Volume 10, Issue 2 ((Autumn & Winter) 2024)
Iranian J. Seed Res. 2024, 10(2): 37-48 |
Back to browse issues page
Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
Ghaderi-Far F, Azimmohseni M, Bagheri H. (2024). Evaluation of the generalized linear model to the germination percentage data and its comparison with the square root transformation. Iranian J. Seed Res.. 10(2), : 3 doi:10.61186/yujs.10.2.37
URL: http://yujs.yu.ac.ir/jisr/article-1-574-en.html
URL: http://yujs.yu.ac.ir/jisr/article-1-574-en.html
, m.azim@gu.ac.ir
Abstract: (917 Views)
Extended abstract
Introduction: In seed research, germination percentage data is the result of counting and has a binomial distribution. Therefore, seed researchers use data transformation, especially square root transformation, to stabilize the variance and normalize the data before performing analysis of variance and comparison of treatments. Despite the use of data transformation, this method has fundamental issues in the structure that misleads the test results. Therefore, it is important to introduce and replace a method that preserves the research assumptions and provides acceptable results for researchers without using data transformation. The use of generalized linear model is an alternative method for analyzing germination data with binomial distribution. In this research, the generalized linear model will be introduced first. Then, the efficiency of this method will be illustrated using simulated and actual germination data.
Materials and Methods: In this research, first the simulated data was generated by the Monte Carlo method. Based on the simulated data, the significance level and the power of test of generalized linear model were computed. Then the actual data related to three experiments including the effect of acidity on germination of wheat varieties, the effect of water stress and salinity on germination of yellow sweet clover seeds, and the effect of alternating temperatures on germination of three lavender populations were used and the results of the generalized linear model were compared with the square root transformation method based on the data of three experiments.
Results: The simulation results showed that the generalized linear model has a high efficiency to preserve the predetermined significance level and a high power in detecting significant differences in germination of the treatments. Moreover, the results of the comparison of the generalized linear model with the square root transformation method illustrated that the generalized linear model had a higher capability to detect significant differences between various treatments, especially in the treatments with unequal seeds in the Petri dish, and in the treatments in which the square root transformation method resulted in no significant difference among treatments, the generalized linear method showed a significant difference.
Conclusions: Generally, the results of this research demonstrated that the generalized linear model can be used as an alternative method to square root transformation in studies on the germination percentage of seeds with binomial distribution, without having the problems of the square root transformation method. Moreover, this model outperforms the square root transformation in detecting significant differences in germination of treatments with fixed and different seeds.
Highlights:
Introduction: In seed research, germination percentage data is the result of counting and has a binomial distribution. Therefore, seed researchers use data transformation, especially square root transformation, to stabilize the variance and normalize the data before performing analysis of variance and comparison of treatments. Despite the use of data transformation, this method has fundamental issues in the structure that misleads the test results. Therefore, it is important to introduce and replace a method that preserves the research assumptions and provides acceptable results for researchers without using data transformation. The use of generalized linear model is an alternative method for analyzing germination data with binomial distribution. In this research, the generalized linear model will be introduced first. Then, the efficiency of this method will be illustrated using simulated and actual germination data.
Materials and Methods: In this research, first the simulated data was generated by the Monte Carlo method. Based on the simulated data, the significance level and the power of test of generalized linear model were computed. Then the actual data related to three experiments including the effect of acidity on germination of wheat varieties, the effect of water stress and salinity on germination of yellow sweet clover seeds, and the effect of alternating temperatures on germination of three lavender populations were used and the results of the generalized linear model were compared with the square root transformation method based on the data of three experiments.
Results: The simulation results showed that the generalized linear model has a high efficiency to preserve the predetermined significance level and a high power in detecting significant differences in germination of the treatments. Moreover, the results of the comparison of the generalized linear model with the square root transformation method illustrated that the generalized linear model had a higher capability to detect significant differences between various treatments, especially in the treatments with unequal seeds in the Petri dish, and in the treatments in which the square root transformation method resulted in no significant difference among treatments, the generalized linear method showed a significant difference.
Conclusions: Generally, the results of this research demonstrated that the generalized linear model can be used as an alternative method to square root transformation in studies on the germination percentage of seeds with binomial distribution, without having the problems of the square root transformation method. Moreover, this model outperforms the square root transformation in detecting significant differences in germination of treatments with fixed and different seeds.
Highlights:
- The generalized linear model was used for the analysis of germination percentage data.
- The data simulated using the Monte-Carlo method was utilized to examine the significance level and power of the generalized linear model test.
- The generalized linear model was compared with the square root transformation method during different germination experiments with fixed and different seeds in each Petri dish.
Article number: 3
Type of Study: Research |
Subject:
General
Received: 2023/02/2 | Revised: 2024/06/9 | Accepted: 2023/08/5 | ePublished: 2024/06/9
Received: 2023/02/2 | Revised: 2024/06/9 | Accepted: 2023/08/5 | ePublished: 2024/06/9
References
1. Ahrens, W.H., Cox, D.J. and Budhwar, G. 1990. Use of the arcsine and square root transformations for subjectively determined percentage data. Weed Science, 38(4-5): 452-458.
https://doi.org/10.1017/S0043174500056824 [DOI:10.1017/S0043174500056824.]
