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Year 2015, Volume: 35 Issue: 1, 123 - 151, 27.01.2015

Şeref Tan

Abstract

In this study, a comparison of beta4 and polynomial loglinear presmoothing methods and the cubic spline postsmoothing method of equipercentile equating with balanced single group design data set for small samples are presented. When the beta4 presmoothing method was applied to Form X and Form Y data, Form X maintained for all the four sample data moments and Form Y maintained for the first 3 sample data moments. According to the chi square statistics beta4 presmoothing method showed good fit with sample data. In the polynomial loglinear presmoothing, presmoothing with second degree polynomial model provided the best data fit for both Form X and FormY. Cubic spline postsmoothing method has provided the most accurate fit for S = .30. As a conclusion, all of the three smoothing methods, used in the study, were effective and relatively beta4 presmoothing method was found the most appropriate method among the three smoothing methods by using both bootstrap standart errors of equating and moment preservation criterion for small samples such as 200-250

Keywords

Beta4 presmoothing Polynomial loglineer presmoothing Cubic postsmoothing Equipercentile equating

References

  • Cui, Z., & Kolen, M. J. (2009). Evaluation of two new smoothing methods in equating, The cubic b-spline presmoothing method and the direct presmoothing method. Journal of Educational Measurement, 46(2), 135–158.
  • de Boor, C. (1978). A practical guide to splines (Applied Mathematical Sciences, Vol. 27). New York, Springer.
  • Fairbank, B. A. (1987). The use of presmoothing and postsmoothing to increase the precision of equipercentile equating. Applied Psychological Measurement, 11, 245–262.
  • Hanson, B. A. (1991). Method of moments estimates for the four-parameter beta compound binomial model and the calculation of classification consistency indexes. Iowa City, IA, ACT. (Research Report 91–5)
  • Hanson, B. A., Zeng, L., & Colton, D. (1994). A comparison of presmoothing and postsmoothing methods in equipercentile equating. Iowa City, IA, ACT. (Research Report 94–4).
  • Holland, P. W., & Thayer, D. T. (1987). Notes on the use of log-linear models for fitting discrete probability distributions. Princeton, NJ, Educational Testing Service. (Technical Report 87–79)
  • Holland, P. W., & Thayer, D. T. (2000). Univariate and bivariate loglinear models for discrete test score distributions. Journal of Educational and Behavioral Statistics, 25, 133–183.
  • http, //www.education.uiowa.edu/centers/casma/computer-programs.
  • Kolen, M. J. (1984). Effectiveness of analytic smoothing in equipercentile equating. Journal of Educational Statistics, 9, 25–44.
  • Kolen M.J., Brennan R.L. (2014). Test Equating, Scaling, and Linking Methods and Practices. (3th edition) New York, NY, Springer.
  • Kolen, M. J. (1991). Smoothing methods for estimating test score distributions. Journal of Educational Measurement, 28, 257–282.
  • Livingston, S. A. (1992). Small-sample equating with loglineer smothing. Princeton, NJ, Educational Testing Service. (Research Report 142).
  • López, F. Olson, A. & Bansal N. (2011). Creating composite age groups to smooth percentile rank distributions of small samples. Journal of Psychoeducational Assessment 29(2) 171–183.
  • Moses, T., & von Davier, A. A. (2006). A SAS macro for loglinear smoothing, Applications and implications. Princeton, NJ, Educational Testing Service. (Research Report 06–05)
  • Moses, T. (2008). An evaluation of statistical strategies for making equating function selections. Princeton, NJ, Educational Testing Service. (Research Report 08–60)
  • Moses, T., Deng, W. & Zhang Y. (2011). Two approaches for using multiple anchors in NEAT equating, A description and demonstration. Applied Psychological Measurement 35(5), 362–379.
  • Moses, T., & Liu, J. (2011). Smoothing and equating methods applied to different types of test score distributions and evaluated with respect to multiple equating criteria. Princeton, NJ, Educational Testing Service. (Research Report 11–20)
  • Reinsch, C. H. (1967). Smoothing by spline functions. Numerische Mathematik, 10, 177–183.
  • Segall, D. O. (1997). Equating the CAT-ASVAB. In W. A. Sands, Computerized adaptive testing, From inquiry to operation (pp. 181 - 198). Washington DC, American Psychological Association.
  • Shin S. (2011). A comparison of Van der Linden's conditional equipercentile equating method with other equating methods under the random groups design. University of Iowa, Dissertation, http, //ir.uiowa.edu/etd/1263 (22 Ocak 2015).
  • Wang, T., & Kolen, M. J. (1996). A quadratic curve equating method to equate the first three moments in equipercentile equating. Applied Psychological Measurement, 20, 27–43.
  • Wang, T. (2006). Standard Errors of Equating for Equipercentile Equating with Log-Linear Pre-Smoothing using the Delta Method. CASMA (Research Report 14).

