C:/Documents and Settings/Stephen/Desktop/Biostatistics Library and Program/Biostatistics/FriedmanGroupsCollection.cs

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using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Windows.Forms;

namespace StephenAshley.Biostatistics
{
   using NUMBER = Decimal;

   public class FriedmanGroupsCollection : GroupsCollection
   {
      public FriedmanGroupsCollection() : base() { }

      public FriedmanGroupsCollection(List<Group> groups) : base(groups) { }

      public override void Add(Group group)
      {
         if (group == null)
            throw new BiostatisticsException(
               "group is a null reference.");

         if (group.n() == 0)
            throw new BiostatisticsException(
               "group has no members.");

         if (groupsArray != null && k() > 0)
         {
            for (int i = 0; i < k(); i++)
            {
               if (group.n() != groupsArray[i].n())
                  throw new BiostatisticsException(
                     "Group size does not match size of other Groups.");
            }
         }

         base.Add(group);
         return;
      }

      public Int32 DegreesOfFreedom()
      {
         if (groupsArray == null)
            throw new BiostatisticsException(
               "FriedmanGroupsCollection contains no Groups.");

         return k() - 1;
      }

      public NUMBER FriedmanStatistic()
      {
         if (N() < 2)
            throw new BiostatisticsException(
               "FriedmanGroupsClass contains fewer than two subjects.");

         if (k() < 2)
            throw new BiostatisticsException(
               "FriedmanGroupsCollection has fewer than two treatments.");

         NUMBER decA = 0.0m;
         foreach (NUMBER value in SumsOfRanks())
            decA += value * value;                 // ΣR^2

         NUMBER decB = N() * k() * (k() + 1);      // nk(k + 1)

         NUMBER decC = 12.0m / decB;               // 12/nk(k + 1)
         NUMBER decD = decA * decC;                // 12/nk(k + 1) * ΣR^2
         NUMBER decE = 3.0m * N() * (k() + 1);    // 3n(k + 1)
         NUMBER decF = decD - decE;                // χ²r
         NUMBER decG = 1 - (NUMBER)SumOfTaus() / (NUMBER)(N() * k() * (k() * k() - 1));
         NUMBER decResult = decF / decG;
         return decResult;
      }

      public NUMBER CriticalValue()
      {
         if (N() < 2)
            throw new BiostatisticsException(
               "FriedmanGroupsClass contains fewer than two subjects.");

         if (k() < 2)
            throw new BiostatisticsException(
               "FriedmanGroupsCollection has fewer than two treatments.");

         if (k() < 3 || k() > 6)
            throw new BiostatisticsException(
               "k is outside the range of the critical values table.");

         if (N() > 15)
            throw new BiostatisticsException(
               "N is outside the range of the critical values table.");

         if (k() > 4 && N() > 10)
            throw new BiostatisticsException(
               "N is outside the range of the critical values table.");

         NUMBER decFriedman = FriedmanStatistic();
         ChiAlpha chiAlpha = GetLowestEntry(k(), N());
         if (decFriedman < chiAlpha.Chi)
            throw new BiostatisticsException("p > " +
               chiAlpha.Alpha.ToString());

         chiAlpha = GetHighestEntry(k(), N());

         if (decFriedman >= chiAlpha.Chi)
            return chiAlpha.Alpha;

         chiAlpha = GetClosestEntry(k(), N(), FriedmanStatistic());

         return chiAlpha.Alpha;
      }

      public Int32 N()
      {
         if (groupsArray == null) return 0;
         else
            return groupsArray[0].n();
      }

      public NUMBER p()
      {
         return (NUMBER)Distributions.ProbabilityChiSq((double)FriedmanStatistic(),
            DegreesOfFreedom());
      }
      public NUMBER[] SumsOfRanks()
      {
         if (groupsArray == null)
            throw new BiostatisticsException(
               "FriedmanGroupsCollection contains no Groups.");

         Rank[,] ranksArray = new Rank[k(), N()];

         // Construct a two-dimensional array of Ranks mirroring 
         // the values in groupsArray.
         for (int iTreatment = 0; iTreatment < k(); iTreatment++)
         {
            for (int iSubject = 0; iSubject < N(); iSubject++)
            {
               ranksArray[iTreatment, iSubject] = new Rank(iTreatment,
                  groupsArray[iTreatment][iSubject], 0.0m);
            }
         }

