Date:         Thu, 29 May 2003 11:58:35 -0500
Reply-To:     king.douglas@aa.com
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         King Douglas <king_d@SWBELL.NET>
Subject:      Re: creating index scores ranging from 0 to 100
Comments: To: "Cohen, Lou" <Lou.Cohen@bhsala.com>
In-Reply-To:  <6B8B84CF5F18D3118FAD0008C79142C604847D83@gobexchm2.bhsala.com>
Content-Type: text/plain; charset="iso-8859-1"

Lou:

Questions of validity aside, I find the most reliable method to convert
scores to a common index is to preserve the endpoints and midpoints and
maintain the standard scores (z-scores) by applying the following formula.

The following is probably overly annotated, but there it is.

King Douglas
American Airlines

* The following formulae convert scores on a scale of one range into
  scores on a scale of another range, such that the z-scores are identical,
  and any score that represents an end-point or mid-point on the old scale
also represents
  an end-point or mid-point on the new scale.

* The basic formula is

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

or

X = (Y-Mo)*(Rn/Ro) + Mn

where

X = Converted score
Y = Original score
Mo = Midpoint of original scale (e.g., 3 if scale is 1-5)
Mn = Midpoint of new scale (e.g., 5.5 if scale is 1-10)
Ro = Range of original scale (e.g., 4 if scale is 1-5 [5-1=4])
Rn = Range of new scale (e.g., 9 if scale is 1-10 [10-1=9])

EXAMPLE:  To convert scores on a 1-5 scale into scores on a 1-10 scale:

COMPUTE NEWVAR = (OLDVAR - 3)*(9/4) + 5.5.

EXAMPLE:  To convert scores on a 1-10 scale into scores on a 1-5 scale:

COMPUTE NEWVAR = (OLDVAR - 5.5)*(4/9) + 3.

* To check the accuracy of the conversions, run descriptives of old
  and new variables.

* Include the subcommand /SAVE in order save the z-scores of both the
  original and the converted scores.

* Any score that is an endpoint on the original scale should be an endpoint
  on the new scale.

DESCRIPTIVES VARIABLES = OLDVAR NEWVAR
  /SAVE
  /SORT.

* Next, run descriptives of the saved z-score variables to check the
  high and low z-scores, which should be the same for the original
  and the converted varibles.

DESCRIPTIVES VARIABLES = ZOLDVAR ZNEWVAR
  /SORT.

-----Original Message-----
From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU]On Behalf Of
Cohen, Lou
Sent: Thursday, May 29, 2003 11:28 AM
To: SPSSX-L@LISTSERV.UGA.EDU
Subject: creating index scores ranging from 0 to 100


I am having a bit of trouble creating an index score that ranges from 0 to
100 from a set of survey items. Would appreciate any helpful suggestions.

The survey contains several scales.  For instance, scale1 contains seven
Likert items (strongly disagree=1 to strongly agree=5). From this set of
seven items I wish to create a summated index score per record from these
items. In another scale, there are 11 items.  Once again I wish to create
summated index score ranging from 0 to 100 from this set of 11 items. Please
note there are missing values for some of items in the data base.

Thanks in advance


Lou Cohen
Director, Strategic Planning & Research
Baptist Health System
3500 Blue Lake Drive
Birmingham, Alabama 35283-0605



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