# ANOVA - 1 dependent Variable - 3 category variables

#### JDB

##### New Member
In a hypothesis testing checklist, it says, "equal variance were assumed for the analysis". What does that actually mean? With only one scalar variable does one just ignore that statement. The Q-Q plot is normal. It is a huge data set, > 22,000 observations, and I trimmed out the outliers > +/- 3 Std Dev. If I am not making sense sorry.

JDB

#### obh

##### Active Member
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

#### JDB

##### New Member
Thanks, I see I was unclear. I am running an ANOVA in JASP with 1 dependent variable and 3 categorical variables. > 22,000 obs. ALL categorical variables are very significant in ANOVA. The Q_Q plot easily pass the fat pencil test for normality.

These are industrial observations.

The 3 categories have p < .00000, p < 3.357 e -103, p < 8.022 -4

Levene's test [ F 26.991, DF 35, Df3, 22,357 p < 9.884 e -172 ]

the data makes very good sense, no interaction of the cat variables, but do I need to address the Levene's test in the paper we are drafting for publication..

thanks for any help.

JDB