         // Rank the observations for each subject.
         List<Rank> lstRanks = new List<Rank>(k());
         for (int iSubject = 0; iSubject < N(); iSubject++)
         { // For each subject, rank the treatment outcomes
            for (int iTreatment = 0; iTreatment < k(); iTreatment++)
            {
               lstRanks.Add(ranksArray[iTreatment, iSubject]);
            }
            lstRanks.Sort(Rank.CompareRanks);
            for (Int32 i = 0; i < k(); i++)
               lstRanks[i] = new Rank(lstRanks[i].iGroup,
                  lstRanks[i].decValue, (NUMBER)(i + 1));
            Rank.AdjustTies(ref lstRanks);

            // For each subject, copy the rank into ranksArray
            for (int iTreatment = 0; iTreatment < k(); iTreatment++)
            {
               for (int i = 0; i < k(); i++)
               {
                  if (ranksArray[iTreatment, iSubject].decValue ==
                     lstRanks[i].decValue)
                  {
                     ranksArray[iTreatment, iSubject].decRank =
                        lstRanks[i].decRank;
                     break;
                  }
               }
            }
            lstRanks.Clear();
         }

         // Sum the Ranks within each treatment
         NUMBER[] returnArray = new NUMBER[k()];
         for (int iTreatment = 0; iTreatment < k(); iTreatment++)
            returnArray[iTreatment] = 0.0m;

         for (int iTreatment = 0; iTreatment < k(); iTreatment++)
            for (int iSubject = 0; iSubject < N(); iSubject++)
               returnArray[iTreatment] += ranksArray[iTreatment, iSubject].decRank;

         return returnArray;
      }

      private Int32 SumOfTaus()
      {
         if (groupsArray == null)
            throw new BiostatisticsException(
               "FriedmanGroupsCollection contains no Groups.");

         Rank[,] ranksArray = new Rank[k(), N()];
         Int32[] tiesArray = new Int32[N()];

         // Construct a two-dimensional array of Ranks mirroring 
         // the values in groupsArray.
         for (int iTreatment = 0; iTreatment < k(); iTreatment++)
         {
            for (int iSubject = 0; iSubject < N(); iSubject++)
            {
               ranksArray[iTreatment, iSubject] = new Rank(iTreatment,
                  groupsArray[iTreatment][iSubject], 0.0m);
            }
         }

         // Rank the observations for each subject.
         List<Rank> lstRanks = new List<Rank>(k());
         for (int iSubject = 0; iSubject < N(); iSubject++)
         {
            for (int iTreatment = 0; iTreatment < k(); iTreatment++)
            {
               lstRanks.Add(ranksArray[iTreatment, iSubject]);
            }
            lstRanks.Sort(Rank.CompareRanks);
            tiesArray[iSubject] = Rank.AdjustTies(ref lstRanks);
            lstRanks.Clear();
         }
         return tiesArray.Sum();
      }

      private ChiAlpha GetLowestEntry(Int32 iTreatmentCount, Int32 iSubjectCount)
      {
         Int32 iRow = 0;
         Int32 iEntry = 2;

         // Find the right row
         while (true)
         {
            Int32 iA = (Int32)CriticalValues[iRow, 0];
            if (iA == iTreatmentCount)
               break;
            else
               iRow++;
         }
         while (true)
         {
            Int32 iB = (Int32)CriticalValues[iRow, 1];
            if (iB == iSubjectCount)
               break;
            else
               iRow++;
         }

         // Find the first entry
         while (true)
         {
            NUMBER? decEntry = CriticalValues[iRow, iEntry];
            if (decEntry == null)
               iEntry++;
            else
               break;
         }

         return new ChiAlpha((NUMBER)CriticalValues[iRow, iEntry], alphas[iEntry]);
      } // GetLowestEntry()

      private ChiAlpha GetHighestEntry(Int32 iTreatmentCount, Int32 iSubjectCount)
      {
         Int32 iRow = 0;
         Int32 iEntry = 10;

         // Find the right row
         while (true)
         {
            Int32 iA = (Int32)CriticalValues[iRow, 0];
            if (iA == iTreatmentCount)
               break;
            else
               iRow++;
         }
         while (true)
         {
            Int32 iB = (Int32)CriticalValues[iRow, 1];
            if (iB == iSubjectCount)
               break;
            else
               iRow++;
         }

