Rescaling a 5-point Likert scale to 6 points? Two groups (A and B) were sent matching surveys with a 6-point Likert scale. However, due to an administrative error, Group A's survey had a 5-point Likert scale instead of a 6-point Likert scale. That is to say, Group A's survey has the mid-point 'No opinion' and Group B's survey has no mid-point but the two central points are 'Somewhat disagree' and 'Somewhat agree'.
I would like to compare how the two groups differ on the individual items of the survey. Is it possible to rescale the results so that they are comparable?
 A: My personal experience with Likert scores is that it makes a difference in
subjects' behavior whether or not there is a 'neutral' category. One possibility
is that subjects who really have no opinion will try to be 'nice' by picking
the slightly favorable response when no neutral response is available.
So it is not obvious that any method of conversion from Likert-five to Likert-six
is going to be without difficulties.
Otherwise, you might try multiplying scores 0 through 4 by $5/4$ to get five
scores evenly spaced between 0 and 5.
Let's try a couple of examples with simulated data to see how this might work in practice.
In the first simulation, available items are chosen at random, so there should be no
difference between the converted Likert-5 items and the native Likert-6 ones,
and a 2-sample Wilcoxon (rank sum) test finds no difference (P-value > 0.05).
set.seed(2020)
x = sample(0:4, 200, rep=T)
table(x)
x
 0  1  2  3  4 
38 37 46 39 40 

x6 = 5*x/4
table(x6)
x6
   0 1.25  2.5 3.75    5 
  38   37   46   39   40 

y = sample(0:5, 200, rep=T)
table(y)
y
 0  1  2  3  4  5 
41 27 32 32 33 35 

wilcox.test(x6,y)

        Wilcoxon rank sum test with continuity correction

data:  x6 and y
W = 20343, p-value = 0.7648
alternative hypothesis: 
 true location shift is not equal to 0

Now we look at a simulation in which respondents tend to choose higher items (with
no difference in 'behavior' with or without a neutral category). Again, no
significant difference.
So with a couple of straightforward cases where the conversion 'ought to' work smoothly, it does work smoothly.  You might explore other (possibly worrisome) scenarios with simulations of
your own.
set.seed(910)
x = sample(0:4, 200, rep=T, p=(1:5)/15)
x6 = 5*x/4
table(x6)
x6
   0 1.25  2.5 3.75    5 
  17   19   42   50   72 
y = sample(0:5, 200, rep=T, p=(1:6)/21)
table(y)
y
 0  1  2  3  4  5 
 8 20 29 38 59 46 
wilcox.test(x6,y)

        Wilcoxon rank sum test with continuity correction

data:  x6 and y
W = 20488, p-value = 0.668
alternative hypothesis: 
 true location shift is not equal to 0

