Date: Sat, 5 Mar 2011 20:44:02 -0800
Reply-To: Justin Carroll <firstname.lastname@example.org>
Sender: "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From: Justin Carroll <email@example.com>
Subject: Re: Question about calculation of % change
Fun question! I hope others weigh in on this and share their thoughts - I
look forward to the thread.
My personal feeling (flavored by my training etc) would be to consider the
usage of your claim of a %-increase and the scale to which you are referring
to. I agree with you that your min and max values on your
summarized/averaged scores is arbitrary (aka your min represents the lowest
possible valuable someone could get on the construct, and the highest the
most someone could get on the construct) - the min and max values can change
and the implied meanings of the terminal endings of your scale would stay
the same (regardless of the value).
More to the point, your statements of %-increase will probably be statements
relating to the score increase, not the construct increase. So when you say
this person had a 20% increase from time1 to time2, and time1 has a value of
20, then you know that the time2 score is 24 (not that their
ability/construct level increased by 20%). Whereas, if you do your
alternatively proposed calculation of shifting the low end of the scale to a
zero-point to do your calculations then the %-increase statements you'll
make will be inaccurate. I think this is tied into the old debate on the
division and classification of parametric data (i.e. the difference between
interval and ratio level data). In this case, like most Likert scales, most
would say you have interval level data (with no True zero-point).
Normally, for statements of proportionality (like %-increase) you need to
have ratio level data, but in this case your scale is interval at best. The
reason WHY you are able to take proportions (whether it makes sense in
practice in this case) is because you have a TRUE zero point (thus making it
ratio) when you take the differences. Time(1) - Time(2) = Difference: 3 -
3 = 0 and in this case a value of 0 is True, because there was no increase
or decrease in the scores.
Time(1) = 3
Time(2) = X
Statement: Ss1 Increased their score by 20%
Increase = 3(.20) = .60
Time(2) = 3 + increase = 3.60
EXAMPLE B (alternative calculation):
Time(1) = 3
Statement: Ss1 increased their score by 20%
Increase = 2(.20) = .40 //Here it is "2" because this is adjusted to
reflect a 0-3 scale versus the original 1-4 scale
Time(2) = 3 + increase = 3.40
So, your statements of "increase" on the composite or average scores should
reflect the scale itself. When you start adjusting the scale to reflect
something different (e.g. shifting to an arbitrary zero-point), the
ratio/percentages you are providing will be disproportionate to the actual
increase observed between the scores (across times in this case) based on
the measure you used - thus, making your statements of "change" difficult to
decode, communicate, and impractical for reporting (as misinterpretation in
this case would make your statements wrong and "worthless" in making
predictions if your reader does not takes steps to comprehend the adjustment
you made to the scale)
My recommendation: don't adjust! Stick with values that keep your
proportional statements accurate and consistent across reporting.
J. R. Carroll
Researcher for Hurtz Labs
Instructor at California State University, Sacramento
Research Methods, Test Development, and Statistics
Cell: 916 628-4204
On Sat, Mar 5, 2011 at 5:57 PM, Max Freund <firstname.lastname@example.org> wrote:
> Hello all,
> 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.
> Any thoughts?
> Max Freund, M.I.I.M. • email@example.com • (909) 632-1624
> Partner, LF Leadership (*www.lfleadership.com*<http://www.lfleadership.com/>
> Doctoral Student in Organizational Behavior, Claremont Graduate University
> (*www.cgu.edu/sbos* <http://www.cgu.edu/SBOS/>)
> Want to book a meeting with me? Check my availability at