![]() ![]() Since the minimum of the 5-point scale is 1, we have a=1, b=5 in the first transformation. That looks just a little messy, but let's apply it to the example of a 5-point scale to be converted to a 7-point scale. Now to put this all together, substitute the whole first transformation in place of X in the second: Substitute 0 for X to see that the result is A, and 1 for X to see that the result is B. To go in the other direction, let's say we want the new minimum to be A and the new maximum to be B. Just substitute a for x to see that the result is 0, and then substitute b for x to see that the result is 1. It is easy to check that for a scale with minimum a and maximum b, the transformation That is, starting with a scale with a minimum of 0 and a maximum of 1, transform it so it has whatever minimum and maximum is required. Second, find the transformation which undoes this. First, find the linear transformation so that in the new scale, the minimum is 0 and the maximum is 1. Notice that a Likert scale is determined by its minimum, which is usually 1, and its maximum, for example 5. Here is how to easily find the right linear transformation to convert one Likert scale to another. ![]()
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