While many advanced mixed-effects models have been proposed and are used in fMRI, the simplest, ordinary least squares (OLS), is still the one that is most widely used. A survey of 90 papers found that 92% of group fMRI analyses used OLS. Despite the widespread use, this simple approach has never been thoroughly justified and evaluated; for example, the typical reference for the method is a conference abstract, (Holmes, A., Friston, K., 1998. Generalisability, random effects & population inference. NeuroImage 7 (4 (2/3)), S754, proceedings of Fourth International Conference on Functional Mapping of the Human Brain, June 7-12, 1998, Montreal, Canada.), which has been referenced over 400 times. In this work we fully derive the simplified method in a general setting and carefully identify the homogeneity assumptions it is based on. We examine the specificity (Type I error rate) of the OLS method under heterogeneity in the one-sample case and find that the OLS method is valid, with only slight conservativeness. Surprisingly, a Satterthwaite approximation for effective degrees of freedom only makes the method more conservative, instead of more accurate. While other authors have highlighted the inferior power of the OLS method relative to optimal mixed-effects methods under heterogeneity, we revisit these results and find the power differences very modest. While statistical methods that make the best use of the data are always to be preferred, software or other practical concerns may require the use of the simple OLS group modeling. In such cases, we find that group mean inferences will be valid under the null hypothesis and will have nearly optimal sensitivity under the alternative.