Attribute VB_Name = "modMethod"
Option Explicit
'雙因素交錯方差分析
'x：試驗數據
'FA：行因素的F檢驗值
'FB：列因素的F檢驗值
'FAB：因素交錯的F檢驗值
Public Sub DoubleAB(x() As Double, FA As Double, FB As Double, FAB As Double)
'p：垂直因素變化個數。q：水平因素變化個數。r：重復試驗次數。n：試驗的總次數
    Dim p As Integer, q As Integer, r As Integer, n As Integer
    Dim I As Integer, J As Integer, K As Integer
    Dim A As Double, B As Double, C As Double, D As Double
    Dim Qa As Double, Qb As Double, W As Double
    Dim Sa As Double, Sb As Double, Sab As Double, Se As Double
    p = UBound(x, 1): q = UBound(x, 2): r = UBound(x, 3)
    n = p * q * r                           'n：試驗的總次數
    For I = 1 To p
        For J = 1 To q
            For K = 1 To r
                A = A + x(I, J, K)
                B = B + x(I, J, K)
                C = C + x(I, J, K)
                W = W + x(I, J, K) ^ 2
            Next K
            D = D + C * C
            C = 0
        Next J
        Qa = Qa + B * B
        B = 0
    Next I
    B = A ^ 2 / n
    Qa = Qa / (q * r)
    For J = 1 To q
        For I = 1 To p
            For K = 1 To r
                C = C + x(I, J, K)
            Next K
        Next I
        Qb = Qb + C * C
        C = 0
    Next J
    Qb = Qb / (p * r)
    D = D / r
    Sa = (Qa - B) / (p - 1)     '行因素引起的平均離差平方和
    Sb = (Qb - B) / (q - 1)     '列因素引起的平均離差平方和
'因素交互作用引起的平均離差平方和
    Sab = (D - Qa - Qb + B) / (p - 1) / (q - 1)
'誤差引起的平均離差平方和
    Se = (W - D) / (p * q * (r - 1))
    FA = Sa / Se                '行因素的檢驗值
    FB = Sb / Se                '列因素的檢驗值
    FAB = Sab / Se              '交錯因素的檢驗值
Debug.Print "行平方和", (Qa - B), "自由度", p - 1, "均方", Sa
Debug.Print "列平方和", (Qb - B), "自由度", q - 1, "均方", Sb
Debug.Print "交錯平方和", (D - Qa - Qb + B), "自由度", (p - 1) * (q - 1), "均方", Sab
Debug.Print "誤差平方和", (W - D), "自由度", (p * q * (r - 1)), "均方", Se
Debug.Print "行檢驗值", FA, "列檢驗值", FB, "交錯檢驗值", FAB
End Sub

'求Gamma函數的對數LogGamma(x)
'x：自變量
'G：Gamma函數的對數
Public Sub lnGamma(x As Double, G As Double)
    Dim y As Double, z As Double, A As Double
    Dim B As Double, B1 As Double, n As Integer
    Dim I As Integer
    If x < 8 Then
        y = x + 8: n = -1
    Else
        y = x: n = 1
    End If
    z = 1 / (y * y)
    A = (y - 0.5) * Log(y) - y + 0.9189385
    B1 = (0.0007663452 * z - 0.0005940956) * z
    B1 = (B1 + 0.0007936431) * z
    B1 = (B1 - 0.002777778) * z
    B = (B1 + 0.0833333) / y
    G = A + B
    If n >= 0 Then Exit Sub
    y = y - 1: A = y
    For I = 1 To 7
        A = A * (y - I)
    Next I
    G = G - Log(A)
End Sub

'求正態分布的分位數
'Q：上側概率
'x：分位數
Public Sub PNorm(q, x)
    Dim p As Double, y As Double, z As Double
    Dim B0 As Double, B1 As Double, B2 As Double
    Dim B3 As Double, B4 As Double, B5 As Double
    Dim B6 As Double, B7 As Double, B8 As Double
    Dim B9 As Double, B10 As Double, B As Double
    B0 = 1.570796288: B1 = 0.03706987906
    B2 = -0.0008364353589: B3 = -0.0002250947176
    B4 = 0.000006841218299: B5 = 0.000005824238515
    B6 = -0.00000104527497: B7 = 8.360937017E-08
    B8 = -3.231081277E-09: B9 = 3.657763036E-11
    B10 = 6.936233982E-13
    If q = 0.5 Then
        x = 0: GoTo PN01
    End If
    If q > 0.5 Then p = 1 - q Else p = q
    y = -Log(4 * p * (1 - p))
    B = y * (B9 + y * B10)
    B = y * (B8 + B): B = y * (B7 + B)
    B = y * (B6 + B): B = y * (B5 + B)
    B = y * (B4 + B): B = y * (B3 + B)
    B = y * (B2 + B): B = y * (B1 + B)
    z = y * (B0 + B): x = Sqr(z)
    If q > 0.5 Then x = -x
PN01:
End Sub

