<- file stat .html -> *********************** computing with correlations **********

... get an average of correlations?

=========================Rich Ulrich, 23 Aug 1996======ssc Message-ID: <4vkiip$bbf@usenet.srv.cis.pitt.edu> William B. Ware (wbware@EMAIL.UNC.EDU) wrote: : On Thu, 22 Aug 1996, Jean-Luc KOP wrote: : > I have to compute the mean of several correlations. Is it statistically : > correct to do so or should I transform the correlations in z values (with : > the Fisher transformation) or is there another method ? : It has "always" been my understanding that you should first transform the : correlation coefficients to z-values using Fisher's transformation. After Since the correlations have an implicit confidence range, based on N, you could note that it is of limited use to average correlations that are INCONSISTENT with each other; and so it is nice to compute a test of homogeneity. LIMITED USE == If the r's are consistent, you *might* assume that the average does *estimate* both, or several, groups/sets/samples. If they are inconsistent, you can only point to the result as "an average". * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

... compare correlations?

=========================Rich Ulrich, 26 Aug 1996=====ssc Subject: Re: Comparing r statistics in linear regression models Message-ID: <4vstgk$5o1@usenet.srv.cis.pitt.edu> steve collins (steve@concern1.demon.co.uk) wrote: : Can anybody give send me the formula or point me to a suitable : reference for performing a t-test to compare two correlation : coefficients -- steve collins Ferguson, "Statistical methods in psychology and education" has formulas for a couple of circumstances of comparing correlations. If there are two samples with the same pair of variables, then you *probably* ought to be testing whether the regression lines are the same, instead of testing r. If you want to compare r(x,y) with r(x,z) [correlated correlations], then, some months ago, I cited a better test than the one shown in my 1966 edition of Ferguson; but I don't have that reference handy. * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

... compare correlated correlations?

=======================Rich Ulrich, =================??? Here is a recent reference about comparing 'correlated' correlations ( Is r(1,2) greater than r(1,3), taking into account r(2,3) ? ), which seems to be a nastier problem than the other. It comes down solidly AGAINST Hotelling's so-called 'exact' solution which treats r as r. Converting r to z as the first step seems to be the RIGHT first step, according to them, and to most people devising tests. Even if it is not perfect, it is better than NOT doing the conversion. Meng, Xiao-Li, Rosenthal, Robert; and Rubin, Donald B. (1992). "Comparing correlated correlation coefficients." _Psychological Bulletin_ , 111, 172-175. Hotelling's solution is included in Ferguson's textbook. [June 17, 2002: vol., above, corrected to '111'. Comment: Hotelling's is an exact test of a particular hypothesis, one that tests positive correlations against a *residual* of error variation in the criterion. The articles I have read have not made clear that one test is proper when the other is not. === Communication, 2002, from Paul von Hippel " ... if you read the appendix and related articles you realize that they're confining themselves to the case where the regressors are random variables. If the regressors are fixed, as in an experimental design, then Hotelling's test is appropriate. Hotelling (1940) was quite explicit about this, so what Meng, Rosenthal, & Rubin are really criticizing is the mistaken practice of using Hotelling's test with random regressors. "Williams (1959) adapted Hotelling's test to the case of random regressors. In simulation studies Williams' test has held up quite well against the alternatives described by Meng, Rosenthal, & Rubin. This is all in the papers cited in MR&R's bibliography." === end of communication ]. =====================Rich Ulrich, 11 Apr 1996========sse Message-ID: <4kj5d0$9eh@usenet.srv.cis.pitt.edu> : > Date: Wed, 10 Apr 96 07:44:00 CDT : > From: Ree, Malcolm J. <Ree@alhrm.brooks.af.mil> : > Subject: Re: McNemar's Test? (fwd) : > : > There is a hypothesis test due to Quinn McNemar for testing the difference : > between dependent correlations. It is distributed as t with appropriate : > degrees of freedom. I used it in my dissertation 20 years ago. I have not : > seen it programmed in any statistical package. When I think of McNemar's test, I automatically do think of the simple Test-for-Changes, computed on certain 2x2 tables. But I think I ran into this other "McNemar's test" a few years ago, when I also learned about what seemed to be a better alternative. Ref: "Comparison of tests of the equality of dependent correlation coefficients," JASA 66:904-908, 1966. OJ Dunn and VA Clark. Best test (i.e., the one that I subsequently revised a program to use) seemed to be Williams' modification of Hotelling's formula. * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

... compare correlation matrices?

