pyequate

pyequate is an open-source package containing different test score equating methods in one location. It includes methods for random groups, common-item/non-equivalent groups, and IRT equating. The version on GitHub will be the most current, with updates pushed to pyPI.

A User Guide is available here.

Areas Currently Under Development

• Standard errors of equating for common-item/non-equivalent groups methods
• pre- and post-smoothing for equipercentile equating

Required Packages

pyequate requires NumPy, Pandas, SciPy, and Statsmodels.

Public Datasets

A number of publicly available datasets are included within this GitHub page to allow testing of functions.

ACTmath

• ACT Mathematics Test Scores
• score distributions of two form of the ACT math test, as presented in table 2.5 of Test Equating, Scaling, and Linking (Kolen and Brennan, 2004; p. 50)
• These data are also provided with the equating software RAGE from the University of Iowa (https://education.uiowa.edu/casma/computer-programs) as well as in the Equate package in R

ADMneatX and ADMneatY

• Contains item-level scores from 2000 examinees on the verbal subscale of an admissions test (Gonzales and Wiberg, 2017)
• First 40 columns: anchor items
• Remaining 80 columns: items unique to each form

CBdatax1y2 and CBdatax2y1

• Data from small field study from international testing program (Von Davier et al., 2004)
• Two different tests: X (75 items) and Y (76 items)
• independent, random samples from single population took each form
• X1Y2: students took form X first, then form Y
• X2Y1: students took form Y first, then form X
• Also contained in the SNSequate package in R

KBneatx and KBneaty

• Contains scores for two forms (x and y) of a 36-item test using nonequivalent groups with anchor items. The 12 anchor items are internal. Examples using this dataset can be seen in Test Equating, Scaling, and Linking (Kolen and Brennan, 2004)
• These data are also provided with the CIPE software from the University of Iowa (https://education.uiowa.edu/casma) as well as in the Equate package in R

Math20EG

• Raw sample frequencies of number-correct scores for two parallel 20-item mathematics tests given to two samples from a national population (Holland and Thayer, 1989; Von Davier et al., 2004)
• Also contained in the SNSequate package in R

Math20SG

• Bivariate sample frequencies of number-correct scores for two parallel 20-item mathematics tests given to a single sample from a national population (Holland and Thayer, 1989; Von Davier et al., 2004)
• Also contained in the SNSequate package in R

PISA

• The following four datasets come from the 2009 PISA administration (Programme for International Student Assessment)
• Available online at www.oecd.org
• Also available in the Equate package in R

PISAbooklets

• Description of 13 general cognitive assessment booklets
• Variables:
  • bookid: unique test booklet ID
  • clusterid: cluster or subset ID in which item placed; items fully nested within clusters. Each item cluster is present in four different booklets.
  • itemid: unique item ID
  • order: order in which cluster appears in a booklet

PISAitems

• Description of items
• Variables:
  • itemid: unique item ID
  • clusterid: cluster or subset ID in which item placed
  • max: maximum possible score; values of 1 (dichotomous) or 2 are possible
  • subject: item subject; first character in itemid and clusterid
  • format: item format; mc = multiple choice; cmc = complex multiple choice; ocr = open constructed response; ccr = closed constructed response
  • noptions: number of options; 0 except for some mc items

PISAstudents

• Contains item response data for 189 items in general cognitive assessment, across 165 schools and 13 different test booklets for 5233 students
• Variables:
  • stidstd: unique student ID
  • schoolid: unique school ID
  • bookid: unique test booklet ID
  • langn: Spoken language at home; English = 313; Spanish = 156; Other = 859.
  • m033q01 to s527q04t: scored item-response data
  • pv1math to pv5read5: scale scores

PISA.RData

• 13 separate data frames (one per booklet)
• Columns correspond to student total scores on each cluster of the booklet

Sources

Gonzalez, J. and Wiberg, M. (2017) Applying Test Equating Methods Using R. Springer Cham. https://doi.org/10.1007/978-3-319-51824-4

Holland, P. and Thayer, D. (1989). The kernel method of equating score distributions. (Technical Report No 89-84). Princeton, NJ: Educational Testing Service.

Kolen, M. J., and Brennan, R. L. (2004). Test Equating, Scaling, and Linking. (2nd ed.), New York: Springer.

Von Davier, A., Holland, P., and Thayer, D. (2004). The Kernel Method of Test Equating. New York, NY: Springer-Verlag.