Re: when to use nonparametric statistics

On Wed, 03 Dec 2003 10:22:28 GMT, "jackson marshmallow"
<[EMAIL PROTECTED]> wrote:

>
>"Jay Weedon" <[EMAIL PROTECTED]> wrote in message
>news:[EMAIL PROTECTED]
>> On Mon, 01 Dec 2003 02:33:13 GMT, "jackson marshmallow"
>> <[EMAIL PROTECTED]> wrote:
>>
>> >1) Two samples of are given and I need to compare their means and
>variances.
>> >The distribution of the population is unknown. Can I use the F-test and
>the
>> >t-test? Is it necessary that the sample _means_ have a Gaussian
>> >distribution? Is it sufficient? Maybe I misunderstand something here...
>>
>> You say "the F-test". There are several F-tests you could be referring
>> to here. Typical procedure would be to use the t-test to compare
>> means, the Levene F-test to compare variances.
>>
>> The t-test assumes that the sampling distribution of the sample means
>> is normal. If the samples are large, this will be true pretty much
>> regardless of the distribution of the scores. If the samples are small
>
>But doesn't it also assume that the distribution of all values in the sample
>is normal?

If the sample is large, the sampling distribution of the sample mean
will be close enough to normal that the p-value of the t-test will be
quite accurate, regardless of the underlying distribution. There is
lots of empirical evidence to support this assertion.

>> and the underlying distribution unknown, this is not a very safe
>> assumption, you'd likely be better off with a Wilcoxon test or a
>> permutation test. The usual form of the t-test also assumes equal
>> variances, so watch for that pitfall.
>>
>
>> >2) I need to calculate the significance of correlation between two
>> >sequences. I would actually prefer to use randomization, but the
>sequences
>> >may be too short. Another option is to perform linear regression and
>> >calculate the significance of the slope using a t-test (?). When is it
>> >valid?
>>
>> The assumption for the test of Pearson correlation (which is
>
>By "test of Pearson correlation" do you mean the actual correlation or its
>significance?

A Pearson correlation is a measure, not a test. You said you "need to
calculate the significance of correlation", which I took to refer to a
test of the null hypothesis that the Pearson correlation is zero. I'm
referring to the test that is usually used in this situation.

>> mathematically the same as linear regression) is (roughly speaking)
>> that the 2 variables are normally distributed and have a linear
>> association. Again, if the samples are small or the association
>> nonlinear, a nonparametric measure (e.g., Spearman correlation) may be
>> safer.

JW