Küçük Örneklemlerde Beta4 ve Polynomial Loglineer Öndüzgünleştirme ve Kübik Eğri Sondüzgünleştirme Metotlarının Uygunluğu

Year 2015, Volume: 35 Issue: 1, 123 - 151, 27.01.2015

Şeref Tan

Abstract

Bu çalışmada eşit yüzdelikli eşitlemede kullanılan beta4 ve polinominal loglineer öndüzgünleştirme ve kübik eğri sondüzgünleştirme yöntemlerinin uygunluğunun gerçek bir veri seti ve küçük örneklemler için karşılaştırılması sunulmuştur. Form X ve Form Y verilerine beta4 öndüzgünleştirme metodu uygulandığında düzgünleştirilmiş dağılım Form X için tüm dört momenti korumuş ve Form Y için ilk üç momenti korumuştur. Ki kare istatistiğine göre beta4 öndüzgünleştirme metodu deneysel veriye uyum göstermiştir. Polinomial loglineer öndüzgünleştirmede, hem Form X hem de Form Y verileri için ikinci dereceden polinomial loglineer modelle yapılan düzgünleştirme en iyi veri uyumunu sağlamıştır. Kübik eğri sondüzgünleştirme metodu, S=.30 düzeyinde en uygun model uyumunu sağlamıştır. Sonuç olarak, bu çalışmada kullanılan üç düzgünleştirme metodu da etkili bulundu ve hem eşitlemenin ortalama bootstrap standart hatası hem de moment korunumu ölçütü dikkate alındığında 200-250 cıvarı gibi küçük örneklemler için üç düzgünleştirme metodundan beta4 öndüzgünleştirme metodunun kullanımının göreceli olarak daha uygun olduğu bulunmuştur.

Keywords

Beta4 öndüzgünleştirme Polinomial loglineer öndüzgünleştirme Kübik eğri sondüzgünleştirme Eşit yüzdelikli eşitleme

References

  • Cui, Z., & Kolen, M. J. (2009). Evaluation of two new smoothing methods in equating, The cubic b-spline presmoothing method and the direct presmoothing method. Journal of Educational Measurement, 46(2), 135–158.
  • de Boor, C. (1978). A practical guide to splines (Applied Mathematical Sciences, Vol. 27). New York, Springer.
  • Fairbank, B. A. (1987). The use of presmoothing and postsmoothing to increase the precision of equipercentile equating. Applied Psychological Measurement, 11, 245–262.
  • Hanson, B. A. (1991). Method of moments estimates for the four-parameter beta compound binomial model and the calculation of classification consistency indexes. Iowa City, IA, ACT. (Research Report 91–5)
  • Hanson, B. A., Zeng, L., & Colton, D. (1994). A comparison of presmoothing and postsmoothing methods in equipercentile equating. Iowa City, IA, ACT. (Research Report 94–4).
  • Holland, P. W., & Thayer, D. T. (1987). Notes on the use of log-linear models for fitting discrete probability distributions. Princeton, NJ, Educational Testing Service. (Technical Report 87–79)
  • Holland, P. W., & Thayer, D. T. (2000). Univariate and bivariate loglinear models for discrete test score distributions. Journal of Educational and Behavioral Statistics, 25, 133–183.
  • http, //www.education.uiowa.edu/centers/casma/computer-programs.
  • Kolen, M. J. (1984). Effectiveness of analytic smoothing in equipercentile equating. Journal of Educational Statistics, 9, 25–44.
  • Kolen M.J., Brennan R.L. (2014). Test Equating, Scaling, and Linking Methods and Practices. (3th edition) New York, NY, Springer.
  • Kolen, M. J. (1991). Smoothing methods for estimating test score distributions. Journal of Educational Measurement, 28, 257–282.
  • Livingston, S. A. (1992). Small-sample equating with loglineer smothing. Princeton, NJ, Educational Testing Service. (Research Report 142).
  • López, F. Olson, A. & Bansal N. (2011). Creating composite age groups to smooth percentile rank distributions of small samples. Journal of Psychoeducational Assessment 29(2) 171–183.
  • Moses, T., & von Davier, A. A. (2006). A SAS macro for loglinear smoothing, Applications and implications. Princeton, NJ, Educational Testing Service. (Research Report 06–05)
  • Moses, T. (2008). An evaluation of statistical strategies for making equating function selections. Princeton, NJ, Educational Testing Service. (Research Report 08–60)
  • Moses, T., Deng, W. & Zhang Y. (2011). Two approaches for using multiple anchors in NEAT equating, A description and demonstration. Applied Psychological Measurement 35(5), 362–379.
  • Moses, T., & Liu, J. (2011). Smoothing and equating methods applied to different types of test score distributions and evaluated with respect to multiple equating criteria. Princeton, NJ, Educational Testing Service. (Research Report 11–20)
  • Reinsch, C. H. (1967). Smoothing by spline functions. Numerische Mathematik, 10, 177–183.
  • Segall, D. O. (1997). Equating the CAT-ASVAB. In W. A. Sands, Computerized adaptive testing, From inquiry to operation (pp. 181 - 198). Washington DC, American Psychological Association.
  • Shin S. (2011). A comparison of Van der Linden's conditional equipercentile equating method with other equating methods under the random groups design. University of Iowa, Dissertation, http, //ir.uiowa.edu/etd/1263 (22 Ocak 2015).
  • Wang, T., & Kolen, M. J. (1996). A quadratic curve equating method to equate the first three moments in equipercentile equating. Applied Psychological Measurement, 20, 27–43.
  • Wang, T. (2006). Standard Errors of Equating for Equipercentile Equating with Log-Linear Pre-Smoothing using the Delta Method. CASMA (Research Report 14).
There are 22 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Şeref Tan

