Re: t-test question posting again
From: Jeff Sauro (jeff_sauro_at_despammed.com)
Date: 11/23/04
- Next message: Jeff Sauro: "Re: ANOVA on ordinal data"
- Previous message: Paige Miller: "Re: ANOVA on ordinal data"
- In reply to: Ross Clement: "Re: t-test question posting again"
- Next in thread: Lady Chatterly: "Re: t-test question posting again"
- Messages sorted by: [ date ] [ thread ]
Date: Tue, 23 Nov 2004 20:21:02 +0000 (UTC)
The recommendation to use both the non-parametric Mann-Whitney test
and the parametric t-test is a good strategy. The t-test turns out to
be a very "robust" test and as you have pointed out, is more resilient
to violations of normality and unequal variances. In your situation,
I think you’ll be fine with the t-test.
A couple additions. How are you determining that your variances are
unequal? Are you using a statistical test or are you just eye-balling
the variances or standard deviations? Even if the variances are not
equal, they REALLY need to be unequal for the t-test to start
providing invalid results (like a ratio of 2 or 4). In fact, the
worst situation for t-tests are when the sample sizes are very unequal
and the variances are very unequal. "Worrisome differences in the
variances that are detectable to the naked eye lead one to correct for
unequal variances without the intermediate step of deciding in fact if
the variances are really unequal." (Miller p. 58)
With the size of sample you have, (600-1000) the central-limit theorem
will have kicked in and almost certainly alleviated any problems with
normality.
So the general rule of thumb is for t-tests, normality is less of a
concern when your sample sizes are >30 (even >10) and the biggest
concern is unequal variances for unequal sample sizes. Most of the
time, the inequality of variances isn’t large enough to invalidate the
results.
I summarized the discussion from "Beyond ANOVA: Basics of Applied
Statistics by Rupert Miller (p40-59).
Jeff
On 23 Nov 2004 05:39:21 -0800, Ross Clement wrote:
>sine_arc@hotmail.com (Jiti) wrote in message
news:<42fbbg04n2ie@legacy>...
>> I posted this question about 2 months back but there was no
response.
>> It would be helpful if I could get some useful advice on the
>> following.
>>
>> I would like to know if it is valid to apply a t-test for comparing
>> means of two unpaired independednt samples in the following
situation.
>>
>> 1) Samples sizes are large ~ 600 to 1000
>> 2) Variances are not equal
>> 3) Samples do not follow normal distribution
>>
>> The samples may have equal or unequal no of observations. I have
read
>> somewhere that if the sample size is large, the assumption
regarding
>> the normal distribution can be ignored and we can apply t-test for
>> unequal variances. But I would like to know others opinions.
>
>I'm no expert statistician, but that rarely shuts me up.
>
>The t-test assumes normality, however it is fairly robust against
>non-normality. When the data is not normal, you can use the Wilcoxon
>(Mann-Whitney) test (<a
href="http://stat.tamu.edu/stat30x/notes/node150.html">http://stat.tamu.edu/stat30x/notes/node150.html>)
>instead. As someone advised me in a posting some time ago, if you're
>worried about non-normality, you can apply both a t-test and a
>wilcoxon test, and see if both tests show that the differences are
>significant.
>
>I use the statistical package R for significance tests, and it takes
>me about half a second extra to perform both t-test and wilcoxon
>tests, hence I always perform both.
>
>Cheers,
>
>Ross-c
Relevant Pages
|
