Question about calculation of % change

[Max Freund-2]

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. • [hidden email] • [phone]

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

[J. R. Carroll]

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: [hidden email]

          [hidden email]

          [hidden email]

On Sat, Mar 5, 2011 at 5:57 PM, Max Freund <[hidden email]> 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. • [hidden email] • [phone]

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

[Swank, Paul R]

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

 

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Max Freund
Sent: Saturday, March 05, 2011 7:58 PM
To: [hidden email]
Subject: Question about calculation of % change

 

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. • [hidden email] • [phone]

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

 

[J. R. Carroll]

Hmm....

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):

http://www.marshu.com/articles/calculate-percentage-increase-decrease-percent-calculator.php

Hand Calc:

Value1
Value2

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

Researcher for Hurtz Labs

Instructor at California State University, Sacramento

Research Methods, Test Development, and Statistics

www.jrcresearch.net

Cell:  916 628-4204

Email: [hidden email]

          [hidden email]

          [hidden email]

On Sat, Mar 5, 2011 at 8:51 PM, Swank, Paul R <[hidden email]> wrote:

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

 

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Max Freund
Sent: Saturday, March 05, 2011 7:58 PM
To: [hidden email]
Subject: Question about calculation of % change

 

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. • [hidden email] • [phone]

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

 

[Bruce Weaver]

This illustrates one of the main problems with percentages -- percentage of what is not always clearly stated.

Justin Carroll wrote

Hmm....

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):

http://www.marshu.com/articles/calculate-percentage-increase-decrease-percent-calculator.php

Hand Calc:

Value1
Value2

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
Researcher for Hurtz Labs
Instructor at California State University, Sacramento
Research Methods, Test Development, and Statistics
www.jrcresearch.net
Cell:  916 628-4204
Email: [e-mail]
          [e-mail]
          [e-mail]



On Sat, Mar 5, 2011 at 8:51 PM, Swank, Paul R <[e-mail]>wrote:

> 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
>
>
>
> *From:* SPSSX(r) Discussion [mailto:[e-mail]] *On Behalf
> Of *Max Freund
> *Sent:* Saturday, March 05, 2011 7:58 PM
> *To:* [e-mail]
> *Subject:* Question about calculation of % change
>
>
>
> 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. • [e-mail] • [phone]
>
> Partner, LF Leadership (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
> http://tungle.me/maxfreund
>
>
>

[Max Freund-2]

Thank you to everyone who weighed in on my question!

I knew in my gut that there was something wrong, and Justin hit it on the head: ordinal-level data from Likert scales are so often treated as interval-level data, it is easy to forget that they're not.  In this case, the bottom line is that zero is not a meaningful point on the scale, so percent increases end up being entirely arbitrary based on the original scale.

As a result, I've decided to dodge what was a badly-conceived goal and speak of the changes in reference to the scale but not express the effect in terms of % change.

Thanks again, all!

--Max

--

Max Freund, M.I.I.M. • [hidden email] • [phone]

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

On Mar 5, 2011, at 8:44 PM, Justin Carroll wrote:

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: [hidden email]

          [hidden email]

          [hidden email]

On Sat, Mar 5, 2011 at 5:57 PM, Max Freund <[hidden email]> 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. • [hidden email] • [phone]

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