         // Find the last entry
         while (true)
         {
            NUMBER? decEntry = CriticalValues[iRow, iEntry];
            if (decEntry == null)
               iEntry--;
            else
               break;
         }

         return new ChiAlpha((NUMBER)CriticalValues[iRow, iEntry], alphas[iEntry]);
      } // GetHighestEntry()

      private ChiAlpha GetClosestEntry(Int32 iTreatmentCount, Int32 iSubjectCount,
         NUMBER decFriedmanStatistic)
      {
         Int32 iRow = 0;

         // Find the right row
         while (true)
         {
            Int32 iA = (Int32)CriticalValues[iRow, 0];
            if (iA == iTreatmentCount)
               break;
            else
               iRow++;
         }
         while (true)
         {
            Int32 iB = (Int32)CriticalValues[iRow, 1];
            if (iB == iSubjectCount)
               break;
            else
               iRow++;
         }

         Int32 i = 2;
         NUMBER decResult = 0.0m;
         NUMBER decAlpha = 0.0m;
         bool[] boolArray = new bool[9];
         for (; i < 11; i++)
         {
            if (CriticalValues[iRow, i] != null
               && decFriedmanStatistic >= CriticalValues[iRow, i])
               boolArray[i-2] = true;
            else
               boolArray[i-2] = false;
         }
         for (int j = 10; j > 1; j--)
         {
            if (boolArray[j - 2])
            {
               decResult = (NUMBER)CriticalValues[iRow, j];
               decAlpha = alphas[j];
               break;
            }
         }
         ChiAlpha chiAlpha = new ChiAlpha(decResult, decAlpha);
         return chiAlpha;
      }