======================Duncan Mackay, 4 Nov 1995======ssm From: bidam@flinders.edu.au (Duncan Mackay) Message-ID: <bidam.11.0008A218@flinders.edu.au> >Some months ago, there was a discussion on this group about >methods to compare correlation or covariance matrices. Though >I recall some problems (low power or sensitivity to assumption >violations, perhaps?), I might need to use this technique. Rayner,JCW; Manly,BFJ; Liddell,GF (1990): Hierarchic likelihood ratio tests for equality of covariance matrices. J. Statist. Comput. Simul. 35, 91-99. Manly,BFJ; Rayer,JCW (1987): The comparison of sample covariance matrices using likelihood ratio tests. Biometrika 74, 841-847. * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

... compare variances in correlated samples?

<< I raised the issue once, that Poisson-variables would also show a difference in variance, without raising ANY question about whether the subsequent t-test is valid. So here is a test which mainly provides a bit of extra information about two samples... and there IS an analogue to the Levene test, below. >> >The standard tests for equality of variance assume independence of >the samples. > What is the appropriate test when the samples are correlated? For > example, when a paired t-test is performed for equality of means, > what should be the corresponding test for equality of variances? ----------------------------------------------------------------------- ==========John Randall, 17 Sep 1996=====ssc From: jhr@MATIES.SUN.AC.ZA (John Randall, Biometrician, Faculty of Agric.Sci.) Message-ID: <jhr.84.000E638A@MATIES.SUN.AC.ZA> See Snedecor & Cochran's "Statistical Methods", published by the Iowa University Press, at the end of the chapter on correlation (e.g. P192 in the 8th edition). jhr@maties.sun.ac.za John. ==========post by Hans-Peter Piepho, Sep 1996=====ssc Hans-Peter Piepho (piepho@WIZ.UNI-KASSEL.DE) wrote: << referring to the Levene test >> : (1) A more robust version is obtained by subtracting the treatment median : from each obseration and doing a paired t-test. This is analogous to the : Brown-Forsthe version of the Levene test. : (2) A ingenious method was proposed by Pitman and Morgan in 1939: Take sums : (s) and differences (d) of measure1 and measure2 on each item and test : Pearson's correlation between s and d. Significance of the test indicates : variance heterogeneity. Unfortunately the procedure is quite sensitive to : non-normality. Using Spearmans rank correlation in stead of Pearson's : correlation gives a reasonably robust test with good power [In my simulation : experience the power tends to be better than (1), but the test is a bit less : robust than (1)]. : Hans-Peter ==============Karl Wuensch, 31 Oct 1994====sse Message-ID: <9411010413.AA10124@jse.stat.ncsu.edu> From: "Karl L. Wuensch" <PSWUENSC@ECUVM.CIS.ECU.EDU> To test homo of variance for two correlated samples, you can use: (F - 1) * Sqrt(N - 2) t = ------------------------- on N - 2 df, where F = larger / smaller var 2 * Sqrt(F * (1 - r **2)) and r = the corr between the two samples See Pittman, Biometrika, 1939, 31, 9-12. * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

... compare (partial) regressions?

=======================Rich Ulrich, 10 Sep 1996=======ssc Subject: Re: testing difference between partial regression coeffs -Reply Message-ID: <513tl5$du2@usenet.srv.cis.pitt.edu> Jerrold Zar (T80JHZ1@WPO.CSO.NIU.EDU) wrote: : I would refer you to texts on multiple regression, or to the introductory : text: Biostatistical Analysis, 3rd ed., 1996, by J. H. Zar, pp. 429-430. : >>> Michael Bailey <jm-bailey@NWU.EDU> 08/05/96 09:00pm >>> : A friend of mine has regressed Y on X1 and X2, and wants to test the : difference between the partial regression coefficients for X1 and X2. I : know you can do this via structural modeling programs such as LISREL. : Is there another way? A simple solution is to note that you can model equal coefficients with b1*(X1+X2) So if you put T which equals (X1+X2) into your regression equation, along with a constructed variable S, then the test on S is a test for their difference, if S is any other function of (X1, X2) -- usually you would use the difference, or else X1, or X2. * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