Publication Date January 27, 2015
Published in Issue Year 2015 Volume: 35 Issue: 1

Cite

APA Tan, Ş. (2015). Küçük Örneklemlerde Beta4 ve Polynomial Loglineer Öndüzgünleştirme ve Kübik Eğri Sondüzgünleştirme Metotlarının Uygunluğu. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi, 35(1), 123-151.
AMA Tan Ş. Küçük Örneklemlerde Beta4 ve Polynomial Loglineer Öndüzgünleştirme ve Kübik Eğri Sondüzgünleştirme Metotlarının Uygunluğu. GEFAD. April 2015;35(1):123-151.
Chicago Tan, Şeref. “Küçük Örneklemlerde Beta4 Ve Polynomial Loglineer Öndüzgünleştirme Ve Kübik Eğri Sondüzgünleştirme Metotlarının Uygunluğu”. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi 35, no. 1 (April 2015): 123-51.
EndNote Tan Ş (April 1, 2015) Küçük Örneklemlerde Beta4 ve Polynomial Loglineer Öndüzgünleştirme ve Kübik Eğri Sondüzgünleştirme Metotlarının Uygunluğu. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi 35 1 123–151.
IEEE Ş. Tan, “Küçük Örneklemlerde Beta4 ve Polynomial Loglineer Öndüzgünleştirme ve Kübik Eğri Sondüzgünleştirme Metotlarının Uygunluğu”, GEFAD, vol. 35, no. 1, pp. 123–151, 2015.
ISNAD Tan, Şeref. “Küçük Örneklemlerde Beta4 Ve Polynomial Loglineer Öndüzgünleştirme Ve Kübik Eğri Sondüzgünleştirme Metotlarının Uygunluğu”. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi 35/1 (April 2015), 123-151.
JAMA Tan Ş. Küçük Örneklemlerde Beta4 ve Polynomial Loglineer Öndüzgünleştirme ve Kübik Eğri Sondüzgünleştirme Metotlarının Uygunluğu. GEFAD. 2015;35:123–151.
MLA Tan, Şeref. “Küçük Örneklemlerde Beta4 Ve Polynomial Loglineer Öndüzgünleştirme Ve Kübik Eğri Sondüzgünleştirme Metotlarının Uygunluğu”. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi, vol. 35, no. 1, 2015, pp. 123-51.
Vancouver Tan Ş. Küçük Örneklemlerde Beta4 ve Polynomial Loglineer Öndüzgünleştirme ve Kübik Eğri Sondüzgünleştirme Metotlarının Uygunluğu. GEFAD. 2015;35(1):123-51.