# Can I interpret mean difference on a Likert scale as a percentage change

I have pre-test data showing a mean of 3.71 for work-stress (7 point likert scale).

My post-test data shows a mean of 3.24 for work-stress (same 7 point likert scale).

Paired sample t-test is showing significant mean difference at p < 0.001.

Can I interpret this drop in work-stress as a $\frac{3.71-3.24}{3.71} = 12.7\%$ decrease in work-stress?

Some extra information: the pre test was a measurement before treatment and the post-test was measurement after treatment with 4 weeks time between pre- and post-test. *the question on the likert scale were statements like: I often worry about work after worktime. (agree - disagree)

• Imagine that you labeled etiquettes of the categories as 1 - "Not at all", 2 - "a little bit more than nothing", 3 - "much less than average", 4 - "average", 5 - "VERY VERY VERY VERY VERY MUCH!!!!!". Now, would you say that the difference between 3 and 4 is the same as between 4 and 5? Likert scale is ordinal. Check stats.stackexchange.com/questions/10/… and stats.stackexchange.com/questions/97/…
– Tim
Commented Jun 23, 2016 at 11:57
• Thanks, that makes sense! For future studies if the scale was interval (via a trackbar for example), would it than be allowed to do so? Commented Jun 23, 2016 at 15:36

## 1 Answer

Imagine that you labeled of the categories as:

1 - "Not at all", 2 - "a little bit more than nothing", 3 - "much less than average", 4 - "average", 5 - "VERY VERY VERY VERY VERY MUCH!!!!!"

Now, would you say that the difference between 3 and 4 is the same as between 4 and 5? Likert scale is ordinal, so it tells you only about the ordering of categories, not about the distances between then. So using means of Likert-scaled items as you described it would be inappropriate.

What you could do is to compare percentages of answers given in different categories. For example: "there was 5% increase in in rating XYZ as 'very good'", or "there was a 20% decrease in rating XYZ as 'good', or 'very good'".

Moreover, you could also check Item Response Theory methods that are designed specifically for this kind of data.