combining scores from questions measuring the same construct but with different scales

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combining scores from questions measuring the same construct but with different scales

Zdaniuk, Bozena-3

Hello everyone, I would like to gather people’s ideas on how to combine data measuring the same construct but with different scales. I have done it in the past by turning scores into z-scores but are there other ways?

e.g, a question “do you like color blue?”

Data set 1:– Answer options “yes” and “no”

Data set 2:- Answer options “1-I don’t like it at all”, “2-I like it a little”, “3 – I like it a lot”

Data set 3: - Answer options “1-I don’t like it at all, 2, 3, 4, 5, 6, 7-I like it a lot”

 

Thanks so much for any ideas, pointers to literature, websites, etc.!

Cheers,

Bozena

 

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Re: combining scores from questions measuring the same construct but with different scales

Art Kendall
For the benefit of those who may look at this topic in the archives:

Unfortunately many intro courses fail to communicate basic principles
clearly. Two of these are:
 (1) that it possible to *coarsen* measurements, but it is not possible to
to refine them, i.e., make them more fine grained.  For measures of
location, if one only asks state, it is not possible to break down results
by county. Recall that the maximum correlation a variable can have is
limited by how many legitimate values are in you data.
 (2) Failing to prompt number line thinking. Note that the first example
first response scale does not go from less to more liking.  In many cultures
"un", less, low, West, etc are on the left end of a number line. Unless you
are stuck with strictly nominal level measurements, it is desirable to
implicitly prompt number line thinking.)

For the OP:

Is it correct that these are not repeated measures of the same construct,
but that the construct was measured differently by different groups of
respondents?

Do you intend to relate the liking construct to other variables in each data
set? If so, an additional approach to z-scores would be to calculate some
association/similarity/correlation, and think in a meta-analytic framework
of analyzing set of coefficients.

If you have just these 3 studies, you could show sets of 3 scatterplots
(with or without regression or loess fits). That would be 1 set for each
variable you want to relate to liking, e.g., age, gender, physical test
results, etc.

List members, I need to go to a meeting, but if someone has the time to
generate syntax to
(1) create a simulation with a known pop correlation with continuous X and
Y, then coarsen Y to 10,9,8,. . .2 levels
(2) correlate Xwith the set of 11 Y variables.

This would be a nice exercise for instructors to have when discussing
measurement levels, etc.




-----
Art Kendall
Social Research Consultants
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Art Kendall
Social Research Consultants
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Re: combining scores from questions measuring the same construct but with different scales

Anthony Babinec
To Art Kendall's point, Paul Barrett has some nice technical white papers.
His paper #8 at the link below gives a demonstration of the effect on
Pearson Correlation when you categorize continuous variables.

http://www.pbarrett.net/techpapers.html


Anthony J. Babinec
Co-Author, Data Analysis with IBM SPSS Statistics. 2017:Packt.
Harry V. Roberts Statistical Advocate of the Year Award Committee,
 American Statistical Association
[hidden email]





-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Art
Kendall
Sent: Wednesday, November 15, 2017 7:48 AM
To: [hidden email]
Subject: Re: combining scores from questions measuring the same construct
but with different scales

For the benefit of those who may look at this topic in the archives:

Unfortunately many intro courses fail to communicate basic principles
clearly. Two of these are:
 (1) that it possible to *coarsen* measurements, but it is not possible to
to refine them, i.e., make them more fine grained.  For measures of
location, if one only asks state, it is not possible to break down results
by county. Recall that the maximum correlation a variable can have is
limited by how many legitimate values are in you data.
 (2) Failing to prompt number line thinking. Note that the first example
first response scale does not go from less to more liking.  In many cultures
"un", less, low, West, etc are on the left end of a number line. Unless you
are stuck with strictly nominal level measurements, it is desirable to
implicitly prompt number line thinking.)

For the OP:

Is it correct that these are not repeated measures of the same construct,
but that the construct was measured differently by different groups of
respondents?

Do you intend to relate the liking construct to other variables in each data
set? If so, an additional approach to z-scores would be to calculate some
association/similarity/correlation, and think in a meta-analytic framework
of analyzing set of coefficients.

If you have just these 3 studies, you could show sets of 3 scatterplots
(with or without regression or loess fits). That would be 1 set for each
variable you want to relate to liking, e.g., age, gender, physical test
results, etc.

List members, I need to go to a meeting, but if someone has the time to
generate syntax to
(1) create a simulation with a known pop correlation with continuous X and
Y, then coarsen Y to 10,9,8,. . .2 levels
(2) correlate Xwith the set of 11 Y variables.

