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

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.

Anahtar Kelimeler:

Beta4 öndüzgünleştirme, Polinomial loglineer öndüzgünleştirme, Kübik eğri sondüzgünleştirme, Eşit yüzdelikli eşitleme

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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,

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