Attribute VB_Name = "eff_size_cramer_v_gof"
'Created by Peter Stikker
'Companion website: https://PeterStatistics.com
'YouTube channel: https://www.youtube.com/stikpet
'Donations welcome at Patreon: https://www.patreon.com/bePatron?u=19398076

Public Sub es_cramer_v_gof_addHelp()
Application.MacroOptions _
    Macro:="es_cramer_v_gof", _
    Description:="Cramer's V for Goodness-of-Fit", _
    category:=14, _
    ArgumentDescriptions:=Array( _
        "the chi-square test statistic", _
        "the sample size", _
        "the number of categories", _
        "optional boolean to indicate the use of the Bergsma correction (default is False)", _
        "output to show, either " & Chr(34) & "value (default)" & Chr(34) & ", or " & Chr(34) & "qual" & Chr(34))
        
Application.MacroOptions _
    Macro:="es_cramer_v_gof_arr", _
    Description:="Cramer's V for Goodness-of-Fit" & vbNewLine & "array function, requires 2 rows and 2 columns as output", _
    category:=14, _
    ArgumentDescriptions:=Array( _
        "the chi-square test statistic", _
        "the sample size", _
        "the number of categories", _
        "optional boolean to indicate the use of the Bergsma correction (default is False)")
        
End Sub

Function es_cramer_v_gof(chi2, n, k, Optional bergsma = False, Optional out = "value")
'this function calculates Cramer's V for a Goodness-of-Fit test
'input is the chi-square value, the total sample size and the number of categories.
'optional the use of a Bergsma correction, and the output to show (either "value", or "qual"
   
df = k - 1

If bergsma Then
    kAvg = k - (k - 1) ^ 2 / (n - 1)
    phi2 = chi2 / n
    phi2Avg = WorksheetFunction.Max(0, phi2 - (k - 1) / (n - 1))
    V = Sqr(phi2Avg / (kAvg - 1))
Else
    V = Sqr(chi2 / (n * df))
End If
   
'Results
If out = "value" Then
    
    res = V
Else
    'Qualification
    Dim qual As String
    
    'convert to w
    w = V / Sqr(df)
    
    'Use Cohen (1988, p. 227).
    If Abs(w) < 0.1 Then
        qual = "negligible"
    ElseIf Abs(w) < 0.3 Then
        qual = "small"
    ElseIf Abs(w) < 0.5 Then
        qual = "medium"
    Else
        qual = "large"
    End If
    
    res = qual
End If
   
es_cramer_v_gof = res
    
End Function

Function es_cramer_v_gof_arr(chiSqValue, n, k, Optional bergsma = False)
'this function calculates Cramer's V for a Goodness-of-Fit test
'input is the chi-square value, the total sample size and the number of categories.
'optional the use of a Bergsma correction
   
df = k - 1

If bergsma Then
    kAvg = k - (k - 1) ^ 2 / (n - 1)
    phi2 = chiSqValue / n
    phi2Avg = WorksheetFunction.Max(0, phi2 - (k - 1) / (n - 1))
    V = Sqr(phi2Avg / (kAvg - 1))
    testUsed = "Cramer's V (GoF), with Bergsma correction"
Else
    testUsed = "Cramer's V (GoF)"
    V = Sqr(chiSqValue / (n * df))
End If
   
'Qualification
Dim qual As String

'convert to w
w = V / Sqr(df)

'Use Cohen (1988, p. 227).
If Abs(w) < 0.1 Then
    qual = "negligible"
ElseIf Abs(w) < 0.3 Then
    qual = "small"
ElseIf Abs(w) < 0.5 Then
    qual = "medium"
Else
    qual = "large"
End If

'Results
Dim res(1 To 2, 1 To 2)
res(1, 1) = testUsed
res(1, 2) = "Qualification"
res(2, 1) = V
res(2, 2) = qual

es_cramer_v_gof_arr = res
    
End Function