Comparing school grades in a population against mean score in the gen. population

#1
First of all, I am not very proficient with statistics, but I am writing on a school project, and I would really appreciate some ideas on which strategy or/and statistical methods I can apply considering the following research question:

I have a population of patients exposed to a specific treatment. I also have the school grades of the individual patients. I'm able to obtain the mean of the grades achieved by the general (country) population by year. Unfortunately however, not with confidence intervals.

Does anyone here have an advice on possible ways to get any meaningful statistics out of the variables mentioned above? Any help would be much appreciated, as I'm currently banging my head against the wall on this one! :)
 

WeeG

TS Contributor
#2
If I understand you correctly...and I emphasize the "if", you have the general mean of the population, and then you have a sample of patients given some treatment and you have their grades. Well, for example, if you think the treatment should lower the grade, you could test if the mean of these patients is lower than the grand mean.

You can set a hypothesis testing like this: H0: mean>=grand mean vs. H1: mean<grand mean

You can of course do it the other way round if the treatment should increase the grades. If this is the case, it is fairly simple to perform.
 

Karabiner

TS Contributor
#3
I also have the school grades of the individual patients. I'm able to obtain the mean of the grades achieved by the general (country) population by year.
I don't know which country you are talking of, or how
the grading system looks like, but in many instances
school grades are ordinal, not interval scaled.

Anyway, if you have population data and want to compare
your sample with it, then it's just a one sample t-test (or
one-sample Wilcoxon), you don't need population variance.

With kind regards

K.
 
#4
Thank you very much for the input! The grade system is ordinal as far as I know. Would it mean that the Wilcoxon test is preferred over the t-test?
 

Karabiner

TS Contributor
#5
Wilcoxon's signed rank test is not exactly for ordinal scales,
but should work acceptably here, whereas the t-test is considered
definetly inappropriate for ordinal scales. So, yes.

With kind regards

K.