# Correct Analysis of Likert score (Product of two Likert scales)?

I have two Likert scale questions measuring perception of risk (Severity & Probability). For example: What kind of injury is caused by falling from a height of ten feet?

1. no injuries
2. slight injuries
3. injuries w/medical no permanent damage
4. injury w/medical permanent damage
5. possible fatal injuries

How likely to occur is an accident caused by falling from a height of ten feet?

1. never
2. unlikely
3. somewhat likely
4. likely
5. very likely

I am multiplying the responses from these two questions to create a perception of risk score (e.g. Fatal(5) & Never (1) = 5). This computed score lacks a zero (not ratio) and gap between scores are not the same therefore it isn't interval. I consolidate these scores into four groups: acceptable risk or no risk (1 – 4), low risk (5 – 9), moderate risk (10 – 15), high risk (16 – 25)

I have successfully conducted Chi-square and Mann-Whitney U tests with the scores converted in the four groupings. But...

My question is:

Should I be analyzing computed scores themselves? Does the nature of obtaining the score LACK meaning UNTIL I place them in the ordinal 4 categories?

Should I ONLY use the consolidated scores (4 groups) in my Chi-square, Mann-Whitney U, and (soon to be done) ordinal regression?

• Why do you want to classify them? Aren't you better leaving the scores as they are for analysis? Apr 11, 2013 at 21:27

I don't think you should be multiplying them in this way without a lot of thought.

In fact, I'd go further and say that you shouldn't even ask the question this way. Rather, it would be better to have people rate the risk of each type of injury. After all, if a person falls 10 feet, he MIGHT have no injuries, he MIGHT die - there are certainly examples of both. So, I might say there is a very slight chance of no injuries, a much higher chance of the middle 3 levels and a very slight chance of fatality. And "possible fatal" is a bad choice of words. What does "very likely possible fatal injuries" mean?

If you've already gathered data ..... well... Clearly "no injuries" and "never" should be 0. not 1. Then you need to consider each combination and whether they are equivalent. Is "unlikely fatal" (2*5 = 10) the same as "very likely slight (5*2 = 10)? I don't think so....

The second scale could probably be made numeric fairly easily: Never = 0, Very likely = 0.9 and the others are intermediate with some reasonable choices. The first scale will be very hard to make numeric. I would do sensitivity analysis with different choices.

Then, you don't avoid any of these issues by making it ordinal. If anything, you make them worse. By doing this you are saying that ALL the combinations in a particular ordinal level are the same. So, your 10-15 category includes:

Slight Very Likely
No permanent Very likely
Fatal Unlikely
Fatal Somewhat likely
No permanent Likely
Permanent Somewhat likely

That can't be right!

Another choice, if you've already got data, is to not multiply the values at all but to use them as separate independent variables; but I am not sure that gets at what you want.

• Peter, Thank you for the response! I am very limited seeing I’ve already collected my data, I now see the complications by multiplying both responses. I was hoping for a quantitative way to measure risk in this way. By not combining the scores and testing each as separate IV’s…are you saying the first question (severity) isn’t ordinal? But should be treated as nominal? Apr 12, 2013 at 20:33
• The first one is doubtless ordinal. But multiplication assumes that it's interval. There are relatively few methods for dealing with ordinal IVs, and it might be better to treat it as nominal. Apr 12, 2013 at 20:36