# Norm Score Calculation

The code below (from a book) is supposed to calculate the "norm score" of an array. The array is populated from the "dvec" range on an Excel spreadsheet, which is used to populate the Znmat array.

Then the z scores and "norm scores" are calculated. The last part of the code (which I have left out) deals with plotting the data in a Normal Probability Plot.

My questions:

1.  What is the meaning of a "norm score"? Why is it calculated as the NORMSINV of the rank divided by the total number of elements?
2.  What is the meaning of the "continuity correction"? How does it work?

These issues are not explained in the book, since the code is provided only as an example for creating a graph in Excel.
``````Sub NPPlotData()
' returns n by 2 matrix where n = no. of elements in dvec
' 1st col z-scores, 2nd col normscores for n obs.
Dim M, V, r, c
Dim i As Integer, n As Integer
Dim Znmat() As Variant
Dim dvec As Range

'data input from worksheet
Set dvec = Sheets("Data").Range("dvec")  'dvec as Range object

n = Application.Count(dvec)
ReDim Znmat(n, 2)

M = Application.Average(dvec)
V = Application.Var(dvec)
For i = 1 To n
Znmat(i, 1) = (dvec(i) - M) / Sqr(V)
r = Application.Rank(dvec(i), dvec, 1)
c = (r - 3 / 8) / (n + 1 / 4)
Znmat(i, 2) = Application.NormSInv(c)
Next i
' [...]
End Sub
``````
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Commented:
Rothbard,

May I ask whether this is homework? I don't have the answer but I'm just curious.

Patrick
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Commented:
Rothbard,

If you put either 'norm score' or "continuity correction" into Google you will have more than enough to read on the subject.

Patrick
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Author Commented:
It's not "homework". I tried googling "norm score" and "continuity correction" but found no useful information to understand the meaning of the code I posted above.
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Commented:
>It's not "homework". I tried googling "norm score" and "continuity correction" but found no useful information to understand the meaning of the code I posted above.

Odd, perhaps I was reading the wrong articles - there seemed to be lots about both subjects.
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Commented:
I think the 'norm score' is related to the normal probability distribution, also known as the z-score. It should return a score based on the standard normal distribution (Bell curve), with the average score being 0.

Continuity correction is associated with turning a value from a binomial distribution into one associated with a normal distribution.

Try googling 'normal distribution' and 'binomial distribution' to understand the differences between these types of distributions.
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Commented:
Hi Rothbard,

http://support.microsoft.com/kb/826772
http://office.microsoft.com/en-us/excel/HP052091951033.aspx

Alternatively as Shellyness and others, suggested Google it.
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Commented:
Found these definitions for norm score:

From Ulrich Raatz, Christine Klein-Braley, Gerhard-Mercator-Universität Duisburg
Glossary of the most frequent concepts in statistics and test theory.
http://www.uni-duisburg.de/FB3/ANGLING/FORSCHUNG/GLOSSARY.HTM :

Norm score
1. shows the place of a person in a reference group (norm-referenced test)
Two kinds: deviation norms (i.e. IQ) and percentile ranks.
2. show what percentage of the criterion the subject has mastered (criterion-referenced test).

From P.J. Tellegen and J.A. Laros, "The Snihders-Oomen Nonverbal Intelligence Tests: General intelligence tests or tests for learning potential?" in Learning Potential Assessment: Theoretical, Methodologica and Practical Issues. Edited by J.H.M. Hamers, et al. :

The norm score is defined as the sum of the standardized true score and the error of measurement. This unbiased estimate of the true score is used for hypothesis testing, research on groups and for computation of the total test score.
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