Re: How can we calculate p-value of one sample mean test if its normality test is insignificant?

jgong8811@xxxxxxxxx wrote:
On Mar 3, 11:37 pm, Richard Ulrich <Rich.Ulr...@xxxxxxxxxxx> wrote:
On Sun, 04 Mar 2007 10:30:41 +1030, randovaro <randov...@xxxxxxxxx>
wrote:



jgong8...@xxxxxxxxx wrote:
Hi there,
I collected 100 hundred data points for one sample, and want to
calculate the p-value of the mean test. However i found that its
normality test is insignificant (p-value is less than 0.0001). Upon
this situation, can I still go on to use one-sample t-test to
calculate the p-value?
Thank you!
A p-value of <0.0001 would be termed highly significant, but to answer
your question a t-test assumes normal distribution of data. However,
you may be able to transform your dataset (e.g. log transform) to reduce
the non-normal effects. Otherwise a non-parametric test would be more
appropriate.
I figure that this is a pretty good answer, given that the
questions have to be guessed-at.

By the way -
There are many manifestations of non-normality that
will not hurt the t-test. For instance, all the scores could
be integers, 1-5, assuredly non-normal by several tests
of normality because of massive counts of ties; and the
t-test would probably be okay.

Is the mean a good measure of the central tendency? - no
outliers or big gaps? ... then Least squared statistics will usually
do pretty well.

I suppose that the Original Poster is planning to test the
mean against zero (or some reasoned, fixed value).

--
Rich Ulrich, wpi...@xxxxxxxxxxxx://www.pitt.edu/~wpilib/index.html

thank you both so much!
I did make a mistake by writing insignificant instead of significant.
I tried more and have further question:

Now I want to compare two independent sample, each has 100
observations. Neither of the sample fit normal
distribution (p-values are less than 1e-3 for normality test), so I
tried to use non-parametric test of Mann-Whitney test. However I found
from http://149.170.199.144/new_rd/contents/nonpara.htm#Mann
that Mann-Whitney test assumpes "the two populations have the same
shape and same variance", which obviously does not apply to my data.
So I am puzzling which test method I can use to compare the central
tendency of the two samples.

thank you again!


I'm sure you can use the Mann-Whitney test as a non-parametric alternative to the t-test. Chapter 11a of http://faculty.vassar.edu/lowry/webtext.html covers the M-W fairly comprehensively...

"The only assumptions of the Mann-Whitney test are

1. that the two samples are randomly and independently drawn;
2. that the dependent variable is intrinsically continuous, capable in principle, if not in practice, of producing measures carried out to the nth decimal place; and
3. that the measures within the two samples have the properties of at least an ordinal scale of measurement, so that it is meaningful to speak of 'greater than', 'less than', and 'equal to'."
.

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