Basic Q about Mann-Whitney and t-test

[Charlotte-9]

Dear all,

This is just a basic general stats question.  Can anyone tell me under
what circumstances the Mann-Whitney U test and the t-test for comparing
two independent samples would provide different results?  The t-test leads
to a significant result (reject null hypothesis) whereas the Mann-Whitney
leads to a non-significant result.  Could this be a violation of the
normality assumption in the t-test?

Thanks!

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[Julius Sim]

If the assumptions of the t test are met, it will be more powerful than
the Mann Whitney (under such circumstances, the t test will normally have
between 105% and 116% of the power of the Mann Whitney to reject the null
hypothesis).

If the assumptions of the t test are not met (e.g. by a violation of
normality such as you mention), the Mann Whitney test is likely to be more
powerful than the t test. So your results are more likely when the t test
assumptions are satisfied, not when they are violated.

When checking the assumptions, you need to check homogeneity of variance
as well as normality. Ideally, do the analysis via the univariate ANOVA
function and look at the saved residuals.

Julius

> Dear all,
>
> This is just a basic general stats question.  Can anyone tell me under
> what circumstances the Mann-Whitney U test and the t-test for comparing
> two independent samples would provide different results?  The t-test leads
> to a significant result (reject null hypothesis) whereas the Mann-Whitney
> leads to a non-significant result.  Could this be a violation of the
> normality assumption in the t-test?
>
> Thanks!
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>

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[Charlotte-9]

Thanks for your response Julius - helpful information.

I'll have a close look at my data.

Charlotte

On Wed, 13 Feb 2008 17:29:58 -0000, Julius Sim <[hidden email]>
wrote:

>If the assumptions of the t test are met, it will be more powerful than
>the Mann Whitney (under such circumstances, the t test will normally have
>between 105% and 116% of the power of the Mann Whitney to reject the null
>hypothesis).
>
>If the assumptions of the t test are not met (e.g. by a violation of
>normality such as you mention), the Mann Whitney test is likely to be more
>powerful than the t test. So your results are more likely when the t test
>assumptions are satisfied, not when they are violated.
>
>When checking the assumptions, you need to check homogeneity of variance
>as well as normality. Ideally, do the analysis via the univariate ANOVA
>function and look at the saved residuals.
>
>Julius
>
>
>> Dear all,
>>
>> This is just a basic general stats question.  Can anyone tell me under
>> what circumstances the Mann-Whitney U test and the t-test for comparing
>> two independent samples would provide different results?  The t-test

leads
>> to a significant result (reject null hypothesis) whereas the Mann-
Whitney

>> leads to a non-significant result.  Could this be a violation of the
>> normality assumption in the t-test?
>>
>> Thanks!
>>
>> =====================
>> To manage your subscription to SPSSX-L, send a message to
>> [hidden email] (not to SPSSX-L), with no body text except the
>> command. To leave the list, send the command
>> SIGNOFF SPSSX-L
>> For a list of commands to manage subscriptions, send the command
>> INFO REFCARD
>>
>
>=====================
>To manage your subscription to SPSSX-L, send a message to
>[hidden email] (not to SPSSX-L), with no body text except the
>command. To leave the list, send the command
>SIGNOFF SPSSX-L
>For a list of commands to manage subscriptions, send the command
>INFO REFCARD

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