User-friendly rescaling: zero point and unit

Winsteps sets the zero point (local origin) at the mean item difficulty (including extreme items if UEXTREME=Yes). The unit of measurement is the logit. Changing the zero point and transforming logits into other units can be done with UIMEAN=, UPMEAN=, USCALE=. These transformed measurements can be more meaningful for particular applications, see Chapter 8 of BTD. Anchor values are treated according to UASCALE=

 

Table 20.1 suggests values for UIMEAN= and USCALE= which produce a more friendly range of measures.

The USCALE= Calculator in the Help menu can do many of the computations in these examples:

 

Example 0: we observe the (current mean) and (current S.D.) of a set of measures. We want (desired mean) and (desired S.D.) then

new USCALE = (current USCALE=) *(desired S.D.) / (current S.D.)

new UIMEAN = desired mean - (current mean - current UIMEAN=)*(new USCALE=) / (current USCALE=)

 

we observe the (current high) and (current low). We want (desired high) and (desired low) then

new USCALE = (current USCALE=) *(desired  high-desired low)) / (current high-current low)

new UIMEAN = desired mean - (current mean - current UIMEAN=)*(new USCALE=) / (current USCALE=)

 

Example 1: CHIPs are a useful transformation, in which 1 logit = 4.55 CHIPs. In this user-scaling system, standard errors tend to be about 1 CHIP in size. The recommended control variable settings are:

USCALE = 4.55

UIMEAN = 50

UDECIM = 1

MRANGE = 50

 

The probability structure of this relationship is:

 

Probability of Success

 Difference between Person Ability Measure and Item Difficulty Measure in CHIPs

.10 -10

.25 -5

.50 0

.75 5

.90 10

 

Example 2: WITs are one tenth the size of CHIPs, enabling the elimination of decimals from your output tables.

USCALE = 45.5

UIMEAN = 500

UDECIM = 0

MRANGE = 500

 

Example 3: You want the lowest reportable person measure to be 0 and the highest to be 100. Looking at Table 20, you see the extreme values are -4.53 and +5.72. You have not used USCALE= and UIMEAN=, so the current values are USCALE=1, UIMEAN=0.

 

Therefore,

"wanted low" person measure = 0

"wanted high" person measure = 100

"wanted range" = "wanted high" - "wanted low" = 100 - 0 = 100

 

"current low" person measure = -4.53

"current high" person measure = 5.72

"current range" = "current high" - "current low" = 5.72 - -4.53 = 10.25

 

USCALE= (wanted range) / (current range) = 100 / 10.25 = 9.76

 

UIMEAN= ( wanted low ) - ( current low * USCALE ) = 0 - ( -4.53 * 9.76 ) = 44.20

 

Required values are:

USCALE = 9.76

UIMEAN = 44.20

UDECIM = 0 to show no decimal places in report

 

Double checking, when previous values are UIMEAN=0, USCALE=1:

low value = (current low)*(USCALE=) + (UIMEAN=) = (-4.53 * 9.76) + 44.20 = -0.01 = 0

high value = (current high)*(USCALE=) + (UIMEAN=) = (5.72 * 9.76) + 44.20 = 100.02 - 100

 

Example 4: You want the lowest reportable person measure to be 0 and the highest to be 100. Looking at Table 20, you see the extreme values are -4.53 and +5.72. The current values are USCALE=2, UIMEAN=1.5

 

Therefore,

"wanted low" person measure = 0

"wanted high" person measure = 100

"wanted range" = "wanted high" - "wanted low" = 100 - 0 = 100

 

"current low" person measure = -4.53

"current high" person measure = 5.72

"current range" = "current high" - "current low" = 5.72 - -4.53 = 10.25

 

"current UIMEAN" = 1.5

"current USCALE" = 2

 

USCALE= [(wanted range) / (current range)]/(current USCALE) = [100 / 10.25]/2 = 9.76/2 = 4.88

 

UIMEAN= ( wanted low ) - [(current low-current UIMEAN) * USCALE ] = 0 - [( -4.53-1.5) * 9.76] = 58.85

 

Required values are:

USCALE = 4.88

UIMEAN = 58.85

UDECIM = 0 to show no decimal places in report

 

Double checking is most easily done by looking at the new Table 20.

 

Example 5: You want the lowest reportable person measure to be 100 and the highest to be 900. Looking at Table 20, you see the extreme values are -4.53 and +5.72. Looking at the second page of output, you see the current values are USCALE=1 and UMEAN=0.

 

USCALE= (previous USCALE=) * (wanted range: 900 - 100) / (reported range: 5.72 - -4.53) = 1 * 800 / 10.25 = 78.05

UMEAN= (wanted low) - (reported low - previous UMEAN=)*(wanted range)/(reported range) = 100 - (-4.53 - 0)*800/10.25 = 453.56

UDECIM = 0 to show no decimal places in report

 

Example 6: You want norm-referenced user-scaling, such that the person mean is 0.0, and the person   standard deviation is 1.0.

