Research Article
Year 2022,
Volume: 9 Issue: 4, 367 - 377, 31.12.2022
Abstract
References
- Akdur, H. T. K., Ozonur, D., Gul, H. H., & Bayrak, H. (2019). Comparison of rank-based tests for ordered alternative hypotheses in randomized complete block designs. Gazi University Journal of Science, 32(2), 705-716.
- Akdur, H. T. K. (2020). Comparison of non-parametric tests of ordered alternatives for repeated measures in randomized blocks. Communications in Statistics - Simulation and Computation, 51(7), 4146-4158. doi:10.1080/03610918.2020.1740262
- Aslan, E., Koskan, O., & Altay, Y. (2021). Determination of the Sample Size on Different Independent K Group Comparisons by Power Analysis. Turkish Journal of Agricultural Research, 8(1), 34-41. doi:10.19159/tutad.792694
- Best, D. J., & Rayner, J. C. W. (2015). An alternative to page’s test permitting both tied and missing data. Journal of Statistical Theory and Practice, 9(3), 524-536. doi:10.1080/15598608.2014.940098
- Dmitrienko, A., Chuang-Stein, C., & D'Agostino Sr, R. B. (2007). Pharmaceutical statistics using SAS: a practical guide. SAS Institute.
- Hollander, M. (1967). Rank tests for randomized blocks when the alternatives have an a priori ordering. Annals of the Institute of Statistical Mathematics, 38(3), 867-877. doi:10.1214/aoms/1177698880
- Kendall, M. G. (1938). A new measure of rank correlation. Biometrika, 30(1/2), 81-93. doi:10.2307/2332226
- Page, E. B. (1963). Ordered hypotheses for multiple treatments: a significance test for linear ranks. Journal of the American Statistical Association, 58(301), 216-230. doi:10.1080/01621459.1963.10500843
- Shan, G., Young, D., & Kang, L. (2014). A new powerful nonparametric rank test for ordered alternative problem. PloS one, 9(11), e112924. doi:10.1371/journal.pone.0112924
- Serdar, C. C., Cihan, M., Yücel, D., & Serdar, M. A. (2021). Sample size, power and effect size revisited: simplified and practical approaches in pre-clinical, clinical and laboratory studies. Biochemia Medica, 31(1), 27-53. doi:10.11613/bm.2021.010502
- Skillings, J. H., & Wolfe, D. A. (1978). Distribution-free tests for ordered alternatives in a randomized block design. Journal of the American Statistical Association, 73(362), 427-431. doi:10.1080/01621459.1978.10481595
- Thas, O., Best, D. J., & Rayner, J. C. W. (2012). Using orthogonal trend contrasts for testing ranked data with ordered alternatives. Statistica Neerlandica, 66(4), 452-471. doi:10.1111/j.1467-9574.2012.00525.x
- Unalan, A. (2021). Sample Size in Clinical Researches: Power of the Test and Effect Size. Black Sea Journal of Health Science, 4(3), 221-227. doi:10.19127/bshealthscience.866556
- Zhang, Y., & Cabilio, P. (2012). A generalized Jonckheere test against ordered alternatives for repeated measures in randomized blocks. Statistics in Medicine, 32(10), Special Issue, 1635-1645. doi:10.1002/sim.5606
Sample Size Estimation of Nonparametric Tests with Ordered Alternatives for Longitudinal Data in Randomized Complete Block Designs
Abstract
Longitudinal studies involve repeated measurements from the same subjects or blocks over short or an extended periods of time. In longitudinal studies, usually the most important step is to decide how many experimental units to use. There are no closed form equations for determining sample size in many complex designs. Monte Carlo simulation method is an effective tool in complex designs to estimate power or sample size. This paper introduces estimating sample size for the number of blocks or experimental units based on a fixed number of treatment/time in randomized complete block designs with correlated longitudinal responses analyzed by nonparametric tests against ordered alternatives. The sample size of subjects is estimated for each test statistics by taking into account the autocorrelation structure of the error terms which form either a stationary first-order moving average or autoregressive with non-normally distributed white noise terms. An extensive sample size/power comparison among the recently proposed Modification of S test and the other two well-known nonparametric tests such as the Page test and the generalized Jonckheere test against ordered alternatives in randomized complete block designs is carried out under stationary first-order autoregressive and moving average error structures with white noise terms distributed with either Laplace or Weibull distributions. Simulation study indicates that the distribution of white noise and the error structure have an important role on sample size estimation for each nonparametric test. The Modification of S test requires large sample size in contrast to other tests for longitudinal data in the specified simulation setting.
