Reassess the t Test: Interact with All Your Data via ANOVA

Abstract

Plant biology is rapidly entering an era where we have the ability to conduct intricate studies that investigate how a plant interacts with the entirety of its environment. This requires complex, large studies to measure how plant genotypes simultaneously interact with a diverse array of environmental stimuli. Successful interpretation of the results from these studies requires us to transition away from the traditional standard of conducting an array of pairwise t tests toward more general linear modeling structures, such as those provided by the extendable ANOVA framework. In this Perspective, we present arguments for making this transition and illustrate how it will help to avoid incorrect conclusions in factorial interaction studies (genotype × genotype, genotype × treatment, and treatment × treatment, or higher levels of interaction) that are becoming more prevalent in this new era of plant biology.

Figure 1.

Case Study 1: Model of ANOVA Testing of How Two Genes May or May Not Interact. Using the model described in the supplemental methods wherein two genes interact to modulate root length in a purely additive fashion, we randomly generated three independent trials involving three independent samples per genotype. These were then used to conduct t tests and ANOVA both within each trial and by combining all the data. The bar graphs show the standard representation of mean ± sd with letters showing if there is a significant difference from the control group using Student’s t test comparisons of the mean. The summary table shows the ANOVA results (full results are shown in Supplemental Table 1). “No” means the term is not significant and “Yes” means it is significant. The ANOVA for each trial and combined across all trials is shown. Trial shows the trial term in the ANOVA combining all the trial data. KO, knockout genotype; WT, wild-type genotype. Data are shown in Supplemental Table 3.

Figure 2.

Case Study 2: Model Showing When Combined Data Resolves Confusion. Using the model described in the supplemental information wherein a mutation alters glucosinolate accumulation in response to a given treatment, we randomly generated three independent trials involving three independent samples per genotype × treatment class. These data were then used to conduct t tests and ANOVA both within each trial and by combining all the data. The bar graphs show the standard representation of mean ± sd with letters showing if there is a significant difference from the control group using Student’s t test comparisons of the mean. The summary table shows the ANOVA results (full results are shown in Supplemental Table 2). “No” means the term is not significant and “Yes” means it is significant. The ANOVA for each trial and combined across all trials is shown. KO, knockout genotype; WT, wild-type genotype; Ctl, control treatment; Treat, alternative treatment. Data are shown in Supplemental Table 4.