Tests of Normality in SPSS

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Dear Experts:

I hope it was a nice weekend to all of you. What could we say if the Sig of Kolmogorov-Smirnov 0.200 and for Shapiro-Wilk 0.016, is the var follow the normal distribution? The reason from the question is because the first value > 0.05 and the second < 0.05.

Thanks.

Omar.

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关键词：normality normal Tests Norm test SPSS Tests normality

Hi Omar,

Both tests foccus on different aspects of non-normality. Shapiro-Wilk
test is considered the best (at least there's a paper, by Shapiro &
Wilk, where they show mathematically that their test is the best to
detect non-normality).

There are, nonetheless, other details to be considered:

- Sample size: SW test tends to be oversensitive with big sample sizes
(let's say... over 100), you don't mention it.

- Skewness & kurtosis: check both coefficients to investigate the
causes of non-normality. Skewness is, in general, more problematic
than kurtosis. Its effects are more important (at least in Student's
t tests) than the effects of kurtosis, although high kurtosis (usually
a sign of the presence of outliers) can reduce dramatically the
efficiency of parametric methods like ANOVA.

- Take also a look at the box-plot.

Dear Ms. Marta:

Do you mean that SW test is more efficient with big sample sizes from KS test?

Many thanks.

Omar.

"Oversensitive" was intended as something negative. I mean that the test tends to give false positive results with big sample sizes, and should be discarded (it is better in that situation to check skewness - if it's absolute value is smaller than 1 then the distribution is reasonably symmetric and SW can be safely ignored.

Regards

Marta

我觉得还是probability integral transform比较准..

Hello, if the Mauchly's Test of Sphericity is significant (I am running
GLM to test MANCOVA), is it absolutely necessary that I use the
Greenhouse-Geisser correction of the degrees of freedom, or can I still
use the df's from the "sphericity assumed' calculation? In other words,
how bad is the violation of sphericity assumption for the validity of
the significant results?

Thanks a lot.

Bozena

Bozena Zdaniuk, Ph.D.

University of Pittsburgh
UCSUR, 6th Fl.
121 University Place
Pittsburgh, PA 15260
Ph.: 412-624-5736
Fax: 412-624-4810
Email: bozena@pitt.edu

Hi Bozena,

First of all have you tested for normality? Mauchly's test is affected
by non-normality, tending to accept the homogeneity assumption too
often for short-tailed distributions (platicurtic) and to reject too
often for heavy-tailed distributions (leptocurtic). Large sample sizes
will not protect against this problem. Check the residuals for the
presence of outliers.

Second: if Mauchly's test is significant, then type I error can go as
high as 10% or 15%. Yes, you MUST use adjusted degrees of freedom.

Source: DESIGNING EXPERIMENTS AND ANALYZING DATA A Model Comparison
Perspective. Scott E. Maxwell & Harold D. Delaney

Perhaps I didn't explain myself correctly. Mauchly's test indicates if
the correlations among the repeated measures are similar (the so
called sphericity assumption). If Mauchly's test is significant
because the correlations are different, then you must adjust the
degrees of freedom using G-G epsilon. But, sometimes (in heavy tailed
distributions) Mauchly's test can be significant even with similar
correlations. Heavy tails are NOT the cause of a failure in
sphericity, but the cause of a FALSE POSITIVE Mauchly's test. In that
case (Mauchly's test significant & very heavy tailed distributions
-outliers present-) you might consider that the sphericity condition
is OK and avoid the use of epsilon correction for the DF.

I'm not really fond of mathematical transformations (you loose contact
with your data in the same degree you gain normality). I remember that
high kurtosis could be prevented by taking two measures, instead of
one, and averaging them. This must be done during data recollection
(has to be foresighted in the designing steps), it can't be done right
now with your data.

Square root or logarithms might eliminate part of the kurtosis, but
the are more indicated for positively skewed data. If your data are
symmetric, then these transformations could add negative skewness to
your problems, but, as the saying goes "the taste of the pudding is in
the eating". Try them and see what happens with your data.

HTH

Marta

Hello group,

I need a quick help on normality test.

I have a 3x2x2 factorial design with two factors being scale(one with 3
levels and one with 2 levels), one factor being nominal (2 levels). I would
like to test for normality (an assumption for factorial ANOVA) and would
like to know how to do that in SPSS? Can somebody also provide some generial
syntax for SPSS?

What are the implications if normality would not hold?

Kind Regards,
Karl

The best approach is to test normality of the residuals of the model. You can output the residuals and use a descriptive procedure to test for non-normality. The normality assumption refers to the residuals anyway. You could also plot the residuals and do an occular test (eyeball it) although some journals are a bit rigid. Whether you have significant deviations from normality will depend on two things: is the data normal and how large is the sample size. With a very large sample size, almost any data will show significant deviations from linearity. With very small samples, almost no data will deviate from linearity. It's a persistent problem with tests of assumptions.

Paul R. Swank, Ph.D.
Professor, Developmental Pediatrics
Director of Research, Center for Improving the Readiness of Children for Learning and Education (C.I.R.C.L.E.)
Medical School
UT Health Science Center at Houston