 

In a standard analysis, set:

UDECIM=4

USCALE=1

UMEAN=0

 

Look at Table 18

 +------------------------------

 |ENTRY    RAW                  

 |NUMBER  SCORE  COUNT  MEASURE 

 |------------------------------

 | MEAN     6.7   14.0  -.3728  

 | P.SD     2.4     .0  2.2202  

 +------------------------------

 

Set (either in a new analysis, or using the "Specification" pull-down menu

USCALE = 1/person S.D. = 1/2.2202 = 0.4504

UMEAN = - person mean/person S.D. = - (-.3728)/2.2202 = 0.1679

Look at Table 18

 +------------------------------

 |ENTRY    RAW                  

 |NUMBER  SCORE  COUNT  MEASURE 

 |------------------------------

 | MEAN     6.7   14.0   .0000  

 | P.SD     2.4     .0  1.0000  

 +------------------------------

 

Example 7: You want to give your pass-fail point the value 400 and 100 to the lowest reported measure. Inspecting your output you see that the pass-fail point is at 1.5 logits, and that -3.3 logits is the lowest reported measure.

 Then 400-100 new units = 1.5 - (-3.3) logits, so

 USCALE = 300 / 4.8 = 62.5

 UMEAN = 400 - (1.5) * 62.5 = 306.25

 Then: 1.5 logits = 306.25 + 1.5*62.5 = 400

  -3.3 logits = 306.25 - 3.3*62.5 = 100

 

Example 8: Form 1 and Form 2 are obtained from an item bank. We rescale Form 1 and want to apply the same rescaling to Form 2.

 

Do the Form 1 analysis:

UASCALE= is the scaling of the item bank scale (1 if logits)

IAFILE= is the list of bank item difficulties for Form 1

No UIMEAN=, UPMEAN=, UMEAN= or USCALE= command.

 

We rescale Form 1 to have its own scale setting UIMEAN= and USCALE= with the scaling calculator.

Note down the values or list them with the Control Variable list from the Output Files menu.

 

In the Form 2 control file:

UASCALE= is the scaling of the item bank scale (1 if logits)

IAFILE= is the list of bank item difficulties for Form 2

No UIMEAN, UPMEAN or UMEAN command.

 

In the Form 2 control file, add these commands:

TFILE=*

; these are actioned after the analysis, at the beginning of the reporting

14.1    ; this will report the bank item anchor values as a check

3.1 ; summary statistics

UIMEAN= value from Form 1  ; the values used for the analysis are rescaled

USCALE= value from Form 1

14.1  ; rescaled items

3.1 ; summary statistics

18.1  ; rescaled persons

*

 

You can add these to an analysis of the Form 1 data to check that it works.

 

Do the analysis of Form 2.


Help for Winsteps Rasch Measurement and Rasch Analysis Software: www.winsteps.com. Author: John Michael Linacre

Facets Rasch measurement software. Buy for $149. & site licenses. Freeware student/evaluation Minifac download
Winsteps Rasch measurement software. Buy for $149. & site licenses. Freeware student/evaluation Ministep download

Rasch Books and Publications: Winsteps and Facets
Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang Statistical Analyses for Language Testers (Facets), Rita Green Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind Rasch Measurement: Applications, Khine Winsteps Tutorials - free
Facets Tutorials - free
Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
Other Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse Rasch Measurement Theory Analysis in R, Wind, Hua Applying the Rasch Model in Social Sciences Using R, Lamprianou Journal of Applied Measurement
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Rasch Models for Measurement, David Andrich Constructing Measures, Mark Wilson Best Test Design - free, Wright & Stone
Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias Diseño de Mejores Pruebas - free, Spanish Best Test Design A Course in Rasch Measurement Theory, Andrich, Marais Rasch Models in Health, Christensen, Kreiner, Mesba Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen
As an Amazon Associate I earn from qualifying purchases. This does not change what you pay.

facebook Forum: Rasch Measurement Forum to discuss any Rasch-related topic

To receive News Emails about Winsteps and Facets by subscribing to the Winsteps.com email list,
enter your email address here:

I want to Subscribe: & click below
I want to Unsubscribe: & click below

Please set your SPAM filter to accept emails from Winsteps.com
The Winsteps.com email list is only used to email information about Winsteps, Facets and associated Rasch Measurement activities. Your email address is not shared with third-parties. Every email sent from the list includes the option to unsubscribe.

Questions, Suggestions? Want to update Winsteps or Facets? Please email Mike Linacre, author of Winsteps mike@winsteps.com


State-of-the-art : single-user and site licenses : free student/evaluation versions : download immediately : instructional PDFs : user forum : assistance by email : bugs fixed fast : free update eligibility : backwards compatible : money back if not satisfied
 
Rasch, Winsteps, Facets online Tutorials


 

 
Coming Rasch-related Events
May 17 - June 21, 2024, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 12 - 14, 2024, Wed.-Fri. 1st Scandinavian Applied Measurement Conference, Kristianstad University, Kristianstad, Sweden http://www.hkr.se/samc2024
June 21 - July 19, 2024, Fri.-Fri. On-line workshop: Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug. 5 - Aug. 6, 2024, Fri.-Fri. 2024 Inaugural Conference of the Society for the Study of Measurement (Berkeley, CA), Call for Proposals
Aug. 9 - Sept. 6, 2024, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Oct. 4 - Nov. 8, 2024, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 17 - Feb. 21, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
May 16 - June 20, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 20 - July 18, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Further Topics (E. Smith, Facets), www.statistics.com
Oct. 3 - Nov. 7, 2025, Fri.-Fri. On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com

 

 

Our current URL is www.winsteps.com

Winsteps® is a registered trademark