In the "individually randomized group treatment" (IRGT) experimental design, individuals are first randomly assigned to a treatment arm or a control arm, but then within each arm, are grouped together (e.g., within classrooms/schools, through shared case managers, in group therapy sessions, through shared doctors, etc.) to receive services. In the common setting where the second-stage grouping is not experimentally controlled, we demonstrate that the standard error estimators for the estimated treatment effects from both random and fixed effects models are biased because parameters required to compute the standard errors are not identifiable from the data. We discuss implications for designing and analyzing IRGTs and provide suggestions for mitigating the bias.