Student’s t-test for equal means

If you do not wish to enter complex formula in Excel and you already have calculated average, count, and variance for your samples(Tip:use a PivotTable), then you can use these user-defined functions to calculate the t-test stat value and degrees of freedom required to do hypothesis testing. Both the functions provide an optional argument for the assumption of equal variances; by default it is set to false.

Here’s the code for t-test:

'---------------------------------------------------------------------------------------
' Procedure : TTESTM
' DateTime  : 10/29/2008 08:35
' Author    :
' Purpose   : To get the t-stat value when comparing two means with an optional input
'               for equal or unequal variances
'               by default the function assumes that the user is comparing means with unequal variances
' davg1 is the mean of first sample
' dcnt1 is the sample size of sample 1 
' dvar1 is the variance of first samaple 
' davg2 is the mean of second sample
' dcnt2 is the sample size of sample 2 
' dvar2 is the variance of second samaple 
' blnEqVar set TRUE to assume equal variance for the test
'---------------------------------------------------------------------------------------
 
Public Function TTESTM(davg1 As Double, dcnt1 As Double, dvar1 As Double, davg2 As Double, dcnt2 As Double, dvar2 As Double, Optional blnEqVar As Boolean = False) As Double
 
On Error GoTo TTESTM_Error
Dim dResult As Double, dNumer As Double, dDenon As Double, dPooledVar As Double
 
dNumer = davg1 - davg2
 
'if equal variances are not assumed
'http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm
If Not blnEqVar Then
	dDenon = Sqr((dvar1 ^ 2 / dcnt1) + (dvar2 ^ 2 / dcnt2))
Else
'if equal variances are assumed, then calculated the pooled variance
	dPooledVar = Sqr((((dcnt1 - 1) * dvar1 ^ 2) + ((dcnt2 - 1) * dvar2 ^ 2)) / (dcnt1 + dcnt2 - 2))
	dDenon = dPooledVar * Sqr((1 / dcnt1) + (1 / dcnt2))
End If
 
dResult = dNumer / dDenon
 
TTESTM = dResult
Exit Function
 
TTESTM_Error:
	TTESTM = Null
 
End Function

Code for degrees of freedom

'---------------------------------------------------------------------------------------
' Procedure : DOFTTESTM
' DateTime  : 10/29/2008 08:50
' Author    :
' Purpose   : To get the degrees of freedom for the t-test when comparing two means with an optional input
'               for equal or unequal variances
'               by default the function assumes that the user is comparing means with unequal variances
 
' dcnt1 is the sample size of sample 1 
' dvar1 is the variance of first samaple 
' dcnt2 is the sample size of sample 2 
' dvar2 is the variance of second samaple 
' blnEqVar set TRUE to assume equal variance for the test
'---------------------------------------------------------------------------------------
'
Public Function DOFTTESTM(dcnt1 As Double, dvar1 As Double, dcnt2 As Double, dvar2 As Double, Optional blnEqVar As Boolean = False) As Double
 
Dim dResult As Double, dNumer As Double, dDenon As Double
 
On Error GoTo DOFTTESTM_Error
'if equal variances are not assumed, then use a complicated formula to compute degrees of freedom
'http://www.itl.nist.gov/div898/handbook/eda/section3/eda353.htm
If Not blnEqVar Then
	dNumer = ((dvar1 ^ 2 / dcnt1) + (dvar2 ^ 2 / dcnt2)) ^ 2
	dDenon = ((dvar1 ^ 2 / dcnt1) ^ 2 / (dcnt1 - 1)) + ((dvar2 ^ 2 / dcnt2) ^ 2 / (dcnt2 - 1))
	dResult = dNumer / dDenon
Else
	dResult = dcnt1 + dcnt2 - 2
End If
 
DOFTTESTM = dResult
 
Exit Function
 
DOFTTESTM_Error:
	DOFTTESTM = Null
 
End Function

About the Author

The author of Tableau Data Visualization Cookbook and an award winning keynote speaker, Ashutosh R. Nandeshwar is one of the few analytics professionals in the higher education industry who has developed analytical solutions for all stages of the student life cycle (from recruitment to giving). He enjoys speaking about the power of data, as well as ranting about data professionals who chase after “interesting” things. He earned his PhD/MS from West Virginia University and his BEng from Nagpur University, all in industrial engineering. Currently, he is leading the data science, reporting, and prospect development efforts at the University of Southern California.

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