﻿ 3 facet dichotomy with item bias: The Knox Cube Test

# 3 facet dichotomy with item bias: The Knox Cube Test

Top Up Down  A A

In a standard two-facet Knox Cube analysis, respondent gender (sex) is indicated, but item bias (DIF, differential item functioning) is not computed. Here we add a DIF detection by coding a dummy "gender" Facet.

The Knox Cube Test measures short term memory (BTD p.28). There are two facets, Children and Tapping Items. Observations are scored dichotomously, 1 for correct and 0 for incorrect.

Facets specifications and data (in file Kcta.txt):

 Title = Knox Cube Test (Best Test Design p.31) ; the report heading line Facets = 3 ; three facets: children and items and gender Positive = 1 ; for facet 1, children, higher score = higher measure Noncenter = 1 ; only facet 1, children, does not have mean measure set to zero Pt-biserial = Yes ; report the point-biserial correlation Vertical = 1*,1A,2N,2A ; show children by distribution and sex, taps by number and name Yard = 112,4 ; Vertical rulers 112 columns wide, with 4 lines per logit Model = ?,?B,?B,D ; look for bias/interaction between 2nd and 3rd Facets Label 1,Children ; Children are facet 1 1-17 = Boy,,1 ; Pretend boys, in group 1, are numbered 1 through 17. 18-35 = Girl,,2 ; Pretend girls, in group 2, are numbered 18 through 35. * ; end of child labels for facet 1 2,Tapping items ; Items are facet 2 1 = 1-4 ; Items labelled by the order in which the four blocks are tapped 2 = 2-3 3 = 1-2-4 4 = 1-3-4 5 = 2-1-4 6 = 3-4-1 7 = 1-4-3-2 8 = 1-4-2-3 9 = 1-3-2-4 10= 2-4-3-1 11= 1-3-1-2-4 12= 1-3-2-4-3 13= 1-4-3-2-4 14= 1-4-2-3-4-1 15= 1-3-2-4-1-3 16= 1-4-2-3-1-4 17= 1-4-3-1-2-4 18= 4-1-3-4-2-1-4 * 3,Gender,A ; Dummy gender facet is anchored 1=boys,0 ; anchor at 0 so do not affect analysis 2=girls,0 ; anchor at 0 so do not affect analysis * ; end of item labels   Data = ; no data file name, so data follows immediately in this file 1,1,1, 1 ; child 1 on item 1 is a boy scored 1  (blanks are ignored) 1,2-18,1, 1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0 ; child 1 on item 2 is a boy scored 1, on item 3 scored 1, etc to item 18 | ; 594 more observations, 18 per data line 35,1-18,2, 1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 ; child 35, a girl, scored 1 on items 1-3, 0 on items 4-18

Here is the DIF report:

The reported DIF is against the overall item difficulty. The boys vs. girls DIF size on item 4, tapping pattern 1-3-4, is:

DIF size = Target Contrast Target measure for boys - Target measure for girls = -.4.47 - -4.08 = -.41.

We can see by comparing the observed and expected scores, that the boys scored 15 when 14.8 was expected, and the girls 17 when 17.1 was expected. So the item was .41 logits easier for the boys than for the girls. The Welch t-test for this DIF size is approximately DIFsize / joint standard error: t = -.41 / sqrt(se(boy)² + se(girl)²) = -.41/ sqrt(1.17²+1.11²) = .43/1.61 = -.25 with (boys count - 1 + girls count - 1) = 32 degrees of freedom. P=.80 for a 2-sided t-test. So this is not statistically significant. The hypothesis of "No DIF" is not rejected.

Help for Facets Rasch Measurement Software: www.winsteps.com Author: John Michael Linacre.

 Facets Rasch measurement software \$149. Winsteps Rasch measurement software \$149.

 Forum Rasch Measurement Forum to discuss any Rasch-related topic

Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch
Applying the Rasch Model 2nd. Ed., Bond & Fox (Winsteps) Best Test Design, Wright & Stone Rating Scale Analysis, Wright & Masters
Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes (Facets) Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. (Facets)
Statistical Analyses for Language Testers, Rita Green (Winsteps, Facets) Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement
Winsteps Tutorials Facets Tutorials Rasch Discussion Groups

Coming Rasch-related Events
June 19-21, 2013, Wed.-Fri. SIS 2013 Conference on Advances in Latent Variables: Methods, Models and Applications, Brescia, Italy, meetings.sis-statistica.org/index.php/sis2013/ALV
July 1 - Nov. 30, 2013, Mon.-Sun. Online Course: Introduction to Rasch Measurement Theory (D. Andrich, RUMM), www.education.uwa.edu.au/ppl/courses
July 5 - Aug. 2, 2013, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
July 15, 2013, Monday Application deadline: UIC Educational Research Methodology online graduate certificate program, www.go.uic.edu/OnlineMESA
July 22, 2013, Monday Submission deadline: 2014 AERA Annual Meeting, Philadelphia PA, www.aera.net
Aug.1-5, 2013, Thur.-Mon. TERA-PROMS Annual Meeting, Kaohsiung, Taiwan, tera.education.nsysu.edu.tw
Aug. 9 - Sept. 6, 2013, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Aug. 22, 2013, Thursday. Symposium in honor of Svend Kreiner, Copenhagen, Denmark, biostat.ku.dk/kreinersymposium
Sept. 4-6, 2013, Wed.-Fri. IMEKO TC1-TC7-TC13 Symposium: Measurement Across Physical and Behavioural Sciences, Genoa, Italy, www.imeko-genoa-2013.it
Sept. 13 - Oct. 11, 2013, Fri.-Fri. On-line workshop: Rasch Applications in Clinical Assessment, Survey Research, and Educational Measurement (W.P. Fisher), www.statistics.com
Sept. 18-20, 2013, Wed.-Fri. In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
Sept. 23-25, 2013, Mon.-Wed. In-person workshop: Intermediate Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
Sept. 26-27, 2013, Thurs.-Fri. In-person workshop: Advanced Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
Oct. 18 - Nov. 15, 2013, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Oct. 20 - Oct. 25, 2013, Sun.-Fri. International Association for Educational Assessment (IAEA) 39th Annual Conference, Tel Aviv, Israel, www.iaea-2013.com
Dec. 11-13, 2013, Wed.-Fri. In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
March 12-14, 2014, Wed.-Fri. In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
April 3-7, 2014, Thurs.-Mon. AERA Annual Meeting, Philadelphia PA, www.aera.net
May 14-16, 2014, Wed.-Fri. In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
May 19-21, 2013, Mon.-Wed. In-person workshop: Intermediate Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
July 4 - Aug. 1, 2014, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
Aug. 8 - Sept. 5, 2014, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Sept. 10-12, 2014, Wed.-Fri. In-person workshop: Introductory Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
Sept. 12 - Oct. 10, 2014, Fri.-Fri. On-line workshop: Rasch Applications in Clinical Assessment, Survey Research, and Educational Measurement (W.P. Fisher), www.statistics.com
Sept. 15-17, 2014, Mon.-Wed. In-person workshop: Intermediate Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric
Sept. 18-19, 2014, Thurs.-Fri. In-person workshop: Advanced Rasch (A. Tennant, RUMM), Leeds, UK, www.leeds.ac.uk/medicine/rehabmed/psychometric