NAG Library Manual, Mark 27.2
```    Program g08akfe

!     G08AKF Example Program Text

!     Mark 27.2 Release. NAG Copyright 2021.

!     .. 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

!     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))

!     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
```