Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
We expect that in the control group 10% (p1 = 0.1) participate in our survey. This expectation relies on former studies of the UKE with the same sample. The power analysis is based on a two-sample proportions test with H0: p2 = p1 versus Ha: p2 != p1; p2 > p1. Study parameters:
alpha = 0.05
power = 0.80
N per group = 3,000
p1 = 0.10
Estimated effect size and experimental-group proportion:
delta = 0.0236 (difference)
p2 = 0.1236
For coming to the open-doors day or stating interest in the planned ideas workshop, we expect 1% = 28 people response respectively.
Study parameters:
alpha = 0.05
power = 0.80
N per group = 2,800
p1 = 0.01
Estimated effect size and experimental-group proportion:
delta = 0.0089 (difference)
p2 = 0.0189
Heterogeneity analysis with low SES group:
In Germany (similarly in the City of Hamburg), around one in six people is considered socially disadvantaged or at risk of poverty. Assuming that this proportion is underrepresented in our sample and that this population group is also less likely to participate in our study in the control treatment, we assume N = 300 per treatment group with p1 = 0.05. Under these assumptions, we could identify a difference of delta = 0.1, i.e., p2 = 0.15 with alpha = 0.05 and power = 0.80. Since such a large effect is not expected with our treatments, we will employ a difference-in-difference estimation with p1 = difference between low SES people and other participants in the control group and p2 = difference between low SES people and other participants in the treatment group. Study parameters:
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| alpha power N N1 N2 delta p1 p2 |
|----------------------------------------------------------------------------------|
| .05 .8 5,600 2,800 2,800 .00894 .01 .01894 |
| .05 .8 5,600 2,800 2,800 .0119 .02 .0319 |
| .05 .8 5,600 2,800 2,800 .01414 .03 .04414 |
| .05 .8 5,600 2,800 2,800 .016 .04 .056 |
| .05 .8 5,600 2,800 2,800 .01761 .05 .06761 |
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