Objective: This study introduces functional analysis of variance as a method for comparing germination trends under different treatments over a given time interval. This approach not only enables the comparison of treatments over the entire time period but also allows for treatment comparisons at each specific moment in time. Moreover, it identifies critical time points at which the maximum significant difference between treatments occurs, which can serve as novel germination indices.
Method: In this study, real experimental data from four germination studies were analyzed: (1) the effect of temperature on Nigella sativa germination, (2) the effect of salinity stress on Zea mays seed germination, (3) the comparison of germination among different Triticum astivum cultivars, and (4) the effect of water stress on Brassica napus germination. Using spline functions, germination data from these experiments were modeled as a function of time. The results of functional analysis were then used to compare treatments in terms of both germination percentage and germination time across the four experiments.
Results: The results of the functional analysis demonstrated its high efficiency in detecting significant or non-significant differences between treatments throughout the germination period. Furthermore, this method enabled comparisons of germination percentages at any given time point, as well as comparisons of germination times at various germination percentiles, providing detailed insights into the nature of differences among treatments. This approach also facilitated the introduction of new germination indices applicable to different seed types.
Conclusions: Overall, the results of this study indicate that the stepwise functional analysis method introduced here is an effective and precise tool for comparing treatments in germination data. This approach not only enhances treatment comparisons but also provides detailed insights into the nature of differences between treatments. Moreover, it overcomes the limitations associated with using conventional germination indices for treatment comparisons.
Highlights
- Functional analysis was applied to compare treatments in germination percentage data.
- The method enabled treatment comparisons in terms of germination percentage at each moment in time, as well as comparisons of germination times at various percentiles.
- Critical germination times and percentiles at which the maximum differences between treatments occur were introduced as novel germination indices.
