Ahn, K., C. Haynes, W. Kim, R. St. Fleur, D. Gordon, and S. J.
Finch. 2007. The effects of SNP genotyping errors on the
power of the cochran-armitage linear trend test for
case/control association studies. Annals of Human Genetics,
71(2):249–261. http://doi.org/10.1111/j.1469-
1809.2006.00318.x
Akgun, I., M. Tosun, K. Haliloglu, M. Aydin. 2011.
Development of autotetraploid perennial rye (Secale
montanum Guss.) and selection for seed set, Turk J Field
Crops, 16(1): 23-28.
Armitage P. 1955. Tests for linear trends in proportions and
frequencies. Biometrics; 11:375–386.
Banks, K. E., D. H. Hunter and D. J. Wachal. 2005. Diazinon in
surface waters before and after a federally-mandated ban.
Science of the Total Environment, 350(1-3):86–93.
http://doi.org/10.1016/j.scitotenv.2005.01.017
Chapman D.G. and J. Nam. 1968. Asymptotic power of chisquare
tests for linear trends in proportions. Biometrics;
24:317–327.
CochranW.G. 1954. Some methods for strengthening common
the tests. Biometrics; 10:417–451.
Cuming Semizer D., F. Altan, H. Akdemir, M. Tosun, A. Gurel
and B. Tanyolac. 2015. Qtl analysis of fiber color and fiber
quality in naturally green colored cotton (Gossypium
hirsutum L.), Turk J Field Crops, 20(1), 49-58
Hintze, J. PASS 11. [Chapter 255 Cochran-Armitage Test for
Trend in Proportions] Kaysville, Utah, USA: NCSS, LLC;
2011:2-5: 595:1-7
Kang, S. H., and J. W. Lee. 2007. The size of the CochranArmitage
trend test in 2 ?? C contingency tables. Journal of
Statistical Planning and Inference, 137(6):1851–1861.
http://doi.org/10.1016/j.jspi.2006.03.009
Lachin, J. M. 2011. Power and sample size evaluation for the
Cochran-Mantel-Haenszel mean score (Wilcoxon rank sum)
test and the Cochran-Armitage test for trend. Statistics in
Medicine, 30(25):3057–3066.http://doi.org/10.1002/sim.4330
Mehta, C. R., N. R.Patel, P. Senchaudhuri and N. Dec. 2007.
Exact Power and Sample-Size Computations for the
Cochran-Armitage Trend Test SHORTER
COMMUNICATIONS EDITOR : Exact Power and SampleSize
Computations for the Cochran-Armitage Trend Test,
54(4):1615–1621.
Mortazavian S. M. M. and S. Azizi-Nia. 2014. Nonparametric
Stability Analysis In Multi-Environment Trial Of Canola,
Turk J Field Crops, 19(1):108-117
Nam J. A. 1987. Simple approximation for calculating sample
sizes for detecting linear trend in proportions. Biometrics;
43:701–705.
Shen, H., Y. Hu, Y. Chen and T. Tung. 2014. Prevalence and
Associated Metabolic Factors of Gallstone Disease in the
Elderly Agricultural and Fishing Population of Taiwan.
Slager S.L. and D.J. Schaid. 2001. Case-Control Studies Of
Genetic Markers: Power And Sample Size Approximation
For Armitage’s Test Of Trend. Human Heredity; 52:149–
153. DOI: 10.1159/000053370.
Tekindal M.A., H. Bayrak, B. Ozkaya, Y. Yavuz. 2014. Secondorder
response surface method: factorial experiments an
alternative method in the field of agronomy, Turk J Field
Crops, 19(1):35-45
Yol E., F. Seymus and B. Uzun. 2013. Genetic Control Of
Purple Plant Color In Sesame, Turk J Field Crops, 18(2),
229-232
Zheng, G., and J.L. Gastwirth. 2006. On estimation of the
variance in Cochran-Armitage trend tests for genetic
association using case-control studies. Statistics in Medicine,
25(18):3150–3159. http://doi.org/10.1002/sim.2250
THE COCHRAN-ARMITAGE TEST TO ESTIMATE THE SAMPLE SIZE FOR TREND OF PROPORTIONS FOR BIOLOGICAL DATA
The biological activity of a substance can be investigated through a series of experiments done with the
increased or decreased dosage of it. One of the purposes of such studies is to determine the trend of responses
based on dosage. In studies carried out for this purpose, appropriate sample size has an indisputable influence
on the reliability of the decisions to be made at the end of the study. There are various statistical methods for
determining the trend of proportions. One of them is the Cochran-Armitage test. In a categorical data
analysis, the trend between two variables with k categories can be determined through the Cochran-Armitage
test. This study aims to explore the sample size calculation method developed by Nam J. (1987) for the
Cochran-Armitage test. The power of the test was investigated in different numbers of categories and in
different sample sizes for each category when the least biologically significant differences changed as Type I
error was taken as 0.05. To this end, the study examined the results obtained by making 10000 repetitions for
each case through the Monte Carlo simulation method. When the least biologically significant differences
change at the end of simulation studies, the power of test highly varies in different combinations. When the
number of categories is 2, determination of trend requires working with very large samples. When the number
of categories is 3 or 4, the desired power can be obtained with smaller samples compared to the case where the
number of categories is 2. When the number of categories is over 4, a substantial increase is needed in sample
size to obtain the desired power. Change in marginal frequencies does not have much influence on sample size.
