Calculations Employee Race Data as Different Percentages

#1
Hello! I have collected data from 37 organizations on the gender and race of their employees. The way the survey worked is that I know, for example, how many total employees they have, how many white employees they have, how many female employees they have, how many white female employees they have, how many white managers they have, and how many white, female, managers they have. There are 7 different races total and 4 occupation levels, and 2 genders.

Are both of these calculations valid?

If I want to show percentage of managers that are white:
Total Number of White Managers/ Total Number of Managers= Percentage of All Managers that are White
Ex: 1810 White Managers / 2565 Total Managers = ~71%

If I want to show what percentage of all whites are managers:
Total Number of White Managers / Total Number of White Employees Across All Occupations = Percentage of All Whites that are Managers
Ex: 1810 White Managers / 12648 White Employees = ~14%

Are both of these calculations valid? I feel like they should be but I'm freaking out that I'm missing something. I want to do this because the second calculation, Occupation as % of All Employees of Each Race, accounts better for population size. In my regional data, there are some regions with a lot more white employees than non-white. So I think it is more meaningful to say that 14% of all Whites are Managers and 5% of all Non-Whites are Managers than to say 71% of Managers are White and 29% are Non-White. Now, in the case of my national data it is about 51% White and 49% Non-white so it doesn't really matter for the national level, but that is not the case for my regional data.
I do have another question about regional vs national data.

So, across all regions, 14% of Whites are Managers. Here is the regional data:
Region 1: 9% of Whites are Managers
Region 2: 13% of Whites are Managers
Region 3: 36% of Whites are Managers
Region 4: 14% of Whites are Managers

Why does the average of these 4 regions (18%) not equal my national value (14%)? Am I doing something wrong?
Thank you!
 

obh

Well-Known Member
#2
Please try to have shorter ... I answer the last one
"Why does the average of these 4 regions (18%) not equal my national value (14%)?"

The average of these 4 regions (18%) gives equal weight to each region.

Uou can do a simple example, 2 regions 1 from 10 and 2 from 4.

(1/10 +2/4)/2=0.3
(1+2)/(10+4)=3/14=0.21