels in vegetarian vs. non-vegetarian pregnant women.

23 women were monitored, 12 of them were pregnant vegetarian, 6 were non-vegetarian and pregnant, and 5 of them were vegetarian and non-pregnant.

when I compare the residuals there does not appear to be equal standard deviation among the groups, but I don't think I know a test yet that is more robust to departures from equal standard deviation that involves comparisons among several groups of data.

Mostly what I am confused about is this. I did an ANOVA F-test and came up with a p-value of .98 which pretty much gives extremely convincing evidence that there is not a statistically significant difference in the means of the three groups, so if there is no evidence for a difference in means between the three groups it isn't necessary to then compare the non-vegetarian mean to the vegetarian means is it?

Also, I am a little bit confused about the extra group of data about the vegetarian pregnant women. I don't see how it applies. I know it is bad form to throw out any data but in this case it seems to me that it would make more sense to compare only the data of the pregnant women.

????????

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