Ahn, K., C. Haynes, W. Kim, R. St. Fleur, D. Gordon, and S. J.
Finch. 2007. The effects of SNP genotyping errors on the
power of the cochran-armitage linear trend test for
case/control association studies. Annals of Human Genetics,
71(2):249–261. http://doi.org/10.1111/j.1469-
1809.2006.00318.x
Akgun, I., M. Tosun, K. Haliloglu, M. Aydin. 2011.
Development of autotetraploid perennial rye (Secale
montanum Guss.) and selection for seed set, Turk J Field
Crops, 16(1): 23-28.
Armitage P. 1955. Tests for linear trends in proportions and
frequencies. Biometrics; 11:375–386.
Banks, K. E., D. H. Hunter and D. J. Wachal. 2005. Diazinon in
surface waters before and after a federally-mandated ban.
Science of the Total Environment, 350(1-3):86–93.
http://doi.org/10.1016/j.scitotenv.2005.01.017
Chapman D.G. and J. Nam. 1968. Asymptotic power of chisquare
tests for linear trends in proportions. Biometrics;
24:317–327.
CochranW.G. 1954. Some methods for strengthening common
the tests. Biometrics; 10:417–451.
Cuming Semizer D., F. Altan, H. Akdemir, M. Tosun, A. Gurel
and B. Tanyolac. 2015. Qtl analysis of fiber color and fiber
quality in naturally green colored cotton (Gossypium
hirsutum L.), Turk J Field Crops, 20(1), 49-58
Hintze, J. PASS 11. [Chapter 255 Cochran-Armitage Test for
Trend in Proportions] Kaysville, Utah, USA: NCSS, LLC;
2011:2-5: 595:1-7
Kang, S. H., and J. W. Lee. 2007. The size of the CochranArmitage
trend test in 2 ?? C contingency tables. Journal of
Statistical Planning and Inference, 137(6):1851–1861.
http://doi.org/10.1016/j.jspi.2006.03.009
Lachin, J. M. 2011. Power and sample size evaluation for the
Cochran-Mantel-Haenszel mean score (Wilcoxon rank sum)
test and the Cochran-Armitage test for trend. Statistics in
Medicine, 30(25):3057–3066.http://doi.org/10.1002/sim.4330
Mehta, C. R., N. R.Patel, P. Senchaudhuri and N. Dec. 2007.
Exact Power and Sample-Size Computations for the
Cochran-Armitage Trend Test SHORTER
COMMUNICATIONS EDITOR : Exact Power and SampleSize
Computations for the Cochran-Armitage Trend Test,
54(4):1615–1621.
Mortazavian S. M. M. and S. Azizi-Nia. 2014. Nonparametric
Stability Analysis In Multi-Environment Trial Of Canola,
Turk J Field Crops, 19(1):108-117
Nam J. A. 1987. Simple approximation for calculating sample
sizes for detecting linear trend in proportions. Biometrics;
43:701–705.
Shen, H., Y. Hu, Y. Chen and T. Tung. 2014. Prevalence and
Associated Metabolic Factors of Gallstone Disease in the
Elderly Agricultural and Fishing Population of Taiwan.
Slager S.L. and D.J. Schaid. 2001. Case-Control Studies Of
Genetic Markers: Power And Sample Size Approximation
For Armitage’s Test Of Trend. Human Heredity; 52:149–
153. DOI: 10.1159/000053370.
Tekindal M.A., H. Bayrak, B. Ozkaya, Y. Yavuz. 2014. Secondorder
response surface method: factorial experiments an
alternative method in the field of agronomy, Turk J Field
Crops, 19(1):35-45
Yol E., F. Seymus and B. Uzun. 2013. Genetic Control Of
Purple Plant Color In Sesame, Turk J Field Crops, 18(2),
229-232
Zheng, G., and J.L. Gastwirth. 2006. On estimation of the
variance in Cochran-Armitage trend tests for genetic
association using case-control studies. Statistics in Medicine,
25(18):3150–3159. http://doi.org/10.1002/sim.2250
Tekındal, M. A., Gullu, O., Yazıcı, A. C., Yavuz, Y. (2016). THE COCHRAN-ARMITAGE TEST TO ESTIMATE THE SAMPLE SIZE FOR TREND OF PROPORTIONS FOR BIOLOGICAL DATA. Turkish Journal Of Field Crops, 21(2), 286-297. https://doi.org/10.17557/tjfc.33765
Turkish Journal of Field Crops is published by the Society of Field Crops Science and issued twice a year. Owner : Prof. Dr. Behçet KIR Ege University, Faculty of Agriculture,Department of Field Crops Editor in Chief : Prof. Dr. Emre ILKER Address : 848 sok. 2. Beyler İşhanı No:72, Kat:3 D.313 35000 Konak-Izmir, TURKEY Email : turkishjournaloffieldcrops@gmail.com contact@field-crops.org Tel : +90 232 3112679 Tel/Fax : : +90 232 3432474