2.2.3. Variability of Peak Coefficient among Weekdays

The water demand can show different trends between working days and weekends, and this can affect the maximum daily water demand. For the investigated dataset, water consumption exhibits a significant weekly cycle, and water demand was clustered in three groups: weekdays, Saturdays, and Sundays [40].

To verify if the sample mean of hourly peak factors has a day-to-day variability, the ANOVA test is used, which is able to identify significant differences in the central values of different groups [49]. In the present study, seven groups, one for each day of the week, are defined and the related sample means are estimated by Equation (6). For each group, summation in Equation (6) is only extended to the days *Di* with *i* = 1, 2, ... , 7 (1 = Mondays, 2 = Tuesdays, ... , 7 = Sundays). In other words, for each value of *N*, seven groups of *M* sample means are evaluated. It is worth noting that the mean of all the 7 × *M* sample means coincides with the population mean μ*N*.

As highlighted in the previous sections, the statistical behaviour of peak factors is influenced by the number *N* of aggregated households; thus, it is expected that the outcomes of ANOVA show a similar dependence. Specifically, for small *N* values any differences of the peak factor values among the days of the week could be covered by the high peak demand variability. In turn, those differences could become more evident for higher *N* values, when peak demand variability is lower due to the stabilization of the aggregated water demand pattern.
