Contrast Coding in Two-Factor Analysis of Variance Studies: An Application to Cotton Data

Year 2022, , 229 - 245, 15.06.2022

Demet Çanga , Ercan Efe

https://doi.org/10.31466/kfbd.1016490

Abstract

In this study, how the contrast analysis is performed in a two-way factorial design consisting of contrast estimates containing specific questions determined to investigate the specific differences between averages was examined in detail. For this purpose, after determining the hypotheses to determine the main effects, contrast coefficients suitable for each hypothesis were created and contrast analysis was performed. In the study, some of the data obtained from the cotton trials conducted in the Field Crops Department of the KSU Faculty of Agriculture were used with permission. Cotton varieties, years and interaction effects were evaluated using the R and SPSS 21.0 package programs. With the use of contrast, while performing two-factor analysis, first the main effects were investigated and then the interaction effects were investigated. Among the estimates made with 1 degree of freedom within the main effect A, the contrast estimation showed the greatest effect (rcontrast=0.7901). Later, among the estimates made with 1 degree of freedom within the main effect B, the contrast estimation showed the greatest effect (rcontrast=0.6370). Likewise, when looking at the interaction effects, it is seen that the effect of the contrast estimation (rcontrast=0.4388) shown by the quadratic effect of is more important, that is, the quadratic effect is more important. As a result, this study showed the researchers where the main effects were found when the average differences in factorial designs were analyzed and gave detailed information about their effect sizes.

Keywords

Contrast coding, Factorial ANOVA, Cotton, Comparisons, Means

İki Faktörlü Varyans Analizinde Kontrast Kodlama: Pamuk Verilerine Bir Uygulama

Abstract

Bu çalışmada, ortalamalar arasındaki belirli farklılıkları araştırmak için belirlenen belirli soruları içeren kontrast tahminlerinden oluşan iki yönlü faktöriyel bir tasarımda kontrast analizinin nasıl yapıldığı ayrıntılı olarak incelenmiştir. Bu amaçla temel etkileri belirlemek için hipotezler belirlendikten sonra her bir hipoteze uygun kontrast katsayıları oluşturulmuş ve kontrast analizi yapılmıştır. Araştırmada KSÜ Ziraat Fakültesi Tarla Bitkileri Bölümü'nde yapılan pamuk denemelerinden elde edilen verilerin bir kısmı izin alınarak kullanılmıştır. Pamuk çeşitleri, yılları ve etkileşim etkileri R ve SPSS 21.0 paket programları kullanılarak değerlendirilmiştir. Kontrast kullanımı ile iki faktörlü analiz yapılırken önce ana etkiler, ardından etkileşim etkileri araştırılmıştır. Ana etki A içinde 1 serbestlik derecesi ile yapılan tahminler arasında en büyük etkiyi (rkontrast = 0.7901) kontrast tahmini göstermiştir. Daha sonra; B ana etkisi içerisinde 1 serbestlik derecesi ile yapılan tahminler arasında en büyük etkiyi (rkontrast = 0.6370) kontrast tahmini göstermiştir. Aynı şekilde interaksiyon etkilerine bakıldığında kontrast tahmininin etkisinin (rkontrast = 0.4388) daha önemli yani ikinci dereceden etkinin daha önemli olduğu görülmektedir. Sonuç olarak bu çalışma, faktöriyel tasarımlardaki ortalama farklar analiz edildiğinde ana etkilerin nerelerde bulunduğunu araştırmacılara göstermiş ve etki büyüklükleri hakkında detaylı bilgi vermiştir.

Keywords

Kontrast kodlama, Faktöriyel ANOVA, Pamuk, Karşılaştırmalar, Ortalamalar

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