This would be a nice exercise for instructors to have when discussing
measurement levels, etc.




-----
Art Kendall
Social Research Consultants
--
Sent from: http://spssx-discussion.1045642.n5.nabble.com/

=====================
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Re: combining scores from questions measuring the same construct but with different scales

Rich Ulrich
In reply to this post by Zdaniuk, Bozena-3

If you "standardize" scores by groups, you definitely remove any differences between groups

from the scoring. Is that desirable or acceptable? And, you might consider scoring by logits rather

than the z-transformation.


The size of the groups can bear on the question of whether you coarsen some measures.

You throw away less information if the 1-9 scores have a tiny sample size; if they have the

much-bigger N, that's more reason to preserve them, and suffer the "noise" introduced by

re-mapping arbitrarily somewhere in the 1-9 range -- it could be (2,8) or (3,7) or whatever,

not /necessarily/ the extremes -- if the whole range of scores is being used, you don't want

the (1,2=> 1, 9) to dominate the variance calculations.


When you do coarsen the data, consider your hypotheses and what you want to say.

Consider (No, ?, Yes)   ... where "?" might be Indifferent/ Don't Know/ Missing. If you want

to write up, eventually, a statement about "NOs" (or one about YESes), you should chose to

collapse the /other/ two groups.


--

Rich Ulrich



From: SPSSX(r) Discussion <[hidden email]> on behalf of Zdaniuk, Bozena <[hidden email]>
Sent: Tuesday, November 14, 2017 3:03:20 PM
To: [hidden email]
Subject: combining scores from questions measuring the same construct but with different scales
 

Hello everyone, I would like to gather people’s ideas on how to combine data measuring the same construct but with different scales. I have done it in the past by turning scores into z-scores but are there other ways?

e.g, a question “do you like color blue?”

Data set 1:– Answer options “yes” and “no”

Data set 2:- Answer options “1-I don’t like it at all”, “2-I like it a little”, “3 – I like it a lot”

Data set 3: - Answer options “1-I don’t like it at all, 2, 3, 4, 5, 6, 7-I like it a lot”

 

Thanks so much for any ideas, pointers to literature, websites, etc.!

Cheers,

Bozena

 

===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
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Re: combining scores from questions measuring the same construct but with different scales

Jon Peck
In a broader context, latent class models might be relevant. (There is an extension command for that.)

On Wed, Nov 15, 2017 at 11:40 AM Rich Ulrich <[hidden email]> wrote:

If you "standardize" scores by groups, you definitely remove any differences between groups

from the scoring. Is that desirable or acceptable? And, you might consider scoring by logits rather

than the z-transformation.


The size of the groups can bear on the question of whether you coarsen some measures.

You throw away less information if the 1-9 scores have a tiny sample size; if they have the

much-bigger N, that's more reason to preserve them, and suffer the "noise" introduced by

re-mapping arbitrarily somewhere in the 1-9 range -- it could be (2,8) or (3,7) or whatever,

not /necessarily/ the extremes -- if the whole range of scores is being used, you don't want

the (1,2=> 1, 9) to dominate the variance calculations.


When you do coarsen the data, consider your hypotheses and what you want to say.

Consider (No, ?, Yes)   ... where "?" might be Indifferent/ Don't Know/ Missing. If you want

to write up, eventually, a statement about "NOs" (or one about YESes), you should chose to

collapse the /other/ two groups.


--

Rich Ulrich



From: SPSSX(r) Discussion <[hidden email]> on behalf of Zdaniuk, Bozena <[hidden email]>
Sent: Tuesday, November 14, 2017 3:03:20 PM
To: [hidden email]
Subject: combining scores from questions measuring the same construct but with different scales
 

Hello everyone, I would like to gather people’s ideas on how to combine data measuring the same construct but with different scales. I have done it in the past by turning scores into z-scores but are there other ways?

e.g, a question “do you like color blue?”

Data set 1:– Answer options “yes” and “no”

Data set 2:- Answer options “1-I don’t like it at all”, “2-I like it a little”, “3 – I like it a lot”

Data set 3: - Answer options “1-I don’t like it at all, 2, 3, 4, 5, 6, 7-I like it a lot”

 

Thanks so much for any ideas, pointers to literature, websites, etc.!

Cheers,

Bozena

 

===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
--
Jon K Peck
[hidden email]

===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
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Re: combining scores from questions measuring the same construct but with different scales

Zdaniuk, Bozena-3
thanks so much to everyone who took time to respond to this tread. It gave me some valuable leads to follow up on.
cheers,
bozena

From: SPSSX(r) Discussion [[hidden email]] on behalf of Jon Peck [[hidden email]]
Sent: Wednesday, November 15, 2017 3:15 PM
To: [hidden email]
Subject: Re: combining scores from questions measuring the same construct but with different scales

In a broader context, latent class models might be relevant. (There is an extension command for that.)

