How to aggregate an ordinal variable

[Luana Goveia]

Dear Stata Forum,

I have an ordinal variable on teacher's experience t_exp: 1 2 3 4 5 6

Considering that one school has many teachers, I need to aggregate this variable at school level.

Calculating the mean does not look sensible as 6 would weight more than 1 for instance. So a school with six teachers with 1 year experience would have the same mean as a school with one teacher with 6 years experience. Well, this does not sound right to me.

Any help on how to aggregate an ordinal variable in a sensible way? Thanks!

[Nick Cox]

There can't be really good advice on what is "sensible" without context on your aims or detail on your data.

Although measurement purists instruct you otherwise, people often take means of ordinal variables, and that can be in full knowledge of their limitations.

It seems to be a way that judgement scores are often aggregated in competitions on diving or dancing, for example. (Using totals rather than means is just cosmetic.)

Flag: Does anyone know a good reference on statistical summaries as used in sports?

One practical reason is that the median can behave poorly too, being either one of the values or halfway between two.

Another practical reason is that anything else is likely to be too complicated to explain, depending on the consumers of the research.

For a Stata discussion a while back, see e.g.

http://www.stata.com/statalist/archi.../msg00661.html and follow-ups

http://www.stata.com/statalist/archi.../msg00728.html

For some general discussion see http://stats.stackexchange.com/quest...dinal-variable

[Luana Goveia]

Thank you Nick Cox! I will have a look at these discussions. But I think I will take means...

[Sebastian Geiger]

So a school with six teachers with 1 year experience would have the same mean as a school with one teacher with 6 years experience. Well, this does not sound right to me.

I might be missing something, but in my mind, the means would not be the same. The mean of the first school is 1, while the second school has a mean of 6.

Is your variable representing years? As you said "ordinal variable", I would expect something like ("no experience", "some experience", ..., "very much experience").
Strictly speaking, there is no way do aggregate ordinal values since we need to know the distance between the values, which is unknown in ordinal data.
However, one may argue that large ordinal scales can be treated similar to cardinal scales. In this case, you can calculate means as usual.

[Richard Williams]

There was a discussion a while back about what to do with ordinal independent variables, e.g. can you treat them as continuous or not? The main points are summarized in

http://www3.nd.edu/~rwilliam/stats3/...ndependent.pdf

How comfortable you with taking means may depend on how evenly the intervals are spaced, e.g. 1 = 1 year, 2 = 2 to 5 years, 3 = 6 to 10 years, ... 6 = 30 or more years would be pretty uneven spacing.