# Variance of the average of two (or more) Net Promoter Scores?

As per Wikipedia,

"The Net Promoter Score is obtained by asking customers a single question on a 0 to 10 rating scale, where 10 is "extremely likely" and 0 is "not at all likely": "How likely is it that you would recommend our company to a friend or colleague?" Based on their responses, customers are categorized into one of three groups: Promoters (9–10 rating), Passives (7–8 rating), and Detractors (0–6 rating). The percentage of Detractors is then subtracted from the percentage of Promoters to obtain a Net Promoter score (NPS). NPS can be as low as -100 (everybody is a detractor) or as high as +100 (everybody is a promoter)."

Suppose I collect information from dependent populations (most of the sample may overlap, but could have different $$n$$'s ) on two different questions. I then get 2 separate NPS scores for question A and question B.

In this case, I am interested in looking at the average between the NPS scores for A and B, i.e. $$NPS_{AB} = \frac{NPS_A+NPS_B}{2}$$

How can I calculate the variance of the average of the two NPS scores for questions A and B? (i.e. $$Var(NPS_{AB})$$)

I am able to calculate separate variances for $$NPS_A$$ and $$NPS_B$$ using whuber's response to this question How can I calculate margin of error in a NPS (Net Promoter Score) result?, but how can I calculate the variance/margin of error for the average of two (or more) NPS scores?

• Since they’re not paired, you’ll have to sample each separately but I suspect that bootstrapping still applies here. – HEITZ Oct 8 '18 at 22:30