Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
To infer a potential effect size for the intervention uptake, we look for evidence from Franklin (2018) study in Addis Ababa, which had about 66% of treated individuals taking up the intervention, i.e. collecting transport subsidy. Because women are more likely to experience additional constraints such as safety issues, requiring a permission to travel, we expect the Woman arm to end up with lower uptake, i.e. proportion of treated couples using the taxi service at least once. Moreover, given randomization of travel credit, we expect participants receiving “high” amount to be more likely to perform at least one trip. Assuming a 10 percent attrition-adjusted sample of 630 couples (360 couples in Woman arm (T1) and 270 couples in Man arm (T2), from which 180 couples in Woman arm (T1.30) and 135 couples in Man arm (T2.30) receive the “low” amount), we will have 80 percent power to detect 14 percentage points difference in intervention uptake (alpha = 0.05).
Data from NHTS (1995) performed in United States suggests that more than 40% of the women in two-adult households with small children chained non-work trips into their commutes compared to 24% of men. Assuming a 10 percent attrition-adjusted sample of 630 couples (360 couples in Woman arm (T1) and 270 couples in Man arm (T2), we will have 80 percent power to detect about 11 percentage points difference in incidence of trip-chaining between two arms (alpha = 0.05).
Moreover, based on the evidence of trip chaining, we expect women to perform trips of longer distances compared to men, hence associated outcome in Woman arm (T1) would be higher than in Man arm (T2). Christensen and Osman (2021) study provides estimate of 11-15 km length of a trip. Our study differs from Christensen and Osman (2021) Uber experiment in Cairo, Egypt in that we do not include a pure control group but rather compare extensive and intensive travel outcomes of treatment arms varying gender of the recipient. Assuming a length of 11 km for Man arm and a 10 percent attrition-adjusted sample of 630 couples, we are powered to detect at least 2 km difference between two arms (alpha = 0.05).
Our prior is that women are more likely to require partner’s permission to travel: according to EDHS (2016), only 18 percent of married women in Addis Ababa mainly make decision to visit their friends and family on their own. As we vary the main recipient of the taxi services, we might observe a gradual decrease in the incidence of traveling with partner from Women (T1) to Couple (T2) to Men (T3) arm, since women, even being main recipient, might need their partner’s presence to perform the trip. Moreover, we might expect women in “high” arm to travel more often alone, since increased travel credit amount allows for more trip, which, after performing several trips with their partner, will build trust in the service and make women more comfortable in traveling alone. Assuming a 10 percent attrition-adjusted total sample of 630 couples (360 couples in Women arm (T1), from which 180 couples will receive the “low” amount (T1.30) and 180 couples will receive the “high” amount (T1.80)), we will have 80 percent power to detect about 10 percentage points difference in incidence of travel with partner between two sub-arms (alpha = 0.05).