PISA 2012 Matematik Okuryazarlığı Testinde Farklı Ölçek Dönüştürme Yöntemlerinin Karşılaştırılması

Year 2018, Issue: 46, 121 - 148, 19.04.2018

Şeyma Uyar , Burcu Aksekioğlu , Neşe Öztürk Gübeş

https://doi.org/10.21764/maeuefd.330613

Abstract

Bu çalışmada farklı ölçek
dönüştürme yöntemlerini PISA 2012 matematik okuryazarlığı verileri üzerinde
karşılaştırmak amaçlanmıştır. Bu amaçla seçilen iki kitapçıktan elde edilen
puanlar madde tepki kuramına dayalı ölçek dönüştürme (ortalama-ortalama,
ortalama-standart sapma, Stocking-Lord, Haebara) ve test eşitleme yöntemleri
(MTK gerçek-puan eşitleme, MTK gözlenen-puan eşitleme) kullanılarak eşitlenmiş
ve farklı yöntemlerden elde edilen sonuçlar incelenmiştir. Çalışma, 4 ve 11
numaralı kitapçıklardaki matematik testlerine verilen cevaplar kullanılarak
yürütülmüştür. Bu nedenle araştırmanın çalışma grubunu Türkiye örnekleminde 4
numaralı kitapçığı cevaplayan 348 ve 11 numaralı kitapçığı cevaplayan 368 olmak
üzere toplam 716 öğrenci oluşturmaktadır. Çalışmada test eşitleme için “denk
olmayan gruplarda ortak madde deseni” kullanılmıştır. Verilerin analizinin ilk
aşamasında madde tepki kuramının tek boyutluluk varsayımı test edilmiştir.
Ardından PARSCALE 4.1 programı ile madde ve yetenek parametreleri
kestirilmiştir. Parametre kestiriminde iki-parametreli lojistik model ve
genelleştirilmiş kısmi kredi modeli kullanılmıştır. Daha sonra STUIRT programı
ile dört farklı yöntem kullanılarak ölçek dönüştürme işlemi yapılmıştır. Son
aşamada ise her iki formdan elde edilen test puanları POLYEQUATE programı ile
eşitlenmiştir. Farklı yöntemlerden elde edilen hata miktarları ise
ağırlıklandırılmış hata kareleri ortalaması (WMSE) ile hesaplanmıştır. Çalışma
sonucunda, en az hata miktarına sahip yöntemin gerçek-puan eşitlemede
Stocking-Lord, gözlenen-puan eşitlemede ise Haebara yönteminin olduğu
bulunmuştur. En yüksek eşitleme hatasını ise ortalama-standart sapma yönteminin
verdiği tespit edilmiştir. 

Keywords

test eşitleme, karma test, ölçek dönüştürme yöntemleri, eşitleme hatası

Comparison of Different Scale Linking Methods in PISA 2012 Mathematics Literacy Test

Abstract

In this study, the
objective was to compare different scale linking methods over the PISA 2012
mathematics literacy data. For this purpose, scores obtained from two selected
booklets were equated using scale linking (mean-mean, mean-sigma,
Stocking-Lord, Haebara) and test equating methods (IRT true-score equating, IRT
observed-score equating) based on the item response theory, and results
obtained from different methods were analyzed. The study was conducted using
answers given to mathematics tests in booklet-4 and booklet-11. Therefore, the
sample consists of 716 students in Turkey; 348 of these participants are the
takers of booklet-4, 368 of them are the takers of booklet-11. In order to equate test forms “the common-item
nonequivalent groups” design was used in this research. In the first
stage of data analysis, unidimensionality assumption of the item response
theory was analysed. Then PARSCALE
4.1 was used to estimate item and ability parameters. Generalized partial
credit and two-parameter logistic model were used to estimate parameters.
Afterwards STUIRT program was used
for scale linking for four different methods. In the last step
test scores obtained from different forms were equated by using POLYEQUATE
program. Equating error obtained from different methods calculated with
weighted mean squares error (WMSE) index. Results
showed that Stocking-Lord method had the smallest equating error
in true-score equating and Haebara method had the smallest equating error in
observed-score equating. The amount of maximum error has been established that
of the mean-sigma method.

Keywords

test equating, mixed test, scale linking methods, equating error

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