# [R] Testing for normality in categorical data

Jim Lemon drj|m|emon @end|ng |rom gm@||@com
Sun Oct 6 02:09:41 CEST 2019

```Hi Nancy,
The chickwts dataset contains one sort-of continuous variable (weight)
and a categorical variable (feed). Two things that will help you to
understand what you are trying to do is to "eyeball" the "weight"
data:

# this shows you the rough distribution of chick weights
hist(chickwts\$weight)
# this shows you how well the distribution of weights fits a normal distribution
qqnorm(chickwts\$weight)

For the Shapiro-Wilks statistic on the distribution of all of the weights:

shapiro.test(chickwts\$weight)

and if you really want to test the normality within the feed groups:

by(chickwts\$weight,chickwts\$feed,shapiro.test)

Now because the p-values returned are all fairly large, you can accept
the null hypothesis of normality.
As Bert has noted, it looks like you are just throwing the data into
the functions without really knowing what you are doing. Hopefully,
the above will get you started.

Jim

On Sat, Oct 5, 2019 at 11:19 PM Nancy Felix <nancyfelix25 using gmail.com> wrote:
>
> Hello
> I have data that are categorical both independent variable and dependent as
> well having levels more than 3. How can i check the normality of my data?
>
> I have tried the example given of Shapiro-Wilk for levels of factors
>
> data
> summary(chickwts)
>
> ## linear model and ANOVA
> fm <- lm(weight ~ feed, data = chickwts)
> anova(fm)
>
> ## QQ plot for residuals + Shapiro-Wilk test
> shapiro.test(residuals(fm))
>
> ## separate tests for all groups of observations
> ## (with some formatting)
> do.call("rbind", with(chickwts, tapply(weight, feed,
>    function(x) unlist(shapiro.test(x)[c("statistic", "p.value")]))))
>
> But ended up with Error message that x should be numeric and more comments
> see below.
> Hope to get some help on this
>
> Thanks,
> Nancy
>
> ## linear model and ANOVA
> > fm <- lm(retaliation ~ occupation, data = kazi)
> Warning messages:
> 1: In model.response(mf, "numeric") :
>   using type = "numeric" with a factor response will be ignored
> 2: In Ops.factor(y, z\$residuals) : ‘-’ not meaningful for factors
> > anova(fm)
> Error in if (ssr < 1e-10 * mss) warning("ANOVA F-tests on an essentially
> perfect fit are unreliable") :
>   missing value where TRUE/FALSE needed
> In Ops.factor(object\$residuals, 2) : ‘^’ not meaningful for factors
> > ## QQ plot for residuals + Shapiro-Wilk test
> > shapiro.test(residuals(fm))
> Error in class(y) <- oldClass(x) :
>   adding class "factor" to an invalid object
> > ## separate tests for all groups of observations
> > ## (with some formatting)
> > do.call("rbind", with(kazi, tapply(retaliation, occupation,
> +                                        function(x)
> unlist(shapiro.test(x)[c("statistic", "p.value")]))))
>
>         [[alternative HTML version deleted]]
>
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