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

Year 2022, Volume: 12 Issue: 1, 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

References

• Abdi, H., Edelman, B., Valentin, D., and Dowling, W.J. (2009). Experimental Design and Analysis for Psychology. New York, USA, Oxford: Oxford University Press.
• Abelson, R. P., and Prentice, D. A. (1997). Contrast tests of interaction hypothesis. Psychological Methods, 2(4), 315–328. https://doi.org/10.1037/1082-989X.2.4.315
• Bek, Y., and Efe, E. (1988). Araştırma ve Deneme Metodları I. Ç.Ü. Ziraat Fakültesi Ders Kitabı No: 71, Ç.Ü Ziraat Fakültesi Ofset ve Teksir Atölyesi, Adana, 395 s.
• Bird, K.D. (2002). Confidence intervals for effect sizes in analysis of variance. Educational and Psychological Measurement, 62,197-226. https://doi.org/10.1177/0013164402062002001
• Cohen, J., Cohen, P., West, S.G., and Aiken, L.S. (2013). Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences. Oxford: Routledge.
• Çanga, D., Efe, C. (2017). Using Contrasts in One-Way Analysis of Variance with Control Groups and an Application. Journal of Agricultural Science and Technology A: David Publishing: 474-478. USA. https://doi.org/10.17265/2161-6256/2017.07.003
• Çanga, D. (2018). Use of Contrast in the Comparison of the Means (Ph.D Thesis) Kahramanmaraş Sütçü Imam University, The Institute of Natural Sciences, Kahramanmaraş, Turkey.
• Çanga, D., Yenipınar, A., Karaokur, Ö., Önem, A., and Efe, E. (2019). Contrast Analysis on Single Factorial Studies and Solution with SPSS. Black Sea Journal of Engineering and Science, 2(1), 1-6. https://dergipark.org.tr/tr/pub/bsengineering/issue/42084/469694
• Çelik, Ş., and Yılmaz, F.C.O. (2015). Investigation by Different Orthogonal Methods of Body Sizes of Turkish Spotted Horses According to Age Group. COMU Journal of Agriculture Faculty, 3(1), 81-87.
• Darlington, R. B., and Hayes, A.F. (2016). Regression Analysis and Linear Models: Concepts, Applications, and Implementation. New York: Guilford Publications.
• Dubcowsky, J. (2015). Orthogonal Contrasts. Retrieved from http://www.plantsciences.ucdavis.edu/agr205/ , (Accessed date:14.10.2021).
• Efe, E., and Çanga, D. (2017). Sub-group Contrast Analysis in Single Factor Studies and Application to Cotton Data. KSU Journal of Agriculture and Nature, 20, 154-159. https://doi.org/10.18016/ksudobil.349183
• Efe, E., Bek, Y., and Şahin, M. (2000). SPSS’te Çözümleri ile İstatistik Yöntemler II. Kahramanmaraş Sütçü İmam Üniversitesi Rektörlüğü Yayın No: 73, Ders Kitapları, Yayın No:9, K.S.Ü.
• Efe, L., Killi, F., and Mustafayev, S.A. (2004). Performance evaluation of some earlier yielding mutant cotton (Gossypium spp.) varieties in the East Mediterranean Region of Turkey. Pakistan Journal of Biological Sciences 7(5): 689-697. https://doi.org/10.3923/pjbs.2004.689.697
• Howell, D.C. (2016). Contrasts on Means in R. Retrieved from https://www.uvm.edu/~dhowell/StatPages/R/ContrastsInR.html, (Accessed date:14.10.2021)
• Haans, A. (2018). Contrast Analysis: A Tutorial. Practical Assessment, Research & Evaluation, 23(9). Available online: http://pareonline.net/getvn.asp?v=23&n=9, https://doi.org/10.7275/7dey-zd62
• Karpinski, A. (2006a). Chapter 5 Contrasts for one-way ANOVA. Retrieved from https://marekrychlik.com/sites/default/files/05_contrasts1.pdf, (Accessed date:14.10.2021)
• Karpinski, A. (2006b). Chapter 6 Planned Contrasts and Post-hoc Tests for one-way ANOVA, Retrieved from http://pirun.ku.ac.th/~faasatp/734462/data/06_contrasts2.pdf, (Accessed date:14.10.2021)
• Karpinski, A. (2006c). Chapter 7 Factorial ANOVA: Two-way ANOVA. http://moderngraphics11.pbworks.com/w/file/fetch/36076148/07_Factorial1.pdf , (Accessed date:14.10.2021)
• Keppel, G.,and Wickens, T.D. (2004). Design and Analysis Chapter 13: The Analysis of Interaction Comparisons. http://www.skidmore.edu/~hfoley/Handouts/K.Ch13.notes.pdf,(Accessed date:14.10.2021)
• Keppel, G. (1973). Design and analysis: A researchers' handbook. Englewood Cliffs, NJ: Prentice-Hall.
• Logan, M. (2010). Factorial ANOVA. Biostatistical Design and Analysis Using R (pp. 313–359). https://doi.org/10.1002/9781444319620.ch12
• Özdamar, K. (1999). Package programs and statistical data analysis. Eskişehir: Nisan Kitabevi.
• R Development Core Team (2021). R: A Language and Environment for Statistical Computing. Vienna, Austria: the R Foundation for Statistical Computing. ISBN: 3-900051-07-0. Available online at http://www.R-project.org/.
• Rosenthal, R., Rosnow, R.L., and Rubin D.B. (1999). Contrasts and effect sizes in behavioral research. Cambridge, England: Cambridge University Press.
• Rosenthal, R., and Rosnow, R. (1985). Contrast analysis: Focused comparisons in the analysis of variance. Cambridge, England: Cambridge University Press.
• Rosnow, R.L., Rosenthal, R., and Donald, B.R. (2000). Contrasts and correlations in effect-size estimation. Psychological Science 11(6), 446-453. https://doi.org/ 10.1111/1467-9280.00287
• Rosnow, R.L., and Rosenthal, R. (1996). Contrasts and interactions redux: Five easy pieces. Psychological Science, 7, 253-257. https://doi.org/10.1111/j.1467-9280.1996.tb00369.x
• Shavelson, R.J. (2016). Statistical reasoning for the behavioral sciences. (N. Güler, Trans.). Pegema: Ankara. (Original work published 1988).
• Thompson, B. (1990). Planned versus Unplanned and Orthogonal versus Nonorthogonal Contrasts: The Neo-Classical Perspective. The Annual Meeting of the American Educational Research Association, Roston, MA. p.49.
• Wiens, S., Nilsson, and M.E. (2017). Performing contrast analysis in factorial designs: From NHST to confidence intervals and beyond. Educational and Psychological Measurement, 77(4), 690-715. https://doi.org/10.1177/0013164416668950
• Zieffler, A.S., Harring, J.R., and Long, J.D. (2011). Comparing groups: Randomization and bootstrap methods using R : John Wiley & Sons. https://doi.org/10.1002/9781118063682