I'm completely new at analyzing survey answers, and it will be great if anybody can help me out here with conversion technique. Survey participants were provided answer choices on a ranking scale of 1-4 and we got the average. We're trying to change the ranking scale to 1-5. I understand that there are different schools of thoughts that participants would have responded differently if they'd been given a different range of scale, but it needs to be converted.

I keep thinking that there must be a formula that can be applied to this, but I cannot come up with it. For instance, if average score is 3.4, what kind of arithmetic formula should I use to get an average score on the 1-5 scale?

Any insight will be greatly appreciated & thank you so much!

  • $\begingroup$ You can't do arithmetic formulas on survey scales, unless somehow you know that the scales are linear. why would they be linear though? Why do you want to re-scale? $\endgroup$
    – Aksakal
    Commented Mar 7, 2018 at 18:56
  • $\begingroup$ @NickCox - I came across the posting! And I tried to wrap around my head but I wasn't clear on whether I can still apply the same formula in my case. You see, I'm pretty clueless here. new=0.5 (1+old) Will truly appreciate it if you could provide the similar formula in this case. Thank you for your attention! $\endgroup$
    – user197893
    Commented Mar 7, 2018 at 19:04
  • $\begingroup$ @Aksakal - Honestly, I haven't thought about that. Would you mind elaborating how it can be problematic? $\endgroup$
    – user197893
    Commented Mar 7, 2018 at 19:08
  • $\begingroup$ The posting covers the principles only, but the details are just algebra, or arithmetic. For your particular numbers, (1) Subtract 1. Now your numbers range 0 to 3. (2) Multiply by 4/3. Now your numbers range 0 to 4. (3) Add 1. @NuclAcc already gave this answer. $\endgroup$
    – Nick Cox
    Commented Mar 7, 2018 at 19:08
  • $\begingroup$ There is a big difference between "can/can't" and "should/shouldn't". No one presumably supposes that if given a scale 1 to 5 any recipient would say "I prefer to think 1,2,3,4 and I really want to say 2, but if you insist on that scale my answer is 7/3." But if there is a context in which e.g. calculating mean scores for questions is desired and makes sense, then what other solution is there (other than saying "That can't be done; measurements were taken on a different scale", a defensible view but not necessarily a practical one)? $\endgroup$
    – Nick Cox
    Commented Mar 7, 2018 at 19:15

1 Answer 1


As you mentioned you probably shouldn't... BUT if you must. 1.33(x - 1) + 1 Should do it. To break that down,

  1. you take the number of response options on the old scale -1 to address your minimum being 1 In your case 3
  2. put that in the denominator and the new scale -1 in the numerator to address your minimum being 1. In your case 4.
  3. That should leave you with 4/3 = 1.33 (your scaling coefficient. Get the scale down to 0 by subtracting 1 from your variable. This is to address the fact that your minimum is 1 (again).
  4. Multiply by the scaling coefficient.
  5. Add the one back unless you want your lowest point to be 0 on a 0-4 scale.

Hope that helps clarify

  • $\begingroup$ This is being automatically flagged as low quality, probably because it is so short. At present it is more of a comment than an answer by our standards. Can you expand on it? We can also turn it into a comment. $\endgroup$ Commented Mar 7, 2018 at 18:54
  • $\begingroup$ Expanded on it. Hopefully it makes a little more sense now. Maybe I need to take the tour to figure out why an answer should be posted as a comment rather than an answer. I'll get on that. $\endgroup$
    – NuclAcc
    Commented Mar 7, 2018 at 19:24
  • $\begingroup$ Thanks. Unfortunately, you won't be able to comment until your reputation is >50. This does help, & turns it into more of an 'answer'. $\endgroup$ Commented Mar 7, 2018 at 19:29

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