From a survey I have data on three similar Likert-type questions (scales are 1 to 5). Because the questions essentially ask the same thing, I'd like to just report the average (mean) score across all three questions*. How do you calculate the margin of error for that?
Do you just lump the data from all three questions together? But then you effectively triple your sample size, and you get a relatively small margin of error.
Do you calculate the average of the three responses for each respondent first, and then calculate the margin of error? But does that reduce your standard deviation?
Do you take the largest margin of error of the three questions? I heard somewhere that one typically reports the largest margin of error. Does that apply in this case?
Or is it something else?
Thanks in advance for any advice.
*PS: I know about the controversy of treating Likert-type data as continuous variables. In this case I have no choice but to accept that.