converting scales

[Dee-17]

I am trying to convert scores from an old scale to a new scale.  The old
scale is a 1 t 6. Where 1 is the minumum value.  The new scale is 1 to 4.
Where 1 is the minumun value. This scale is to be used for the HR
evaluation of employees where 1 is poor and 4 is excellent.

When using the old scale someone who received a 4.5 had to review their
performance with a supervisor and 4.0 with the VP. I am trying to find the
equivalent scoring for the  1 to 4 scale.


Director Institutional Research

[Oliver, Richard]

If all you need is a simple linear conversion:

compute newscale=oldscale*(4/6).



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Dee
Sent: Friday, September 07, 2007 2:26 PM
To: [hidden email]
Subject: converting scales

I am trying to convert scores from an old scale to a new scale.  The old
scale is a 1 t 6. Where 1 is the minumum value.  The new scale is 1 to 4.
Where 1 is the minumun value. This scale is to be used for the HR
evaluation of employees where 1 is poor and 4 is excellent.

When using the old scale someone who received a 4.5 had to review their
performance with a supervisor and 4.0 with the VP. I am trying to find the
equivalent scoring for the  1 to 4 scale.


Director Institutional Research

[Oliver, Richard]

Oops. One of our statisticians (you can tell that I'm not one) pointed out that my solution would produce a minimum of 2/3, not 1. He suggested this instead:

Compute newscale=.4+.6*oldscale.

-----Original Message-----
From: Oliver, Richard
Sent: Friday, September 07, 2007 2:42 PM
To: 'Dee'; [hidden email]
Subject: RE: converting scales

If all you need is a simple linear conversion:

compute newscale=oldscale*(4/6).



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Dee
Sent: Friday, September 07, 2007 2:26 PM
To: [hidden email]
Subject: converting scales

I am trying to convert scores from an old scale to a new scale.  The old
scale is a 1 t 6. Where 1 is the minumum value.  The new scale is 1 to 4.
Where 1 is the minumun value. This scale is to be used for the HR
evaluation of employees where 1 is poor and 4 is excellent.

When using the old scale someone who received a 4.5 had to review their
performance with a supervisor and 4.0 with the VP. I am trying to find the
equivalent scoring for the  1 to 4 scale.


Director Institutional Research

[Melissa Ives]

So in the new scale a value of 3 is comparable to 4.5 in the old scale
and a score of 2.67 is comparable to a value of 4 in the old scale.

Melissa

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Oliver, Richard
Sent: Friday, September 07, 2007 2:42 PM
To: [hidden email]
Subject: Re: [SPSSX-L] converting scales

If all you need is a simple linear conversion:

compute newscale=oldscale*(4/6).



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Dee
Sent: Friday, September 07, 2007 2:26 PM
To: [hidden email]
Subject: converting scales

I am trying to convert scores from an old scale to a new scale.  The old
scale is a 1 t 6. Where 1 is the minumum value.  The new scale is 1 to
4.
Where 1 is the minumun value. This scale is to be used for the HR
evaluation of employees where 1 is poor and 4 is excellent.

When using the old scale someone who received a 4.5 had to review their
performance with a supervisor and 4.0 with the VP. I am trying to find
the equivalent scoring for the  1 to 4 scale.


Director Institutional Research


PRIVILEGED AND CONFIDENTIAL INFORMATION
This transmittal and any attachments may contain PRIVILEGED AND
CONFIDENTIAL information and is intended only for the use of the
addressee. If you are not the designated recipient, or an employee
or agent authorized to deliver such transmittals to the designated
recipient, you are hereby notified that any dissemination,
copying or publication of this transmittal is strictly prohibited. If
you have received this transmittal in error, please notify us
immediately by replying to the sender and delete this copy from your
system. You may also call us at [phone] for assistance.

[King Douglas]

The problem with using a simple linear conversion is that, depending on the two scales, neither the scale end-points nor the standard scores (z-scores) will be maintained.

Although you don't say it, I'm assuming you are talking about averages across a number of ratings, so maintaining z-scores is important.  A simple linear conversion as suggested would underestimate the mean score, leaving more employees vulnerable to review.

I suggest using this formula:

New score = (old score - old scale midpoint)*(new range/old range) + new scale midpoint.

For instance, the converted score on a 4-point scale for a value of 3 on a 6-point scale would be

(3-3.5)*(3/5)+2.5 = 2.2

As opposed to 3*4/6 = 2 using the simple, linear transformation suggested below.

Using the formula above and converting from 6- to 4- point scale
1=1
2=1.6
3=2.2
4=2.8
5=3.4
6=4

King Douglas
American Airline Customer Research



elissa Ives <[hidden email]> wrote: So in the new scale a value of 3 is comparable to 4.5 in the old scale
and a score of 2.67 is comparable to a value of 4 in the old scale.

Melissa

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Oliver, Richard
Sent: Friday, September 07, 2007 2:42 PM
To: [hidden email]
Subject: Re: [SPSSX-L] converting scales

If all you need is a simple linear conversion:

compute newscale=oldscale*(4/6).



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Dee
Sent: Friday, September 07, 2007 2:26 PM
To: [hidden email]
Subject: converting scales

I am trying to convert scores from an old scale to a new scale.  The old
scale is a 1 t 6. Where 1 is the minumum value.  The new scale is 1 to
4.
Where 1 is the minumun value. This scale is to be used for the HR
evaluation of employees where 1 is poor and 4 is excellent.

When using the old scale someone who received a 4.5 had to review their
performance with a supervisor and 4.0 with the VP. I am trying to find
the equivalent scoring for the  1 to 4 scale.


Director Institutional Research


PRIVILEGED AND CONFIDENTIAL INFORMATION
This transmittal and any attachments may contain PRIVILEGED AND
CONFIDENTIAL information and is intended only for the use of the
addressee. If you are not the designated recipient, or an employee
or agent authorized to deliver such transmittals to the designated
recipient, you are hereby notified that any dissemination,
copying or publication of this transmittal is strictly prohibited. If
you have received this transmittal in error, please notify us
immediately by replying to the sender and delete this copy from your
system. You may also call us at [phone] for assistance.