Hello,
I have a categorical variable (main teaching assignment) with 12 options (early childhood, mathematics, English, etc) and I am trying to determine which groups earn significantly higher and/or significantly lower than the average income for all teachers. I don't need ALL of the groups, necessarily, for reporting, just those for which the differences seem most disparate and I don't want to run pairwise tests because I care less if English teachers vs math teachers is significant and more about the difference from the average.
Since I am comparing an overall mean to a subgroup mean and the means aren't independent I'm assuming I can't run a standard independent t-test. What CAN I run??
In my opinion, it should be taken into account whether they are independent or dependent groups. Because the way to calculate the means through t of student is different, each case has its equation.
The distribution of normality and variance of the data has to be evaluated, to determine if to use t-test or u of mann withney, which now is possible to quantify the hypothesis of difference by means of the factor bayes in a simple way because it comes integrated in free programs like JAMOVI or JASP
You can find the average salary of teachers from other sources for a population of interest to you e.g. data available with the government agencies, the pay scales of teachers in these categories, internet. Then You can draw a random sample from different categories and compare the mean salary of different categories by analysis of variance. If that is significant, then you can compare the individual means to the mean for the population or with other categories depending on the objectives of your study.
Wilmer Lopez, sorry if I didn't make that clear. The reason I'm asking the question is because they are NOT independent groups; the all teachers variable includes the average salary of all teachers in all public schools, while the categorical teaching assignment variable separates them by main teaching assignment. I'm trying to determine if the average salary of an English teacher is statistically different than the average salary of ALL teachers, which is going to be dependent because English teachers are considered part of the whole.
And Nicolas Boco I wish I could! But I'm not trying to see the difference between the subgroups, just between average of all vs average of English teachers, and average of all vs average of Math teachers, etc. I would only have two groups, so an ANOVA wouldn't be a good fit.
Cristian Ramos-Vera thank you! I've already run tests for normality and variance and the sample has already been cleaned, imputed, and weights added. It's a pretty large and normal sample. Also a Mann-Whitney test wouldn't work here because the dependent variable is 'average salary,' which is continuous and the observations are not independent (see above, since English teachers are included in the part and in the whole).
Harinder Mahajan, it wouldn't work in this instance to use data from other sources because of the nature of the work, but I could probably do the rest of your suggestion with my own estimates. I am still wondering if a t-test would be appropriate here to compare the individual means to the means of the population given that the two means are not independent from one another.
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