Re: Confidence interval is mathematically equivalent to hypothesis test

[Mark Hancock]

This is a good point, yes. I'm not the original requester, but I think they were really asking for a simple way to get a CI when reporting summary/descriptive statistics (without having a second mean to compare to). In SPSS you can do this: https://en.wikibooks.org/wiki/Using_SPSS_and_PASW/Confidence_Intervals

Maybe this is just my misunderstanding of AGGREGATE and PSPP syntax, but my point was just that there's nothing inherent about the question that should require a t-test - i.e., you can use z by default (and t-tests are really just extensions of z-scores anyway). z=1.96 works for 95% CIs, and Alan's suggestion does what I think the original requester was asking.

Pointing to t-tests isn't a bad idea either, though, and maybe providing syntax for how to reduce it to a z-score would help the original requester (though I don't think they have another mean or value to compare it to).

On Fri, Oct 12, 2018 at 9:33 AM Dr. Oliver Walter <address@hidden> wrote:

A confidence interval is mathematically equivalent to its corresponding hypothesis test. The hypothesis test is significant if the corresponding confidence interval does not contain the parameter value of the null hypothesis. The confidence interval does not contain the parameter value of the null hypothesis if the hypothesis test is significant. Hence, wether you calculate the confidence interval or conduct the hypothesis test, doesn't really matter.

mean(X) +/- t * sd/sqrt(n): confidence interval for the expected value of X, mu, X normally distributed with unknown population variance

t = (mean - mü0)/ (sd/sqrt(n)) : test statistic for testing if mu equals the value in the null hypothesis, mu0, X normally distributed with unknown population variance

If mü0 is not contained in the confidence interval, the hypothesis test is significant.

Dr. Oliver Walter

Am 12.10.2018 um 15:01 schrieb Mark Hancock:

I unfortunately don't know enough about PSPP syntax to suggest how to do this, but a CI is not always associated with a hypothesis and can be calculated from just a mean and SD (and a cumulative distribution function, which is typically the normal one). Typically the formula is something like:

mean ± z(SD/sqrt(n)), where z is from the CDF.

On Fri, Oct 12, 2018 at 6:29 AM John Darrington <address@hidden> wrote:

The confidence interval is a concept associated with a hypothesis.
If it's the confidence interval on the test for a mean value, typically you
would get that by using a T-Test.


On Fri, Oct 12, 2018 at 10:40:22AM +0200, Werner LEMBERG wrote:

     Folks,


     I would like to get a 95% confidence interval so that I could use it
     in AGGREGATE, e.g.,

       AGGREGATE OUTFILE * MODE ADDVARIABLES
         /BREAK=...
         /Mean = mean(V)
         /CI = ci(V, 0.95)

     What must I do to get the result of my hypothetical `ci' function?
     I'm a PSPP novice, so maybe there is a better solution than AGGREGATE
     ??? what I ultimately want is to emit the confidence interval of a
     variable to a CSV file using SAVE TRANSLATE.


         Werner
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