5 Ways To Calculate Spearmans Rank In Excel

In statistics, Spearman's rank correlation coefficient is a non-parametric measure of rank correlation that assesses how well the relationship between two variables can be described using a monotonic function. If there are no repeated data values, a perfect Spearman correlation of 1 or -1 occurs when each of the variables is a perfect monotone function of the other. In Excel, there are several ways to calculate Spearman's rank correlation coefficient. Here are five methods to do so.

Method 1: Using the CORREL Function

The CORREL function in Excel calculates the Pearson correlation coefficient between two sets of data. However, this function can also be used to calculate Spearman's rank correlation coefficient by ranking the data first. Here's how to do it:

• Rank your data using the RANK.EQ function.
• Use the CORREL function to calculate the Pearson correlation coefficient between the ranked data.

For example, suppose you have two sets of data in columns A and B. To calculate Spearman's rank correlation coefficient using the CORREL function, you can use the following formula:

=CORREL(RANK.EQ(A1:A10,A1:A10),RANK.EQ(B1:B10,B1:B10))

Method 2: Using the SPEARMAN Function (Excel 2016 and later)

In Excel 2016 and later, you can use the SPEARMAN function to calculate Spearman's rank correlation coefficient. This function takes two arrays of data as input and returns the Spearman correlation coefficient.

For example, suppose you have two sets of data in columns A and B. To calculate Spearman's rank correlation coefficient using the SPEARMAN function, you can use the following formula:

=SPEARMAN(A1:A10,B1:B10)

Method 3: Using VBA (Visual Basic for Applications)

You can also use VBA to calculate Spearman's rank correlation coefficient in Excel. Here's an example code that calculates the Spearman correlation coefficient between two sets of data:

Function SpearmanRankCorrelation(arr1 As Variant, arr2 As Variant) As Double
    Dim i As Long
    Dim j As Long
    Dim n As Long
    Dim sum_d2 As Double
    Dim rank1 As Variant
    Dim rank2 As Variant
    
    'Rank the data
    rank1 = Application.WorksheetFunction.Rank.Eq(arr1, arr1)
    rank2 = Application.WorksheetFunction.Rank.Eq(arr2, arr2)
    
    'Calculate the sum of the squared differences
    n = UBound(arr1)
    sum_d2 = 0
    For i = 1 To n
        sum_d2 = sum_d2 + (rank1(i) - rank2(i)) ^ 2
    Next i
    
    'Calculate the Spearman correlation coefficient
    SpearmanRankCorrelation = 1 - (6 * sum_d2) / (n * (n ^ 2 - 1))
End Function

To use this function, simply enter the following formula in a cell:

=SpearmanRankCorrelation(A1:A10,B1:B10)

Method 4: Using the RSQ Function (Excel 2013 and earlier)

In Excel 2013 and earlier, you can use the RSQ function to calculate the Spearman correlation coefficient. However, this function requires you to rank the data first using the RANK.EQ function.

For example, suppose you have two sets of data in columns A and B. To calculate Spearman's rank correlation coefficient using the RSQ function, you can use the following formula:

=RSQ(RANK.EQ(A1:A10,A1:A10),RANK.EQ(B1:B10,B1:B10))

Method 5: Using a User-Defined Function (UDF)

You can also use a UDF to calculate Spearman's rank correlation coefficient in Excel. Here's an example code that calculates the Spearman correlation coefficient between two sets of data:

Function SpearmanCorrelation(arr1 As Variant, arr2 As Variant) As Double
    Dim i As Long
    Dim j As Long
    Dim n As Long
    Dim sum_d As Double
    Dim sum_d2 As Double
    Dim sum_d3 As Double
    Dim rank1 As Variant
    Dim rank2 As Variant
    
    'Rank the data
    rank1 = Application.WorksheetFunction.Rank.Eq(arr1, arr1)
    rank2 = Application.WorksheetFunction.Rank.Eq(arr2, arr2)
    
    'Calculate the sum of the differences
    n = UBound(arr1)
    sum_d = 0
    For i = 1 To n
        sum_d = sum_d + Abs(rank1(i) - rank2(i))
    Next i
    
    'Calculate the sum of the squared differences
    sum_d2 = 0
    For i = 1 To n
        sum_d2 = sum_d2 + (rank1(i) - rank2(i)) ^ 2
    Next i
    
    'Calculate the sum of the cubed differences
    sum_d3 = 0
    For i = 1 To n
        sum_d3 = sum_d3 + (rank1(i) - rank2(i)) ^ 3
    Next i
    
    'Calculate the Spearman correlation coefficient
    SpearmanCorrelation = 1 - (6 * sum_d2) / (n * (n ^ 2 - 1))
End Function

To use this function, simply enter the following formula in a cell:

=SpearmanCorrelation(A1:A10,B1:B10)

These are five ways to calculate Spearman's rank correlation coefficient in Excel. You can use any of these methods depending on your version of Excel and your personal preference.

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We hope this article has helped you learn more about calculating Spearman's rank correlation coefficient in Excel. If you have any questions or need further assistance, please don't hesitate to ask.