R help - Feb 2010 - Shapiro-Wilk for levels of factor

Hello,
  I have data for an ANOVA where the between-subjects factor has three
levels. How do I run a test of normality (using shapiro.test) on each
of the levels of the factor for the dependent variable separately
without creating extra datasets?

  Thanks,

    Ravi

On Sun, 14 Feb 2010, Ravi Kulkarni wrote:
> Hello,
>  I have data for an ANOVA where the between-subjects factor has three
> levels. How do I run a test of normality (using shapiro.test) on each
> of the levels of the factor for the dependent variable separately
> without creating extra datasets?
You can use tapply(y, x, shapiro.test) which will then conduct as many 
Shapiro-Wilk tests as x has levels (without adjusting for multiple 
testing).

Another approach might be to look at shapiro.test(residualslm(y ~ x))) 
which tests the null hypothesis that the residuals in all groups come from 
the same normal distribution.

A worked example for the chickwts data is included below.
Z

## 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")]))))

>  Thanks,
>
>    Ravi
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

Thanks! Exactly what I wanted.

  Ravi
-- 
View this message in context:
http://n4.nabble.com/Shapiro-Wilk-for-levels-of-factor-tp1555254p1555720.html
Sent from the R help mailing list archive at Nabble.com.

Achim showed you how, but you might want to consider why.

If you are trying to learn more about your data, then plots or other strategies
may work better than the test.

If you are testing for normality in order to meet the assumptions of a test,
then the test may not be accomplishing what you think.  The assumptions of
normality are most important when sample sizes are low, but when sample sizes
are low, most normality tests have low power to detect non-normality (I only
know of one that has high power in this case, but there are other issues with
that one), so a lack of significance does not mean that your routine is safe to
use.  As sample sizes get larger, the normality tests become more powerful, but
the need for normality goes away (CLT).   So testing normality to satisfy
assumptions is usually meaningless for small sample sizes, and meaningless in a
different way for large samples.  See fortune(234) and fortune(117).

-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Ravi Kulkarni
> Sent: Sunday, February 14, 2010 9:49 AM
> To: r-help at r-project.org
> Subject: [R] Shapiro-Wilk for levels of factor
> 
> Hello,
>   I have data for an ANOVA where the between-subjects factor has three
> levels. How do I run a test of normality (using shapiro.test) on each
> of the levels of the factor for the dependent variable separately
> without creating extra datasets?
> 
>   Thanks,
> 
>     Ravi
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-
> guide.html
> and provide commented, minimal, self-contained, reproducible code.