Re: What are the Parameters for Algorithm AS 62 APPL. STATIST. (1973) VOL.22, NO.2

From: Roland (roland_at_nospam)
Date: 09/10/04 

Date: Fri, 10 Sep 2004 07:14:48 +0200

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

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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