```
Program g08akfe
! G08AKF Example Program Text
! Mark 27.1 Release. NAG Copyright 2020.
! .. Use Statements ..
Use nag_library, Only: g08ahf, g08akf, nag_wp
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Integer, Parameter :: nin = 5, nout = 6
! .. Local Scalars ..
Real (Kind=nag_wp) :: p, pexact, u, unor
Integer :: ifail, liwrk, lwrk, lwrk1, lwrk2, &
mn, n1, n2, nsum
Logical :: ties
Character (1) :: tail
! .. Local Arrays ..
Real (Kind=nag_wp), Allocatable :: ranks(:), wrk(:), x(:), y(:)
Integer, Allocatable :: iwrk(:)
! .. Intrinsic Procedures ..
Intrinsic :: max, min
! .. Executable Statements ..
Write (nout,*) 'G08AKF Example Program Results'
Write (nout,*)
! Skip heading in data file
Read (nin,*)
! Read in problem size
Read (nin,*) n1, n2, tail
! Calculate sizes of various workspaces
nsum = n1 + n2
mn = min(n1,n2)
! Workspace for G08AHF
lwrk1 = nsum
! Workspace for G08AKF
lwrk2 = mn + mn*(mn+1)*nsum - mn*(mn+1)*(2*mn+1)/3 + 1
liwrk = 2*nsum + 2
lwrk = max(lwrk1,lwrk2)
Allocate (x(n1),y(n2),ranks(nsum),wrk(lwrk),iwrk(liwrk))
! Read in data
Read (nin,*) x(1:n1)
Read (nin,*) y(1:n2)
! Display title
Write (nout,*) 'Mann-Whitney U test'
Write (nout,*)
! Display input data
Write (nout,99999) 'Sample size of group 1 = ', n1
Write (nout,99999) 'Sample size of group 2 = ', n2
Write (nout,*)
Write (nout,*) 'Data values'
Write (nout,*)
Write (nout,99998) ' Group 1 ', x(1:n1)
Write (nout,*)
Write (nout,99998) ' Group 2 ', y(1:n2)
! Perform test
ifail = 0
Call g08ahf(n1,x,n2,y,tail,u,unor,p,ties,ranks,wrk,ifail)
! Calculate exact probabilities
If (ties) Then
ifail = 0
Call g08akf(n1,n2,tail,ranks,u,pexact,wrk,lwrk,iwrk,ifail)
End If
! Display results
Write (nout,*)
Write (nout,99997) 'Test statistic = ', u
Write (nout,99997) 'Normal statistic = ', unor
Write (nout,99997) 'Tail probability = ', p
Write (nout,*)
If (ties) Then
Write (nout,*)
Write (nout,*) 'Ranks'
Write (nout,*)
Write (nout,99998) ' Group 1 ', ranks(1:n1)
Write (nout,*)
Write (nout,99998) ' Group 2 ', ranks((n1+1):nsum)
Write (nout,*)
Write (nout,*)
Write (nout,99997) 'Exact tail probability = ', pexact
Else
Write (nout,*) &
'There are no ties in the pooled sample so G08AKF was not called.'
End If
99999 Format (1X,A,I5)
99998 Format (1X,A,8F5.1,2(/,14X,8F5.1))
99997 Format (1X,A,F10.4)
End Program g08akfe
```