Association studies use statistical links between genetic markers and the phenotype variation across many individuals to identify genes controlling variation in the target phenotype. However, this approach, particularly conducted on a genome-wide scale (GWAS), has limited power to identify the genes responsible for variation in traits controlled by complex genetic architectures. In this study, we employ real-world genotype datasets from four crop species with distinct minor allele frequency distributions, population structures and linkage disequilibrium patterns. We demonstrate that different GWAS statistical approaches provide favourable trade-offs between power and accuracy for traits controlled by different types of genetic architectures. FarmCPU provides the most favourable outcomes for moderately complex traits while a Bayesian approach adopted from genomic prediction provides the most favourable outcomes for extremely complex traits. We assert that by estimating the complexity of genetic architectures for target traits and selecting an appropriate statistical approach for the degree of complexity detected, researchers can substantially improve the ability to dissect the genetic factors controlling complex traits such as flowering time, plant height and yield component