Evaluation of the generalized linear model to the germination percentage data and its comparison with the square root transformation

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.

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.

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.

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.