Does children's energy intake at one meal influence their intake at subsequent meals?  Or do we just think it does? 
It is widely believed that young children are able to adjust their energy intake across successive meals to compensate for higher or lower intakes at a given meal.  This conclusion is based on past observations that although children's intake at individual meals is highly variable, total daily intakes are relatively constant.  We investigated how much of this reduction in variability could be explained by the statistical phenomenon of the variability of individual components (each meal) always being relatively larger than the variability of their sum (total daily intake), independent of any physiological compensatory mechanism.  We calculated, theoretically and by simulation, how variable a child's daily intake would be if there was no correlation between intakes at individual meals.  We simulated groups of children with meal/snack intakes and variability in meal/snack intakes based on previously published values.  Most importantly, we assumed that there was no correlation between intakes on successive meals.  In both approaches, the coefficient of variation of the daily intakes was roughly 15%, considerably less than the 34% for individual meals.  Thus, most of the reduction in variability found in past studies was explained without positing strong 'compensation'.  Although children's daily energy intakes are indeed considerably less variable than their individual components, this phenomenon was observed even when intakes at each meal were simulated to be totally independent.  We conclude that the commonly held belief that young children have a strong physiological compensatory mechanism to adjust intake at one meal based on intake at prior meals is likely to be based on flawed statistical reasoning.