29.1 Introduction: Insulation
The Electricity Council in Bristol wanted to determine if a certain type of wall-cavity insulation reduced energy consumption in winter, on average (The Open University 1983). Their RQ was:
Is there a mean saving in energy consumption due to adding insulation?
The data collected are shown in the table below. These data were used in Sect. 23, where a CI was constructed for the mean energy saving.
For these data, finding the difference in energy consumption for each house seems sensible. The data are paired (Sect. 23.1): the same unit of analysis is measured twice on the same variable (before and after), and the mean change is of interest. Pairing the values for each house makes sense; hence finding the difference in energy consumption at each house makes sense.
The parameter is \(\mu_d\), the population mean saving in energy consumption.
Making clear how the differences are computed is important. Here, the differences could be computed as the Before minus After (the energy consumption saving), or the After minus Before (the energy consumption increase). Either is fine, as long as you are consistent throughout. The meaning of any conclusions will be the same.
In this case, discussing energy savings seems most natural, so we compute the differences as Before minus After.