The Effect of Sample Size on Full MIRT Equating under Random Group Design

Year 2024, Issue: 71, 53 - 82, 31.07.2024

Burcu Demiröz Nuri Doğan

https://doi.org/10.21764/maeuefd.1361350

Abstract

The purpose of this study is to determine the effect of different sample size levels on the Full MIRT observed score equating method under the random group design contingent upon the number of items present in the dimensions. The study utilized simulated data sets generated under the random group design condition. To examine a wide range of sample size, the sample size (N) was incremented by 500 from 500 to 8,000. The standard error of equating (SEE), bias (BIAS), and root mean square error (RMSE) values of equating were examined for 16 sample size levels and 3 different numbers of items in dimensions. According to the results of the study, SEE and RMSE values increase towards outlier values. BIAS values are negative for scores below the mean raw score and positive for scores above the mean raw score. It was observed that as the sample size increases, SEE, BIAS and RMSE values decrease. When the sample sizes are 4000 or above, there is no significant change in error values. The study concluded that sample size of 4000 is sufficient under the item number condition in the dimensions for the Full MIRT observed score equating method under the random group design.

Keywords

test equating, error, sample size, mirt, full MIRT observed score equating

RANDOM GRUP DESENİ ALTINDA TAM MIRT EŞİTLEMEDE ÖRNEKLEM BÜYÜKLÜĞÜNÜN ETKİSİ

Abstract

Bu çalışmanın amacı random grup deseni altında Tam ÇB-MTK gözlenen puan eşitleme yönteminin doğruluğu üzerinde farklı örneklem büyüklüğü düzeylerinin etkisini boyutlarda yer alan madde sayısı koşulu altında belirlemektir. Çalışmada random grup deseni altında üretilen simülasyon veri setlerinden yararlanılmıştır. Geniş bir örneklem büyüklüğü aralığını incelemek için, örneklem büyüklüğü (N) 500’den 8.000'e kadar 500’er arttırılmıştır. 16 örneklem büyüklüğü düzeyi ve boyutlarda yer alan 3 farklı madde sayısı koşulu için eşitlemenin standart hatası (SEE), yanlılık (BIAS) ve hata kareler ortalamasının karekökü (RMSE) değerleri incelenmiştir. Araştırmanın sonuçlarına göre SEE ve RMSE değerleri uç değerlere doğru artmaktadır. BIAS değerleri, ortalama ham puanın altındaki puanlar için negatif, üstündeki puanlar için ise pozitiftir. Örneklem büyüklüğü arttıkça SEE, BIAS ve RMSE değerlerinin azaldığı gözlenmiştir. Örneklem büyüklüğü 4000 ve üzerinde olduğunda hata değerlerinde önemli değişim gözlenmemektedir. Random grup deseni altında Tam ÇB-MTK gözlenen puan eşitleme yöntemi için boyutlarda yer alan madde sayısı koşulu altında 4000 örneklem büyüklüğünün yeterli olduğu sonucuna ulaşılmıştır.

Keywords

Test eşitleme, hata, örneklem büyüklüğü, çok boyutlu madde tepki kuramı, tam ÇB-MTK gözlenen puan eşitleme

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