... compare two regressions? (Chow test)

=======================Rich Ulrich, 01 May 1995==========ssc Subject: Comparing coefficients in different regressions: T-test but how many DF? Hume Winzar (winzar@commerce.murdoch.edu.au) wrote: : I have two different samples for which I want to compare : selected coefficients in a multiple regression problem. : I know I can test whether the whole models are different using a Chow test or : similar, but I want to know WHICH of the 16 estimates are different in the : two regressions. Since these estimates are `partial' coefficients, using the total equation to look at single-variable differences is pretty unintelligible to me, including your suggestion [omitted] to construct t-tests in a simple way. [Sentence added-] If you set up your model for a complete Chow test, it will be easy to drop some dummy variables, to examime sub-sets: The direct way that you can computer-program the CHOW test (comparing the residual for one set of regressors with the sum of residuals for two separate set of regressors), leads to something that might be helpful, though there is a real hazard here of data-dredging. For the set of variables A,B,C,... , <original> construct dummy variables A',B',C',... <o-prime> such that for the cases in one sample, A'=A, B'=B, ... and in the other sample, 0= A'=B'=C' ... < compute a'=a; if(grp=2) then a'=0 > Then, the CHOW test is the test on variance accounted for when the o-prime variables are added as a set to the original variables, at a single step. Your regression program should have this option. Else, compute the F by hand, from the difference in residuals and DF. For each o-prime variable, you have a test for what it adds, regarded as the last thing added in the equation. Presumably, you could remove the o-prime variables one at a time, to find some smaller subset of variables that distinguish the regressions of the two samples. Then, you will probably be strongly tempted to make false statements such as, `Therefore, the variables that were dropped don't matter... ' even if something has been retrained that is practically IDENTICAL to what has been dropped. But that is a problem that people have with regressions, anyway. * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

... partial corr. with a categorical var?

========================Rich Ulrich, 24 Jul 1996======ssc Subject: Partial correlations involving categorical and continuous variables? Message-ID: <4t5dmm$k65@usenet.srv.cis.pitt.edu> Noam Tractinsky (noamt@bgumail.bgu.ac.il) wrote: < deleted, problem defined, for continuous A, B, and categorical C ... > : I would like to find the partial correlation between Var A and Var B, : adjusted for Var C. Is this possible at all? I would appreciate any : advice or reference to the literature. It looks to me like you would like the "within-groups correlation" which SPSS (for instance) provides as optional output when doing discriminant function. Basically, it pools "sums of squared-deviations", as computed around separate group means. In humdrum cases, it will be about what you get if you average the correlations obtained for each category of C. * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

What is the test on correlation shown with the paired t-test?

=======================Rich Ulrich, 19 Oct 1995==========ssc,ssm Subject: Re: excel t-test p-values? Message-ID: <465m1o$2d3@usenet.srv.cis.pitt.edu> Vanessa L. Gates (Papillon@umich.edu) wrote: : Please explain or give a good reference: <snip> : Question 2: : Using the paired t-test, I get a p-value of 0.005. However, a regression : fit gives a slope of 1.05 with a p-value of 3E-38. The two means are : within 2% of each other as well as the sample variance. The data are two : sample calculation methods which calculate the same result using the : same set of data. I understand that this p-value indicates that there : exist a significant difference between the two samples assumming an : alpha of 0.05. Is this correct? [commenting on the test with p nearly 0, E-38] NO! You are reporting the test on the SLOPE, which was assessed as near to 1.0 - this test tells you that the line drawn on a scatterplot DOES tend to predict one value from the other, and the p-value says that it does it nearly perfectly. The regression tests the SIMILARITY. The paired t-test tests whether one score is systematically higher than the other: one revealing way to compute the paired t-test is to subtract one score from the other, and compare that set of numbers to zero. For your data, the t-test shows that that difference is "0.005", "significant" at .05 or .01 (even though the actual difference in points may be very tiny, it is somewhat REGULAR). * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

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