      private readonly NUMBER?[,] CriticalValues =
      {
         {3.0m, 2.0m, 3.0m, 4.0m, null, null, null, null, null, null, null},
         {3.0m, 3.0m, 2.667m, 4.667m, null, 6.0m, null, null, null, null, null},
         {3.0m, 4.0m, 2.0m, 4.5m, 6.0m, 6.5m, null, null, 8.0m, null, null},
         {3.0m, 5.0m, 2.8m, 3.6m, 5.2m, 6.4m, null, 8.4m, null, null, 10.0m},
         {3.0m, 6.0m, 2.33m, 4.0m, 5.33m, 7.0m, 8.33m, 9.0m, null, 10.33m, 12.0m},
         {3.0m, 7.0m, 2.0m, 3.714m, 5.429m, 7.143m, 8.0m, 8.857m, 10.286m, 11.143m, 12.286m},
         {3.0m, 8.0m, 2.25m, 4.0m, 5.25m, 6.25m, 7.75m, 9.0m, 9.75m, 12.0m, 12.25m},
         {3.0m, 9.0m, 2.0m, 3.556m, 5.556m, 6.222m, 8.0m, 9.556m, 10.667m, 11.556m, 12.667m},
         {3.0m, 10.0m, 1.8m, 3.8m, 5m, 6.2m, 7.8m, 9.6m, 10.4m, 12.2m, 12.6m},
         {3.0m, 11.0m, 1.636m, 3.818m, 4.909m, 6.545m, 7.818m, 9.455m, 10.364m, 11.636m, 13.273m},
         {3.0m, 12.0m, 1.5m, 3.5m, 5.167m, 6.167m, 8.0m, 9.5m, 10.167m, 12.167m, 12.5m},
         {3.0m, 13.0m, 1.846m, 3.846m, 4.769m, 6.0m, 8.0m, 9.385m, 10.308m, 11.538m, 12.923m},
         {3.0m, 14.0m, 1.714m, 3.571m, 5.143m, 6.143m, 8.143m, 9.0m, 10.426m, 42.0m, 13.286m},
         {3.0m, 15.0m, 1.733m, 3.6m, 4.933m, 6.4m, 8.133m, 8.933m, 10.0m, 12.133m, 12.933m},
         {4.0m, 2.0m, 3.6m, 5.4m, null, 6.0m, null, null, null, null, null},
         {4.0m, 3.0m, 3.4m, 5.4m, 6.6m, 7.4m, 8.2m, 9.0m, null, 9.0m, null},
         {4.0m, 4.0m, 3.0m, 4.8m, 6.3m, 7.8m, 8.4m, 9.6m, null, 10.2m, 11.1m},
         {4.0m, 5.0m, 3.0m, 5.16m, 6.36m, 7.8m, 9.24m, 9.96m, 10.92m, 11.64m, 12.6m},
         {4.0m, 6.0m, 3.0m, 4.8m, 6.4m, 7.6m, 9.4m, 10.2m, 11.4m, 12.2m, 12.8m},
         {4.0m, 7.0m, 2.829m, 4.886m, 6.429m, 7.8m, 9.343m, 10.371m, 11.4m, 12.771m, 13.8m},
         {4.0m, 8.0m, 2.55m, 4.8m, 6.3m, 7.65m, 9.45m, 10.35m, 11.85m, 12.9m, 13.8m},
         {4.0m, 9.0m, null, null, 6.467m, 7.8m, 9.133m, 10.867m, 12.067m, null, 14.467m},
         {4.0m, 10.0m, null, null, 6.36m, 7.8m, 9.12m, 10.8m, 12.0m, null, 14.640m},
         {4.0m, 11.0m, null, null, 6.382m, 7.909m, 9.327m, 11.073m, 12.273m, null, 14.891m},
         {4.0m, 12.0m, null, null, 6.4m, 7.9m, 9.2m, 11.1m, 12.3m, null, 15.0m},
         {4.0m, 13.0m, null, null, 6.415m, 7.965m, 7.369m, 11.123m, 12.323m, null, 15.277m},
         {4.0m, 14.0m, null, null, 6.343m, 7.386m, 9.343m, 11.143m, 12.514m, null, 15.257m},
         {4.0m, 15.0m, null, null, 6.440m, 8.040m, 9.4m, 11.24m, 12.52m, null, 15.4m},
         {5.0m, 2.0m, null, null, 7.2m, 7.6m, 8.0m, 8.0m, null, null, null},
         {5.0m, 3.0m, null, null, 7.467m, 8.533m, 9.6m, 10.133m, 10.667m, null, 11.467m},
         {5.0m, 4.0m, null, null, 7.6m, 8.8m, 9.5m, 11.2m, 12.0m, null, 13.2m},
         {5.0m, 5.0m, null, null, 7.68m, 8.96m, 10.24m, 11.68m, 12.48m, null, 14.4m},
         {5.0m, 6.0m, null, null, 7.733m, 9.067m, 10.4m, 11.867m, 13.067m, null, 15.2m},
         {5.0m, 7.0m, null, null, 7.771m, 9.143m, 10.514m, 12.114m, 13.257m, null, 15.657m},
         {5.0m, 8.0m, null, null, 7.8m, 9.3m, 10.6m, 12.3m, 13.5m, null, 16.0m},
         {5.0m, 9.0m, null, null, 7.733m, 9.244m, 10.667m, 12.444m, 13.689m, null, 16.356m},
         {5.0m, 10.0m, null, null, 7.76m, 9.28m, 10.72m, 12.48m, 13.48m, null, 16.48m},
         {6.0m, 2.0m, null, null, 8.286m, 9.143m, 9.429m, 9.714m, 10.0m, null, null},
         {6.0m, 3.0m, null, null, 8.714m, 9.857m, 10.81m, 11.762m, 12.524m, null, 13.286m},
         {6.0m, 4.0m, null, null, 9.0m, 10.286m, 11.429m, 12.712m, 13.571m, null, 15.286m},
         {6.0m, 5.0m, null, null, 9.0m, 10.486m, 11.743m, 13.229m, 14.257m, null, 16.429m},
         {6.0m, 6.0m, null, null, 9.048m, 10.571m, 12.0m, 13.619m, 14.762m, null, 17.048m},
         {6.0m, 7.0m, null, null, 9.122m, 10.674m, 12.061m, 13.857m, 15.0m, null, 17.612m},
         {6.0m, 8.0m, null, null, 9.143m, 10.714m, 12.214m, 14.0m, 15.286m, null, 18.0m},
         {6.0m, 9.0m, null, null, 9.127m, 10.778m, 12.302m, 14.143m, 15.476m, null, 18.27m},
         {6.0m, 10m, null, null, 9.143m, 10.8m, 12.343m, 14.299m, 15.6m, null, 18.514m}
      }; // CriticalValues

      private readonly NUMBER[] alphas =
      {
         0.0m, 0.0m, 0.5m, 0.2m, 0.1m, 0.05m, 0.02m, 0.01m, 0.005m, 0.002m, 0.001m
      };


   } // FriedmanGroupsCollection class

   struct ChiAlpha
   {
      public NUMBER Chi;
      public NUMBER Alpha;

      public ChiAlpha(NUMBER decX, NUMBER decY)
      {
         Chi = decX;
         Alpha = decY;
      }
   } // ChiAlpha struct
}

---