# Converting Likert Scales

We collected data on a 7-point survey and it should have been on a 9-point scale. How do you convert a 7-point scale to a 9-point scale?

• I would say that the general answer is "you don't". But why do you say it "should" have been collected on a 9 point scale? Are you are trying to compare it to other data that was collected using a 9 point scale? Or are you attempting to merge it with other data? Or something else? Dec 18 '19 at 14:34

However, if you want to compare your work in the 7 point scale with a different work on a 9 point scale, you can make a linear transform of the type: $$y = \frac{x-m}{a}$$ where $$x$$ is the mean or the median in the 7 point scale, $$m$$ is the minimum of that scale, $$m=1$$ in your case, and $$a$$ is the amplitude of the scale, in that case it will be $$a = 7 - 1 = 6$$. For the 9 point scale, the transformation formula is the same, but $$a = 9 - 1 = 8$$. Note that the standard deviation and the variance will each have their own transformations.
The transformed value will be in the interval $$[0; 1]$$ and you may find that, for instance, $$4.2$$ in the 7 point scale corresponds to a higher value than $$4.8$$ in the 9 point scale.