Table 20.2 Person score and measure distribution

Table 20.1 Complete score-to-measure table on test of all items  

Table 20.2 Person score and measure distribution

Table 20.3 Complete score-to-calibration table for tests based on whole sample

 

TABLE OF SAMPLE NORMS (500/100) AND FREQUENCIES CORRESPONDING TO COMPLETE TEST

+---------------------------------------------------------------------------+

| SCORE   MEASURE    S.E.|NORMED S.E.  FREQUENCY %   CUM.FREQ. %  PERCENTILE|

|------------------------+--------------------------------------------------|

|     0    -6.17E    1.83|  147  107       0    .0       0    .0        0   |

|     1    -4.86     1.08|  225   63       0    .0       0    .0        0   |

|     2    -3.94      .85|  278   50       1   2.9       1   2.9        1   |

|     3    -3.27      .79|  318   46       2   5.9       3   8.8        6   |

|     4    -2.64      .78|  355   46       2   5.9       5  14.7       12   |

|     5    -1.97      .83|  394   49       2   5.9       7  20.6       18   |

|     6    -1.19      .92|  440   54       3   8.8      10  29.4       25   |

|     7     -.23     1.00|  496   59      12  35.3      22  64.7       47   |

|     8      .80      .97|  557   57       5  14.7      27  79.4       72   |

|     9     1.72      .92|  610   54       4  11.8      31  91.2       85   |

|    10     2.55      .89|  660   52       1   2.9      32  94.1       93   |

|    11     3.37      .89|  707   52       2   5.9      34 100.0       97   |

|    12     4.21      .93|  756   54       0    .0      34 100.0      100   |

|    13     5.23     1.12|  817   66       0    .0      34 100.0      100   |

|    14     6.60E    1.84|  897  108       0    .0      34 100.0      100   |

+---------------------------------------------------------------------------+

THE NORMED SCALE IS EQUIVALENT TO UIMEAN= 516.7919 USCALE= 45.0404

 

The columns in the Table of Sample Norms and Frequencies are:

Measures on the Complete Test:

SCORE

raw score on a complete test containing all calibrated items: TOTALSCORE=Yes includes extreme items. TOTALSCORE=No excludes extreme items (if any)

MEASURE

measure corresponding to score


If a person did not take all items or items are weighted, then that person is stratified with the measure on the complete test nearest the person's estimated measure (as reported in Table 18), regardless of that person's observed score.

S.E.

standard error of the measure (model). The statistical Test Information is (USCALE/S.E.)²

Statistics for this sample:

NORMED

measures linearly locally-rescaled so that the mean person measure for this sample is 500 and the population standard deviation is 100. Equivalent to UPMEAN=500, USCALE=100/(Person P.SD)

S.E.

standard error of the normed measure (for a score based on all the items)

FREQUENCY

count of sample with measures at or near (for missing data) the complete test measure

%

percentage of sample included in FREQUENCY

CUM.FREQ.

count of sample with measures near or below the test measure, the cumulative frequency.

%

percentage of sample include in CUM. FREQ.

PERCENTILE

The percent of the sample below the current measure.There are several definitions of percentile. Winsteps uses this one: Percentile Rank: The percentile is the cumulative frequency percent for the score below + half the frequency percent for the current score, half-rounded, and constrained to the range 1-99 for non-zero frequencies: . Percentiles for other definitions can be computed from the CUM. FREQ column. See, for instance, how-to-calculate-percentile

If the data are complete, then the raw data and the Rasch measures produce the same percentiles. If the data are incomplete, then the Rasch measures are used because they are robust against missing data.

NORMED SCALE

This shows the UIMEAN= and USCALE= values in order to report the person MEASURES at their NORMED (500/100) values.

 

Logit measures support direct probabilistic inferences about relative performances between persons and absolute performances relative to items. Normed measures support descriptions about the location of subjects within a sample (and maybe a population). Report the measures which are most relevant to your audience.

 

To paste this Table into Excel, set BOXSHOW=No to remove the vertical | and then copy-and-paste this table into Excel. Use Excel's "data", "text to columns" feature to put the scores and measures into columns.

 

Example: I want to stratify my sample into low, medium, high ability groups.

The separation index is based on the statistical fiction that your data accord exactly with a normal distribution and that the average measurement error (RMSE) precisely summarizes the precision of your data. In practice, these assumptions are only met approximately.

 

If your data are "complete" (everyone responds to every item), then a convenient places to start is Table 20.2. Starting at the lowest score, look down the scores until you find the score that best characterizes (as a first guess) your "low group". Then mentally multiply its S.E. by 3, and add it to the measure for the low group. This will take you to the measure for the middle group, which will be approximately statistically significantly different (p≤.05) from the low group. Do the same again for the middle group, and it will take you to the high group. Same again may take you to an even higher group, or up into the outliers at the top of the test. The cut-points will be half-way between the group centers that you have identified.

 

Do the same process from the top score downwards for another version of the stratification.

 

Then synthesize the two stratifications by adjusting the group by moving their center scores further apart (not closer together).

 

 

 

 


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
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn, 2024 George Engelhard, Jr. & Jue Wang 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
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes 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 Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
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 El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
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: Winsteps and Facets
Oct 21 - 22 2024, Mon.-Tues. In person workshop: Facets and Winsteps in expert judgement test validity - UNAM (México) y Universidad Católica de Colombia. capardo@ucatolica.edu.co, benildegar@gmail.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