forum questions

[drfg2008]

two questions that come up time and again in statistics forums :

(1) the chi-square test gives a p-value for a two-sided hypothesis. How can we calculate the p value for the  one-sided test? (Chi-Square is not symmetrically distributed)

(2) The regression analysis yields b coefficients. How is it possible to determine which coefficients are significantly different? (they should be t-distributed)

Some answers are familiar to me of course, but what is right....

[Maguin, Eugene]

Embedded. Gene Maguin

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of drfg2008
Sent: Monday, August 19, 2013 9:12 AM
To: [hidden email]
Subject: forum questions

two questions that come up time and again in statistics forums :

(1) the chi-square test gives a p-value for a two-sided hypothesis. How can we calculate the p value for the  one-sided test? (Chi-Square is not symmetrically distributed)

>>Are you asking about a crosstabulation or another type of test where the test statistic is distributed as a chi-square? What would be an example of a directional hypothesis in cross-tabulation?

(2) The regression analysis yields b coefficients. How is it possible to determine which coefficients are significantly different? (they should be
t-distributed)

>> from 0? From each other in the same equation ? from each other in different equations? I think this covers the possibilities.

Some answers are familiar to me of course, but what is right....



-----
Dr. Frank Gaeth
FU-Berlin

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[Andy W]

Your confused about 1, almost invariably Chi-square tests are examining the area of the PDF only above the test statistic. One notable example of examining the PDF below the test statistic is Fisher's critique of Mendel's pea experiments as being fabricated- see http://digital.library.adelaide.edu.au/dspace/bitstream/2440/15123/1/144.pdf or Mendel's wikipedia page, http://en.wikipedia.org/wiki/Gregor_Mendel. (Some quick googling turned up a variety of other discussion on the topic, in particular a series of articles in a journal named Genetics.)

The answer is then fairly trivial (at least in terms of SPSS). Given a chi-square distribution with particular degrees of freedom, you estimate CDF.CHISQ for your given estimate and it default gives you the p-value for the area to the left of your statistic. Or if you are examining the output of a test procedure you could just take [1 - p-value].

Two I agree with Gene, it needs to be more clear what exact test your are interested in. Tests for differences between coefficients requires an estimate of the covariance between coefficients. Like you said, I'm sure many have come up before, so just trawl the forums and see if you can find the answer your interested in. (In this way I'm confused about what you want for an answer.)

[drfg2008]

B: from each other in the same equation

---------

The example was: chi-square directional in a crosstabulation; male/female - smoker/nonsmoker. The Hypothesis would be directional: "men smoke more than women". Similar to: "men are taller than women". µ(i) > µ(j).

I only know it as: H0:p(ij) = pi.p.j
Test on independence. Never heard of a directional Hypothesis here.

[p = pi]

[Bruce Weaver]

For a 2x2 table, the square root of Pearson's chi-square gives you the test value for the usual z-test comparing two independent proportions, so you can use the standard normal distribution to get a one-tailed p-value.  But remember that when using a one-tailed test, you must be willing to treat an enormous difference in the "wrong" direction exactly the same as no difference.  Quite often, people are not really willing to do so, I suspect.

drfg2008 wrote

B: from each other in the same equation

---------

The example was: chi-square directional in a crosstabulation; male/female - smoker/nonsmoker. The Hypothesis would be directional: "men smoke more than women". Similar to: "men are taller than women". µ(i) > µ(j).

I only know it as: H0:p(ij) = pi.p.j
Test on independence. Never heard of a directional Hypothesis here.

[p = pi]

[Rich Ulrich]

1) The "chi" in chi-squared is distributed as a Normal z.  Statistical
forums should not have to spend much time on the answer.

Basic statistical theory derives chi-squared with k degrees of
freedom as equal to the sum of k independent z-squared's. 

If you have a 2x2 table of proportions (say), tested for independence
with chi-squared, you can create a simple two-tailed test by using
the corresponding z.  Or you can get the p-value by dividing what is
reported for chi-squared by 2.

2)  Two regression coefficients are typically correlated, and a
test is usually written in matrix notation, using the correlation
matrix.  But if you want to know whether two coefficients are equal,
for x1 and x2, you can test an equation that uses v1= x1-x2  and
v2= x1+x2  and report the test on v1.  The test on v2 is whether
their common coefficient is "significant", with the test on v1
showing the test on the difference.

--
Rich Ulrich

> Date: Mon, 19 Aug 2013 06:12:12 -0700

> From: [hidden email]
> Subject: forum questions
> To: [hidden email]
>
> two questions that come up time and again in statistics forums :
>
> (1) the chi-square test gives a p-value for a two-sided hypothesis. How can
> we calculate the p value for the one-sided test? (Chi-Square is not
> symmetrically distributed)
>
> (2) The regression analysis yields b coefficients. How is it possible to
> determine which coefficients are significantly different? (they should be
> t-distributed)
>
> Some answers are familiar to me of course, but what is right....
>
>
> ...

[Maguin, Eugene]

You need the variance-covariance matrix for coefficients, which is BCOV in the Statistics subcommand. Like Andy said you have to take the covariance between the two coefficients into account. So, assume the unstandardized coefficients b1 and b2 have variances, Var(b1) and Var(b2), and a covariance, Cov(b1,b2). The formula for the variance of summed variables, x and y, is Var(x+y) = Var(x) + Var(y) + 2*Cov(x,y).
Gene Maguin



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of drfg2008
Sent: Monday, August 19, 2013 11:31 AM
To: [hidden email]
Subject: Re: forum questions

B: from each other in the same equation

---------

The example was: chi-square directional in a crosstabulation; male/female - smoker/nonsmoker. The Hypothesis would be directional: "men smoke more than women". Similar to: "men are taller than women". µ(i) > µ(j).

I only know it as: H0:p(ij) = pi.p.j
Test on independence. Never heard of a directional Hypothesis here.

[p = pi]



-----
Dr. Frank Gaeth
FU-Berlin

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View this message in context: http://spssx-discussion.1045642.n5.nabble.com/forum-questions-tp5721644p5721649.html
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