Re: What are the Parameters for Algorithm AS 62 APPL. STATIST. (1973) VOL.22, NO.2
From: Alan Miller (amiller_at_bigpond.net.au)
Date: 09/10/04
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Date: Fri, 10 Sep 2004 04:50:37 GMT
"Roland" <roland@nospam> wrote in message
news:XuCdnU3zcbwjtNzcRVn-hA@giganews.com...
> Many thanks, however I am still at loss regarding how to interpret the
> matrix. For example, assuming I have 2x2 elements, how can I get the 0.95
> critical value? (I know very little about the Mann Whitney test as you can
> see...)
>
> Assuming I didn't make a mistake translating the algorithm I get:
> FRQNCY = 0.2, 0.4, 0.8, 1 ,1
>
Well, 0.8 is less than 0.95 and 1.0 is greater.
As the frequencies relate to values 0. 1, 2, 3 and 4, the last two are are
greater than your critical value.
That is looking at a one-tailed test.
For a two-tailed test, your critical values are those below 0.025 and above
0.975.
-- Alan Miller Retired Formerly with CSIRO, Division of Mathematics & Statistics > Thanks in advance. > > > "Alan Miller" <amiller@bigpond.net.au> wrote in message > news:R%70d.25212$D7.17652@news-server.bigpond.net.au... > > By 'parameters', do you mean the arguments of the routine? > > The algorithm was published in the journal Applied Statistics in 1973 in > > volume 22. > > The description of array FRQNCY given is: > > Output: the full sampling distribution for the Mann-Whitney U statistic > for > > sample sizes > > M and N, stored in the first (M*N + 1) elements. The first element of > > FRQNCY > > holds the sampling frequency for U = 0. Any elements beyond (M*N + 1) > are > > left > > unchanged. > > > > Cheers > > > > -- > > Alan Miller > > Retired > > Formerly with CSIRO, > > Division of Mathematics & Statistics > > > > "Roland" <roland@nospam> wrote in message > > news:ya6dnbC0x8H3n9zcRVn-rg@giganews.com... > > > Does anyone know what the parameters mean in this one? I do not have > > access > > > to the original article. > > > Specifically, how do I interpret the FRQNCY array (how is it indexed)? > > TIA. > > > > > > Here is the Fortran algorithm (http://lib.stat.cmu.edu/apstat/62): > > > > > > c AS 62 generates the frequencies for the Mann-Whitney U-statistic. > > > c Users are much more likely to need the distribution function. > > > c Code to return the distribution function has been added at the end > > > c of AS 62 by Alan Miller. Remove the C's in column 1 to activate it. > > > c > > > SUBROUTINE UDIST(M, N, FRQNCY, LFR, WORK, LWRK, IFAULT) > > > C > > > C ALGORITHM AS 62 APPL. STATIST. (1973) VOL.22, NO.2 > > > C > > > C The distribution of the Mann-Whitney U-statistic is generated for > > > C the two given sample sizes > > > C > > > INTEGER M, N, LFR, LWRK, IFAULT > > > REAL FRQNCY(LFR), WORK(LWRK) > > > C > > > C Local variables > > > C > > > INTEGER MINMN, MN1, MAXMN, N1, I, IN, L, K, J > > > REAL ZERO, ONE, SUM > > > DATA ZERO /0.0/, ONE /1.0/ > > > C > > > C Check smaller sample size > > > C > > > IFAULT = 1 > > > MINMN = MIN(M, N) > > > IF (MINMN .LT. 1) RETURN > > > C > > > C Check size of results array > > > C > > > IFAULT = 2 > > > MN1 = M * N + 1 > > > IF (LFR .LT. MN1) RETURN > > > C > > > C Set up results for 1st cycle and return if MINMN = 1 > > > C > > > MAXMN = MAX(M, N) > > > N1 = MAXMN + 1 > > > DO 1 I = 1, N1 > > > 1 FRQNCY(I) = ONE > > > IF (MINMN .EQ. 1) GO TO 4 > > > C > > > C Check length of work array > > > C > > > IFAULT = 3 > > > IF (LWRK .LT. (MN1 + 1) / 2 + MINMN) RETURN > > > C > > > C Clear rest of FREQNCY > > > C > > > N1 = N1 + 1 > > > DO 2 I = N1, MN1 > > > 2 FRQNCY(I) = ZERO > > > C > > > C Generate successively higher order distributions > > > C > > > WORK(1) = ZERO > > > IN = MAXMN > > > DO 3 I = 2, MINMN > > > WORK(I) = ZERO > > > IN = IN + MAXMN > > > N1 = IN + 2 > > > L = 1 + IN / 2 > > > K = I > > > C > > > C Generate complete distribution from outside inwards > > > C > > > DO 3 J = 1, L > > > K = K + 1 > > > N1 = N1 - 1 > > > SUM = FRQNCY(J) + WORK(J) > > > FRQNCY(J) = SUM > > > WORK(K) = SUM - FRQNCY(N1) > > > FRQNCY(N1) = SUM > > > 3 CONTINUE > > > C > > > 4 IFAULT = 0 > > > C > > > C Code to overwrite the frequency function with the distribution > > > C function. N.B. The frequency in FRQNCY(1) is for U = 0, and > > > C that in FRQNCY(I) is for U = I - 1. > > > C > > > C SUM = ZERO > > > C DO 10 I = 1, MN1 > > > C SUM = SUM + FRQNCY(I) > > > C FRQNCY(I) = SUM > > > C 10 CONTINUE > > > C DO 20 I = 1, MN1 > > > C 20 FRQNCY(I) = FRQNCY(I) / SUM > > > C > > > RETURN > > > END > > > > > > > > > > > >
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