!
! one-way analysis of variance test
!
nameList = ?1
!
@splitString nameList k names error
if (error) then
  display 'an error occurred splitting the name list into vector names'
  return
endif
!
! k    = number of populations
! n[i] = i_th population size
! T[i] = total of the observations for the i_th population
! TT   = grand total of all observations from all populations
! df   = population degrees of freedom
! dfe  = error degrees of freedom
! dft  = total degrees of freedom
! SSTr = sum of squares for the populations
! SSE  = error sum of squares
! SST  = total sum of squares
! MSTr = population mean square
! MSE  = error mean square
!
df = k-1
dfe = 0
do i = [1:k]
 T[i] = sum(names[i])
 n[i] = len(names[i])
 dfe = dfe + n[i] - 1
enddo
dft = df + dfe
TT = sum(T)
SSTr = sum(T^2/n)-TT^2/sum(n)
SST = 0
do i = [1:k]
 do j = [1:n[i]]
   SST = SST + (names[i])[j]^2
 enddo
enddo
SST = SST - TT^2/sum(n)
MSTr = SSTr/df
SSE = SST - SSTr
MSE = SSE/dfe
F = MSTr/MSE
='Source of        Degrees of      Sum of          Mean              F'
='Variation         Freedom        Squares         Square'
='----------------------------------------------------------------------'
='Populations '//rchar(df,'%12.0f')//rchar(SSTr,'%15.1f')//rchar(MSTr,'%15.1f')//rchar(F,'%15.1f')
='Error       '//rchar(dfe,'%12.0f')//rchar(SSE,'%15.1f')//rchar(MSE,'%15.1f')
='Total       '//rchar(dft,'%12.0f')//rchar(SST,'%15.1f')
=' '
criticalValue = 1-fisher(df,dfe,F)
='Null hypothesis: the differences among the sample means can be atributed to chance'
='Accept the null hypothesis at a significance level of '//rchar(criticalValue*100)//'%'
=' '
destroy error k n df dfe dft i j T TT SST SSTr MSTr SSE MSE F nameList names rowLen numberOfPopulations