Missing values when calculating z score

[Nitsan Machlis]

Hi, I have a database of grades organized by subject and exam year. I have calculated z scores for each grade relative to subject and year, using the following command:

egen z_grade = std(grade), by(subject year)

The code seems to work, however the variable z_grade has missing values for about a third of the observations in the database, despite the fact that these observations are not missing grade, subject or year data. Does anyone know why this may be happening? I have tried various solutions to no avail. Thank you.

[Carlo Lazzaro]

NItsan:
is it a cross-sectional or a panel dataset^

[Nitsan Machlis]

Cross-sectional. I have summarized the missing values and think the problem may be that many of the observations with missing z score values have 0 as their grade. In this case, what should the z score be?

[Carlo Lazzaro]

Nitsan:
your intuition seems correct:

. set obs 3
Number of observations (_N) was 0, now 3.

. g id=_n

. g grade=0

. egen wanted=std(grade), by(id)
(3 missing values generated)

. list

     +---------------------+
     | id   grade   wanted |
     |---------------------|
  1. |  1       0        . |
  2. |  2       0        . |
  3. |  3       0        . |
     +---------------------+

.

[Andrew Musau]

The issue is not observations with test scores of zero, but no variance within a particular group defined by subject and year. Therefore, the standard deviation is zero and you cannot compute a z-score. To identify such groups:

bys subject year (grade): gen zerovariance= grade[1]==grade[_N]
list if zerovariance, sepby(subject year)

[Nick Cox]

I agree with Andrew Musau, but I think it not absurd to argue that if all values are the same then a z-score of 0 for all makes sense, but you have to code that explicitly.

[Nitsan Machlis]

Yes this was my thinking too. Thanks.