References
- Akdur, H. T. K., Ozonur, D., Gul, H. H., & Bayrak, H. (2019). Comparison of rank-based tests for ordered alternative hypotheses in randomized complete block designs. Gazi University Journal of Science, 32(2), 705-716.
- Akdur, H. T. K. (2020). Comparison of non-parametric tests of ordered alternatives for repeated measures in randomized blocks. Communications in Statistics - Simulation and Computation, 51(7), 4146-4158. doi:10.1080/03610918.2020.1740262
- Aslan, E., Koskan, O., & Altay, Y. (2021). Determination of the Sample Size on Different Independent K Group Comparisons by Power Analysis. Turkish Journal of Agricultural Research, 8(1), 34-41. doi:10.19159/tutad.792694
- Best, D. J., & Rayner, J. C. W. (2015). An alternative to page’s test permitting both tied and missing data. Journal of Statistical Theory and Practice, 9(3), 524-536. doi:10.1080/15598608.2014.940098
- Dmitrienko, A., Chuang-Stein, C., & D'Agostino Sr, R. B. (2007). Pharmaceutical statistics using SAS: a practical guide. SAS Institute.
- Hollander, M. (1967). Rank tests for randomized blocks when the alternatives have an a priori ordering. Annals of the Institute of Statistical Mathematics, 38(3), 867-877. doi:10.1214/aoms/1177698880
- Kendall, M. G. (1938). A new measure of rank correlation. Biometrika, 30(1/2), 81-93. doi:10.2307/2332226
- Page, E. B. (1963). Ordered hypotheses for multiple treatments: a significance test for linear ranks. Journal of the American Statistical Association, 58(301), 216-230. doi:10.1080/01621459.1963.10500843
- Shan, G., Young, D., & Kang, L. (2014). A new powerful nonparametric rank test for ordered alternative problem. PloS one, 9(11), e112924. doi:10.1371/journal.pone.0112924
- Serdar, C. C., Cihan, M., Yücel, D., & Serdar, M. A. (2021). Sample size, power and effect size revisited: simplified and practical approaches in pre-clinical, clinical and laboratory studies. Biochemia Medica, 31(1), 27-53. doi:10.11613/bm.2021.010502
- Skillings, J. H., & Wolfe, D. A. (1978). Distribution-free tests for ordered alternatives in a randomized block design. Journal of the American Statistical Association, 73(362), 427-431. doi:10.1080/01621459.1978.10481595
- Thas, O., Best, D. J., & Rayner, J. C. W. (2012). Using orthogonal trend contrasts for testing ranked data with ordered alternatives. Statistica Neerlandica, 66(4), 452-471. doi:10.1111/j.1467-9574.2012.00525.x
- Unalan, A. (2021). Sample Size in Clinical Researches: Power of the Test and Effect Size. Black Sea Journal of Health Science, 4(3), 221-227. doi:10.19127/bshealthscience.866556
- Zhang, Y., & Cabilio, P. (2012). A generalized Jonckheere test against ordered alternatives for repeated measures in randomized blocks. Statistics in Medicine, 32(10), Special Issue, 1635-1645. doi:10.1002/sim.5606
There are 14 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Statistics |
| Authors | |
| Publication Date | December 31, 2022 |
| Submission Date | June 13, 2022 |
| Published in Issue | Year 2022 Volume: 9 Issue: 4 |