On Wed, Nov 15, 2017 at 11:40 AM Rich Ulrich <[hidden email]> wrote:

If you "standardize" scores by groups, you definitely remove any differences between groups

from the scoring. Is that desirable or acceptable? And, you might consider scoring by logits rather

than the z-transformation.


The size of the groups can bear on the question of whether you coarsen some measures.

You throw away less information if the 1-9 scores have a tiny sample size; if they have the

much-bigger N, that's more reason to preserve them, and suffer the "noise" introduced by

re-mapping arbitrarily somewhere in the 1-9 range -- it could be (2,8) or (3,7) or whatever,

not /necessarily/ the extremes -- if the whole range of scores is being used, you don't want

the (1,2=> 1, 9) to dominate the variance calculations.


When you do coarsen the data, consider your hypotheses and what you want to say.

Consider (No, ?, Yes)   ... where "?" might be Indifferent/ Don't Know/ Missing. If you want

to write up, eventually, a statement about "NOs" (or one about YESes), you should chose to

collapse the /other/ two groups.


--

Rich Ulrich



From: SPSSX(r) Discussion <[hidden email]> on behalf of Zdaniuk, Bozena <[hidden email]>
Sent: Tuesday, November 14, 2017 3:03:20 PM
To: [hidden email]
Subject: combining scores from questions measuring the same construct but with different scales
 

Hello everyone, I would like to gather people’s ideas on how to combine data measuring the same construct but with different scales. I have done it in the past by turning scores into z-scores but are there other ways?

e.g, a question “do you like color blue?”

Data set 1:– Answer options “yes” and “no”

Data set 2:- Answer options “1-I don’t like it at all”, “2-I like it a little”, “3 – I like it a lot”

Data set 3: - Answer options “1-I don’t like it at all, 2, 3, 4, 5, 6, 7-I like it a lot”

 

Thanks so much for any ideas, pointers to literature, websites, etc.!

Cheers,

Bozena

 

===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
--
Jon K Peck
[hidden email]

===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD
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Re: combining scores from questions measuring the same construct but with different scales

Art Kendall
This paper uses Statistica.  If someone has the time, I might make a good
teaching and planning tool to do the simulation in SPSS with provision for
inputting pop R in the ranges for the discipline.  One run would use a huge
number of cases, others would use numbers of cases common in the discipline.

In my experience, in most pretests of administrations people can usually
deal with 7 categories, although there have been a few situations where they
could always deal with 5 categories. YMMV.

a rule of thumb I would suggest is:
in the first development of an instrument  use as many categories as the
pre-tests shows people from the relevant population can deal with.

Another rule of thumb is to use the response categories of an instrument
developed by others UNLESS administration pre-tests show the relevant
population can only deal with a smaller number.

Can anybody think of situations where these rules of thumb would be
contr-indicated?



-----
Art Kendall
Social Research Consultants
--
Sent from: http://spssx-discussion.1045642.n5.nabble.com/

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Art Kendall
Social Research Consultants
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Re: combining scores from questions measuring the same construct but with different scales

Bruce Weaver
Administrator
I believe Art is referring to paper #8 here:

   http://www.pbarrett.net/techpapers.html



Art Kendall wrote

> This paper uses Statistica.  If someone has the time, I might make a good
> teaching and planning tool to do the simulation in SPSS with provision for
> inputting pop R in the ranges for the discipline.  One run would use a
> huge
> number of cases, others would use numbers of cases common in the
> discipline.
>
> In my experience, in most pretests of administrations people can usually
> deal with 7 categories, although there have been a few situations where
> they
> could always deal with 5 categories. YMMV.
>
> a rule of thumb I would suggest is:
> in the first development of an instrument  use as many categories as the
> pre-tests shows people from the relevant population can deal with.
>
> Another rule of thumb is to use the response categories of an instrument
> developed by others UNLESS administration pre-tests show the relevant
> population can only deal with a smaller number.
>
> Can anybody think of situations where these rules of thumb would be
> contr-indicated?
>
>
>
> -----
> Art Kendall
> Social Research Consultants
> --
> Sent from: http://spssx-discussion.1045642.n5.nabble.com/
>
> =====================
> To manage your subscription to SPSSX-L, send a message to

> LISTSERV@.UGA

>  (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD





-----
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bweaver@lakeheadu.ca
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"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.