I think the change can be measured in the terms you are talking about, but when you get to proportional statements of change you can't alter the scale (linearly transform so to speak) without altering the proportional statements itself.
For example a 40% increase from "1" would be 1.40
A 40% increase from the original value of 100 would result in 140.
It's not the range that is critical for the computation but the actual values from Value1 to Value2; change the numbers, change the percent increase (or decrease) - regardless of the 'range'.
The difference between 1 and 4 is 3.. (as you said), and the difference between 100 and 103 is also 3, but the % increased is dependent on the numbers of Value_1 and Value_2. In this case, going from a score of 1 to score of 4 is a 300% increase. An increase from 100 to 102, the same "range", but is only 2% increase.
Here is a quick and dirty calculator for percentage increase I found online (and of course you can do the hand-calculations as well):
Value2 - Value1 = Difference
Difference / Value1 = % of original value and the % of increase/decreased.
To recalculate Value2 you can do an old accounting trick where you take the original value * (1+percentage changed). So for example, if I had Value1 = 10, Value2 = 14, the difference would be 4, but 4 is .40 (4/10) of 10 (Value1). So if I want to reverse this, to get Value2, I could take the original value of 10 and multiple by 1.40 (1 + the % change) which gets me a value of 14 again.
Maybe I missed the OP's question or I am just not understanding the problem/question - my apologies if that is the case; I assume he is interested in commenting on percentage increase or decrease from the original value, not the difference/distance from Time1 to Time2.
J. R. Carroll
The range on a 1 – 4 scale is 3 not 2.5 and the range on a 0 – 3 scale is also 3, so a 1 unit change is 33% either way.
Dr. Paul R. Swank,
Professor and Director of Research
Children's Learning Institute
University of Texas Health Science Center-Houston
This is an embarrassingly basic question and not really SPSS-related, but I've got myself confused about it so I'm hoping this brain trust can help straighten me out.
I have a variable measured on a 1-4 Likert scale at Time 1 and Time 2. I want to compute the percent change from T1 to T2. Would it be more accurate to transpose the scores to a 0-3 scale before calculating the % change?
For example, a change from T1=2.5 to T2=3.5 measured on a 1-4 scale would result in a 40% increase (1/2.5=.4). When transposed to a 1-3 scale, however, it results in a 67% increase (1/1.5=.67). So basically, I'm wondering if starting the scale at 1 is a false minimum.
The variable in question is an average of several items rating different aspects of organizational capacity and management practice, with 1 being little to no capacity in that area and 4 indicating robust capacity.
Strictly speaking I know it may not be conceptually meaningful to compute percent changes in Likert items anyway (this one is actually an aggregate of several items). However, this is for an evaluation of a project that had as one of its objectives an X% increase in participants' capacity scores.