Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Depending on the take-up rate, we will have a treatment group (customers that received the invitation email) of 192,000 to 480,000 customers, and a control group of 1,268,000 to 980,000 customers corresponding to a take-up rate of 25% to 10% respectively. We assume that there is no sign-up among non-invited customers.
We use data from a random sample of 16,000 OE smart meter domestic customers to estimate the Minimum Detectable Effect Size for our trial. To do so, we simulate the impact of a placebo treatment (being invited to join CrowdFlex) on consumption data for peak hours over 30 events. We use the standard errors from our placebo regressions and predict their change for higher sample sizes. We then use the rule of 2.8 to estimate the effect we could capture to have a power of 80% and 5% significance level.
We find that the MDES on sign-up invitation (the ITT) would be between 0.0006 kWh (if the sign-up rate is 25%, resulting in 192,000 invited customers) or 0.0004 kWh (if the sign-up rate is 10%, resulting in 480,000 invited customers).
Estimates from Saving Sessions 2022-2023 (an implementation of the Demand Flexibility Service by Octopus Energy), from Jacob at al. (2023) Table AT.4 indicate potential effect sizes of:
-0.1 kWh per half-hour from signing up
-0.15 kWh per half-hour from opting in
We anticipate a smaller effect as incentives are smaller, closer to 0.08 kWh per sign-up.
Assuming this 0.08 kWh effect per sign-up, the ITT effect, diluted by non-sign-up, would be:
If 10%: 10% * 0.08 = 0.008 kWh per invitation
If 25%: 25% * 0.08 = 0.02 kWh per invitation.
Our MDES estimates are comfortably below these expected ITT effects.