How to convert percentage values from 7 point scale to 5 point scale? Suppose in one year I had a survey with 7-point scale and the values are like
Scale7, 1: 28%
Scale7, 2: 12%
Scale7, 3: 10%
Scale7, 4: 15%
Scale7, 5: 15%
Scale7, 6: 10%
Scale7, 7: 10%

where % are the percentage of responses for each scale from the sample size.
Now for next year if I have survey on the same question but with 5-point scale like
Scale5, 1: 25%
Scale5, 2: 25%
Scale5, 3: 10%
Scale5, 4: 20%
Scale5, 5: 20%

where % are the percentage of responses for each scale from the sample size.
Then if I have to convert the 7 point scale responses to 5 point scale how do I do that?

Subject behavior between Likert-7 and Likert-5 is clearly different, but poorly understood.
Suppose the following are true.

*

*Unless bored or uninterested, subjects tend to avoid the middle value as a wasted vote.


*Subjects may regard 1 on a 7-point scale as more of a rebuke than 1 on a 5-point scale.


*Unless very highly pleased and motivated, subjects are unwilling to vote 7 on a 7-point scale.
Then, the only fair conversion is to make both Likert-7 and Likert-5 into No/Yes scales: 1,2,3 or 1,2 become No; 5,6,7 or 4,5 become Yes. (Ignore middle values.)
This would mean subjects in the first year gave $40/85 = 47\%$ Yes votes
and subjects in the second year gave $4/9 = 44\%$ Yes votes --- perhaps an unimportant difference, even if there were
enough subjects for it to be 'significant'.
For a one-sided test, a thousand subjects might not suffice for significance:
prop.test(c(.44,.47)*1000, c(1000,1000), alt="less", cor=F)

        2-sample test for equality of proportions 
        without continuity correction

data:  c(0.44, 0.47) * 1000 out of c(1000, 1000)
X-squared = 1.8147, df = 1, p-value = 0.08897
alternative hypothesis: less
95 percent confidence interval:
 -1.000000000  0.006614161
sample estimates:
 prop 1 prop 2 
   0.44   0.47 

