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We are trying to reproduce the outcome of a discriminant analysis done in SPSS and run into a mystery.

This link: https://stats.idre.ucla.edu/spss/output/discriminant-analysis/ explains that discrimant scores produced by SPSS are a of the form coefficient_1*standardized_variable_1 + ... + coefficient_n * standardized_variable_n.

Our question is: HOW are the variables standarized?

Obtaining the value of the standardized variables is easy,

Here is a simplified example:

value  group centralizedvalue  valuestandardizedbyspss  mysteryfactor
1      1     -4                -2.73                    1.46
2      1     -3                -2.05                    1.46
3      1     -2                -1.37                    1.46
4      1     -1                -.68                     1.46
5      2     -0                0                        1.46
6      2     1                 0.68                     1.46
7      2     2                 1.37                     1.46
8      2     3                 2.05                     1.46
9      2     4                 2.73                     1.46

Here value are just numbers we made up to be as boring as possible.

In this case there is only one variable, so only one coefficient, which moreover is taken to be 1 so here the standardized variable `Valuestandardizedbyspss' is just the discriminant score produced by SPSS

We see, by simple computation, that it is obtained by centralizing the original variable (i.e. subtracting the mean) and then multiplying by some mystery factor. In this case we obtained that the mystery factor is 1.46 by simple dividing centralizedvalue by valuestandardizedbyspss.

But what is this mystery factor? It is not the standard-deviation or anything else we could think of.

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