'計算F分布的分布函數
'n1：自由度，已知
'n2：自由度，已知
'F：F值，已知
'p：下側概率，所求
'd：概率密度，所求
Public Sub F_DIST(n1 As Integer, n2 As Integer, F As Double, _
            p As Double, D As Double)
    Dim x As Double, U As Double, Lu As Double
    Dim IAI As Integer, IBI As Integer, nn1 As Integer, nn2 As Integer
    Dim I As Integer
    Const PI As Double = 3.14159265359
    If F = 0 Then
        p = 0: D = 0: Exit Sub
    End If
    x = n1 * F / (n2 + n1 * F)
    If (n1 \ 2) * 2 = n1 Then
        If (n2 \ 2) * 2 = n2 Then
            U = x * (1 - x): p = x: IAI = 2: IBI = 2
        Else
            U = x * Sqr(1 - x) / 2: p = 1 - Sqr(1 - x): IAI = 2: IBI = 1
        End If
    Else
        If (n2 \ 2) * 2 = n2 Then
            p = Sqr(x): U = p * (1 - x) / 2: IAI = 1: IBI = 2
        Else
            U = Sqr(x * (1 - x)) / PI
            p = 1 - 2 * Atn(Sqr((1 - x) / x)) / PI: IAI = 1: IBI = 1
        End If
    End If
    nn1 = n1 - 2: nn2 = n2 - 2
    If U = 0 Then
        D = U / F
        Exit Sub
    Else
        Lu = Log(U)
    End If
    If IAI = n1 Then GoTo LL1
    For I = IAI To nn1 Step 2
        p = p - 2 * U / I
        Lu = Lu + Log((1 + IBI / I) * x)
        U = Exp(Lu)
    Next I
LL1:
    If IBI = n2 Then
        D = U / F: Exit Sub
    End If
    For I = IBI To nn2 Step 2
        p = p + 2 * U / I
        Lu = Lu + Log((1 + n1 / I) * (1 - x))
        U = Exp(Lu)
    Next I
    D = U / F
End Sub

'計算F分布的分位數
'n1：自由度，已知
'n2：自由度，已知
'Q：上側概率，已知
'F：分位數，所求
Public Sub PF_DIST(n1 As Integer, n2 As Integer, _
                q As Double, F As Double)
    Dim DF12 As Double, DF22 As Double, A As Double, B As Double
    Dim A1 As Double, B1 As Double, p As Double, YQ As Double
    Dim E As Double, FO As Double, pp As Double, D As Double
    Dim GA1 As Double, GA2 As Double, GA3 As Double
    Dim K As Integer
    DF12 = n1 / 2: DF22 = n2 / 2
    A = 2 / (9 * n1): A1 = 1 - A
    B = 2 / (9 * n2): B1 = 1 - B
    p = 1 - q: PNorm q, YQ
    E = B1 * B1 - B * YQ * YQ
    If E > 0.8 Then
        FO = ((A1 * B1 + YQ * Sqr(A1 * A1 * B + A * E)) / E) ^ 3
    Else
        lnGamma DF12 + DF22, GA1
        lnGamma DF12, GA2
        lnGamma DF22, GA3
        FO = (2 / n2) * (GA1 - GA2 - GA3 + 0.69315 + (DF22 - 1) * Log(n2) _
            - DF22 * Log(n1) - Log(q))
        FO = Exp(FO)
    End If
    For K = 1 To 30
        F_DIST n1, n2, FO, pp, D
        If D = 0 Then
            F = FO: Exit Sub
        End If
        F = FO - (pp - p) / D
        If Abs(FO - F) < 0.000001 * Abs(F) Then Exit Sub Else FO = F
    Next K
End Sub