The methods should be appropriate for the hypothesis being tested and have adequate controls. A key feature of research that is scientifically sound is adequate replication of the data. The results must be reproducible, that is there must be sufficient replication - this means experimental replication not just technical replicates of the same experiment - to provide confidence that the observations are not due to chance.
There are many different ways to design and statistically analyze plant-related experiments. Depending on the nature of the experiment, experimental replication can be achieved by growing and/or treating plants on separate occasions, the use of different alleles of a mutation, multiple independent transgenic lines, or growth of plants in different environments or across several seasons. The replication required also depends on the question being asked. Here are a couple of examples that illustrate this point: the test is for a cold treatment. One has multiple plants within a growth chamber. A scientist will call these individual plants, biological replicates, which indeed they are. However, these are not experimental replicates, they are technical replicates of a single cold treatment. For statistical purposes, we need replication of the cold treatment in the form of multiple growth chambers (at least 3 replicates) or replication in time using the same growth chamber and treatment. However, if the test is for the cold response of different genotypes, then the different plants within the cold chamber (described as biological replicates above) will provide the replication of the genotypes treatment under that specific treatment. A common mistake is to pool the material from individual experimental/biological replicates prior to library preparation and sequencing for transcriptomic experiments, for example. Pooling material at that stage hides any variation between the experimental replicates and therefore cannot be statistically tested for experimental effects. Depending on the experimental design, ANOVA (analysis of variance) may be a more powerful method for testing your hypothesis than a simple t-test.
If on the other hand, the investigator does a study with many observations taken over time, space or both, then replication and ANOVA become obsolete. Such studies can be conducted on-farm, in unmanaged ecosystems, in the rhizosphere of one plant or a community of plants, in a climate chamber with a time series of observations, etc. In these circumstances, treatments may not be applied, but variability of processes is observed while boundary conditions are controlled. The investigator can base design and analysis on widely known analytical tools such as auto- and cross correlation, auto-regressive state-space models, Fourier-based techniques (e.g. spectral and wavelet analysis) and a variety of geo-statistical methods. All these approaches allow for efficient identification of spatial or temporal processes or the diagnosis of symptoms; they do not depend on treatments, nor do they prohibit experimental treatments. Replicates are not necessary either. Proof that observations are not based on chance, but are reflecting a signal, is obtained from their autocovariance structure. These techniques differ from ANOVA because they are not based on uncorrelated or randomness of observations, but rather they are based on variability structure. Variability is not an obstacle but an opportunity. Are data from one year sufficient to publish? Yes, if as many as possible boundary conditions are observed that made the data turn out the way they did. Most observations of ecosystem processes are hard to replicate exactly, but there is no need when using tools such as these that are common in hydrologic sciences, economic time series, climate change, medical sciences, landscape ecology, physical geography among others.
If in doubt, a statistician should be consulted on the experimental design before starting the experiment, otherwise a considerable amount of time, effort and money may be wasted. Don’t forget that just because a result is statistically significant does not imply that it is biologically relevant, so think carefully about the interpretation of your data.