Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
Küçük Örneklem Büyüklüğüne Sahip 2x2 Çapraz Tablolar İçin Ki-Kare Yöntemlerinin Karşılaştırılması: Bir Simülasyon Çalışması
Comparison of Chi-Square Methods for 2x2 Crosstabs with Small Sample Size: A Simulation Study
İsmet DOĞANa , Nurhan DOĞANa
aAfyonkarahisar Sağlık Bilimleri Üniversitesi Tıp Fakültesi, Biyoistatistik ve Tıbbi Bilişim AD, Afyonkarahisar, Türkiye
Turkiye Klinikleri J Biostat. 2024;16(2):71-83
doi: 10.5336/biostatic.2023-100817
Article Language: TR
Full Text
ÖZET
 Amaç: Bu çalışmanın amacı, 2x2 çapraz tablolarda kullanılan klasik ve süreklilik düzeltmeli ki-kare testlerini tanıtmak ve bunları karşılaştırmaktır. Gereç ve Yöntemler: Çalışmada serbestlik derecesi 1 (bir) olan ki-kare testleri dikkate alınmıştır. Çünkü bu testler, verilerin kesikli olmasından ciddi şekilde etkilenmektedir. Python-random kütüphanesi kullanılarak 10 ≤ n ≤25 aralığında yer alan 4 farklı n değeri için veri türetilmiştir. Verilerin türetilmesinde önce a,b,c ve d ile gösterilen gözelerden hangisine değer atanacağı sonra da ilgili gözeye atanacak değer belirlenmiştir. n=10 için 246, n=15 için 756, n=20 için 958, n=25 için 963 farklı veri seti çalışmada kullanılmıştır. Yöntemlerin karşılaştırılmasında hem her bir yöntemin hipotetik H0 hipotezini farklı örneklem büyüklüğü ve önemlilik düzeyleri için reddetme yüzdeleri hem de yöntemlerin birbirlerine göre hipotetik H0 hipotezini ret/ret, ret/kabul, kabul/ret ve kabul/kabul oranları kullanılmıştır. Bulgular: Çalışmada dikkate alınan yöntemlere ait sonuçlar, yöntemlerden birinin önerilen tüm yöntemler içerisinde en iyi yöntem olarak seçilmesini sağlamamaktadır. Farklı yöntemler farklı örneklem büyüklüklerinde ve önemlilik düzeylerinde öne çıkmaktadır. Bu durum, bir araştırmadan elde edilecek sonucunun doğru şekilde yorumlanamayacağı anlamına gelir. Tüm yöntemlerin örneklem büyüklüğü ve önemlilik düzeyinden etkilendiği, örneklem büyüklüğünün artması ve önemlilik düzeyinin de 0,01'den 0,10'a doğru değişmesi durumunda H0 hipotezinin reddedilme oranlarının da arttığı belirlenmiştir. Sonuç: Kikare testinin büyük örneklemler için uygun olduğu, beklenen değerlerden en az birinin 5'ten küçük olması durumunda gerek klasik gerekse süreklilik düzeltmeli ki-kare yöntemlerinin kullanılmaması gerektiği sonucuna ulaşılmıştır.

Anahtar Kelimeler: Hipotez testi; ki-kare testi; 2x2 çapraz tablo; süreklilik düzeltmesi
ABSTRACT
 Objective: The aim of this study is to introduce and compare the classical and continuity corrected chi-square tests used in 2x2 contingency tables. Material and Methods: Chi-square tests with 1 (one) degree of freedom were taken into consideration in the study. Because these tests are seriously affected by the discontinuity of the data. Using the Python-random library, data was derived for 4 different values in the range of 10 ≤ n ≤25. In deriving the data, first the value to be assigned to the cells indicated by a, b, c and d was determined, and then the value to be assigned to the relevant cell was determined. 246 different data sets for n=10, 756 for n=15, 958 for n=20, and 963 for n=25 were used in the study. In the comparison of the methods, both the rejection percentages of each method for the hypothetical H0 hypothesis for different sample sizes and significance levels, and the rejection/rejection, rejection/acception, acception/rejection and acception/acception rates of the hypothetical H0 hypothesis of the methods relative to each other were used. Results: The results of the methods considered in the study do not enable one of the methods to be chosen as the best method among all the proposed methods. Different methods stand out at different sample sizes and significance levels. This means that the result of a study cannot be interpreted correctly. It has been determined that all methods are affected by the sample size and significance level, and if the sample size increases and the significance level changes from 0.01 to 0.10, the rejection rates of the H0 hypothesis also increase. Conclusion: It was concluded that the chi-square test is suitable for large samples, and if at least one of the expected values is less than 5, both the classical and continuity corrected chi-square methods should not be used.

Keywords: Hypothesis test; chi-square test; 2x2 contingency table; continuity correction
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