# Comparing two users answers to likert questions

I am trying to compare two users who have answered a likert-scale set of questions. The output should be, ideally, a % agree or disagree, averaged across the question set.

How should I calculate this?

• What do you mean by "% agree or disagree"? Do you have only 2 people & want to know how many questions they selected the sme answer? – gung - Reinstate Monica Sep 28 '15 at 22:29

and welcome to the site. A reasonable choice to measure disagreement for an individual question with max score $M$, min score $m$, person 1's score $x$, and person 2's score $y$ would be:

$$\frac{|y-x|}{M-m}.$$

Across an entire survey, if we index the above notation by $i$ with a total of $n$ questions, both of the following would be reasonable:

$$\frac{\sum_i |y_i - x_i|}{\sum_i M_i - m_i}$$

-or-

$$\frac{1}{n}\sum_i \frac{|y_i-x_i|}{M_i-m_i}.$$

The latter is probably better because it ignores differences in range from question to question. Both of these have the property that total similarity gives 0, while maximal dissimilarity gives 1.