Do you have specific quantitative figures for this problem? (The way you have stated it is too vague).
given that the standard error is calculated as sd/sqrt(n), the standard error in different sub groups will differ according to their sd and how big n is for the sub-group. (I think)
the question is
"By how many standard errors is the mean experience of teachers in "regular classess with teacher's aides" different from the mean experience of "teachers in small classes"
For the question above, which standard error would you use? The standard error of "regular classess with teacher's aides" or "teachers in small classes"?
sorry about that: The project I have been given involves using STATA to find out about a given data set on k-3 education, class sizes, teacher experience and other factors.
The quiz first asks us to find the mean number of years of experience for kindergarteners in each of three class room sizes: "small" "regular" and "regular with an aid"
I used STATA to get
1900 teachers teach in small class rooms with a median number of years of experience of 8.92 years and sd of 5.812893
2194 teachers teach in regular class rooms with a median number of years of experience of 9.07 years and sd of 5.733309
2210 teachers teach in regular class rooms with aide and a median number of years of experience of 9.74 years and sd of 5.850766
So calculated that the standard error of the mean for each was
sigma/sqrt(n) and I got (to two decimal places)
class size small: 5.812893/sqrt(1900) = 0.13
regular class size: 5.733309/sqrt(2194)= 0.12
regular class size with aid: 0.850766/sqrt(2210) = 0.12
The next question is: By how many standard errors is the mean experience of teachers in "regular classess with teacher's aides" different from the mean experience of "teachers in small classes"
I would take the mean for the largest class size minus the mean from the smallest class size and divide by the standard error...but which standard error?
(9.74-8.92)/0.12 = 6.83
(9.74-8.92)/0.13 = 6.31
If you are looking at the standard error of the mean, then your base-line standard error will be the standard error of the mean in small classes.
This is a little confusing though and I am making an educated guess based on what you are trying to do which is to do statistics on the means which involve a SEM (Standard Error of the Mean).
The difference can be found as a ratio of the different SEM's in which the denominator will be the baseline SEM (which is the small-class SEM).