  Universal scaling laws form one of the central issues in physics. A
non-standard scaling law or a breakdown of a standard scaling law, on the other
hand, can often lead to the finding of a new universality class in physical
systems. Recently, we found that a statistical quantity related to fluctuations
follows a non-standard scaling law with respect to system size in a
synchronized state of globally coupled non-identical phase oscillators
[Nishikawa et al., Chaos $\boldsymbol{22}$, 013133 (2012)]. However, it is
still unclear how widely this non-standard scaling law is observed. In the
present paper, we discuss the conditions required for the unusual scaling law
in globally coupled oscillator systems, and we validate the conditions by
numerical simulations of several different models.
