I have race as a variable in my model and my measurement reflects the executives' race in the company's management (score 1 if any specific race is in the management). The problem is that managements of companies have more than one race in their executives. So when I want to statistically summarize race which are four, the total percentage is more than 100% What is the best way to demonstrate the results?
Your suggestions are highly appreciated
Add a category "more than one race".
If you have the raw data, you can figure out which people were combinations of which races and (if you like) list more than one "more than one race" category and also create "White only" etc for people who checked only "White" etc.
If you only have the summary data then you can only approximate the total "more than one race" since you don't know if anyone checked three boxes. But you can assume that few if any did. Then you can figure it out. Suppose the following:
White 60%
Black 20%
Asian 20%
Other 10%
total = 110 so, if some checked two boxes but none checked three, then 5% checked two boxes.
E.g. suppose everyone who checked two boxes checked "Black" and "other" then if we reduce each of these by 5% we get to 100%. And 5% checked two boxes.
Method 1: recode the race variables
See this data set:
Suppose the orange part represents the original data. The culprits that inflated the percentage are cases 4 and 5.
To recode them, first count the total response per case by adding across the columns, resulting is the column Sum. For those who has just 1, they chose only one race and will retain that race. For those with 2 or more, we will recode them into multi-racial, as suggested in the answer of @PeterFlom.
The coding scheme would be something like:
if white = 1 and sum = 1 then newRace = 1;
if black = 1 and sum = 1 then newRace = 2;
if asian = 1 and sum = 1 then newRace = 3;
if others = 1 and sum = 1 then newRace = 4;
if sum > 1 then newRace = 5;
You can see the newRace and its labeling scheme in blue. The frequency of the variable newRace should give percentages adding up to 100%. This method requires you to have executive level data, if you only have company level aggregated data, then it not possible to work this out without some assumptions.
Method 2: use the variables as is
In descriptive statistics table, it's also acceptable to footnote the table saying "percentages do not add up to 100% due to multiple choices."
