```Date: Sat, 5 Mar 2011 20:44:02 -0800 Reply-To: Justin Carroll Sender: "SPSSX(r) Discussion" From: Justin Carroll Subject: Re: Question about calculation of % change Comments: To: Max Freund In-Reply-To: Content-Type: multipart/alternative; Max, 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. Example A: 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 Time(2)= X 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 www.jrcresearch.net Cell: 916 628-4204 Email: jrcarroll@jrcresearch.net jrcarroll@hurtzlab.com jrc.csus@gmail.com On Sat, Mar 5, 2011 at 5:57 PM, Max Freund 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? > > Thanks, > Max > > > -- > Max Freund, M.I.I.M. • max@lunafreund.com • (909) 632-1624 > Partner, LF Leadership (*www.lfleadership.com* > ) > Doctoral Student in Organizational Behavior, Claremont Graduate University > (*www.cgu.edu/sbos* ) > > Want to book a meeting with me? Check my availability at > http://tungle.me/maxfreund > > [text/html] ```

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