Hi JDB

I assume you mean one category variable with 3 values? say, 3 groups?

It means that the standard deviations of all the groups are equal.

You may check it using the Levene's test.

The normal assumption is not important for a large sample size. (usually, the averages will distribute normally per CLT)

With such a large sample size you expect to get on average 59 outliers, (0normal assumption) you should remove the outliers only if you have a good reason to believe that the outliers are wrong observations.

Example of R Levene's test

library(car)

value <- c(1,2,3,4, 4,5,6,7,8)

group1 <- c(rep("Group1", 4), rep("Group2", 5))

my.dataframe<-data.frame(value, group1)

leveneTest(value~group1, data=my.dataframe, center=median)

The following runs one way ANOVA and also checks the equal variance assumption using the Levene's test.

http://www.statskingdom.com/180Anova1way.html