2. Amorim, D.J., dos Santos, A.R.P., da Piedade, G.N., de Faria, R.Q., da Silva, E.A.A. and Sartori, M.M.P. 2021. The Use of the Generalized Linear Model to Assess the Speed and Uniformity of Germination of Corn and Soybean Seeds. Agronomy, 11(3): 588.
https://doi.org/10.3390/agronomy11030588 [DOI:10.3390/agronomy11030588.]
3. Bolker, B.M., Brooks, M.E., Clark, C.J., Geange, S.W., Poulsen, J.R., Stevens, M.H.H. and White, J.S.S. 2009. Generalized linear mixed models: a practical guide for ecology and evolution. Trends in ecology and evolution, 24(3):127-135.
https://doi.org/10.1016/j.tree.2008.10.008 [DOI:10.1016/j.tree.2008.10.008.] [PMID]
4. Carvalho, F.J., Santana, D.G.D. and Araújo, L.B.D. 2018. Why analyze germination experiments using Generalized Linear Models. Journal of Seed Science, 40: 281-287. http://dx.doi.org/10.1590/2317-1545v40n3185259. [DOI:10.1590/2317-1545v40n3185259]
5. Dey, P. and Pandit, P. 2020. Relevance of data transformation techniques in weed science. Journal of Research in Weed Science, 3(1): 81-89.
https://doi.org/10.26655/JRWEEDSCI.2020.1.8 [DOI:10.26655/JRWEEDSCI.2020.1.8.]
6. Dobson, A.J. and Barnett, A.G. 2018. An introduction to generalized linear models. Chapman and Hall/CRC.
7. Greenland, S., Senn, S.J., Rothman, K.J., Carlin, J.B., Poole, C., Goodman, S.N. and Altman, D.G. 2016. Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations. European Journal of Epidemiology, 31: 337-350.
https://doi.org/10.1007/s10654-016-0149-3 [DOI:10.1007/s10654-016-0149-3.] [PMID] [PMCID]
8. Jaeger, T.F. 2008. Categorical data analysis: Away from ANOVAs (transformation or not) and towards logit mixed models. Journal of Memory and Language, 59(4): 434-446.
https://doi.org/10.1016/j.jml.2007.11.007 [DOI:10.1016/j.jml.2007.11.007.] [PMID] [PMCID]
9. Johnston, G. 1993. SAS software to fit the generalized linear model. In SUGI Proceedings (pp. 1-8). SAS Institute Inc., Cary, NC.
10. Moder, K. 2007. How to keep the type I error rate in ANOVA if variances are heteroscedastic. Austrian Journal of Statistics, 36(3): 179-188.
https://doi.org/10.17713/ajs.v36i3.329 [DOI:10.17713/ajs.v36i3.329.]
11. Moder, K. 2010. Alternatives to F-test in one-way ANOVA in case of heterogeneity of variances (a simulation study). Psychological Test and Assessment Modeling, 52(4): 343.
12. Osborne, J. 2010. Improving your data transformations: Applying the Box-Cox transformation. Practical Assessment, Research, and Evaluation, 15(1): 12. [DOI:10.7275/qbpc-gk17.]
13. Piepho, H.P. 2003. The folded exponential transformation for proportions. Journal of the Royal Statistical Society: Series D (The Statistician), 52(4): 575-589.
https://doi.org/10.1046/j.0039-0526.2003.00509.x [DOI:10.1046/j.0039-0526.2003.00509.x.]
14. Ribeiro-Oliveira, J.P. and Ranal, M.A. 2016. Sample size in studies on the germination process. Botany, 94(2): 103-115.
https://doi.org/10.1139/cjb-2015-0161 [DOI:10.1139/cjb-2015-0161.]
15. Ribeiro-Oliveira, J.P., Santana, D.G.D., Pereira, V.J. and Santos, C.M.D. 2018. Data transformation: an underestimated tool by inappropriate use. Acta Scientiarum. Agronomy, 40. http://dx.doi.org/10.4025/actasciagron.v40i1.35300. [DOI:10.4025/actasciagron.v40i1.35300]
16. Rizzardi, D.A., Contreras-Soto, R.I., Figueiredo, A.S.T., Andrade, C.A.D.B., Santana, R.G. and Scapim, C.A., 2017. Generalized mixed linear modeling approach to analyze nodulation in common bean inbred lines. Pesquisa Agropecuária Brasileira, 52: 1178-1184. [DOI:10.1590/s0100-204x2017001200006]
17. Robert, C.P., Casella, G. and Casella, G. 2010. Introducing Monte Carlo methods with R (Vol. 18). New York: Springer. [DOI:10.1007/978-1-4419-1576-4]
18. Sileshi, G.W., 2012. A critique of current trends in the statistical analysis of seed germination and viability data. Seed Science Research, 22(3): 145-159. [DOI:10.1017/S0960258512000025]
19. Stroup, W.W. 2013. Generalized linear mixed models. CRC Press, Boca Raton, FL.
20. Stroup, W.W. 2015. Rethinking the analysis of non-normal data in plant and soil science. Agronomy Journal, 107(2): 811-827.
https://doi.org/10.2134/agronj2013.0342 [DOI:10.2134/agronj2013.0342.]
21. Warton, D.I. and Hui, F.K. 2011. The arcsine is asinine: the analysis of proportions in ecology. Ecology, 92(1): 3-10.
https://doi.org/10.1890/10-0340.1 [DOI:10.1890/10-0340.1.] [PMID]
Send email to the article author
| Rights and permissions | |
 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |
