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Field
Sample size (or number of clusters) by treatment arms
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Before
In Wave 1 we plan to have 240 participants per treatment except for the conditions where each individual is uniquely observed by twenty others in Wave 2. For those conditions we plan on 60 participants in Wave 1. The reason is that otherwise Wave 2 sample sizes would become extremely large. (240 Wave 1 participants in this condition would correspond to 4800 Wave 2 participants for this condition alone). We will have 300 participants (240+60) in the baseline treatment (without influence/observability).
In sum we will have the following sample sizes for our Wave 1 treatments:
Baseline: 300; Influence 1-1: 240; Influence 1-20: 60; Influence 20-1: 240; Influence 20-20: 240
Observability 1-1: 240; Observability 1-20: 60; Observability 20-1: 240; Observability 20-20: 240, where Influence x-y denotes an influence treatment where each Wave 1 participant is observed by x others who each observe y others in total.
Sample sizes in Wave 2 then directly follow from these.
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After
In Wave 1 we plan to have 240 participants per treatment except for the conditions where each individual is uniquely observed by twenty others in Wave 2. For those conditions we plan on 60 participants in Wave 1. The reason is that otherwise Wave 2 sample sizes would become extremely large. (240 Wave 1 participants in this condition would correspond to 4800 Wave 2 participants for this condition alone). We will have 300 participants (240+60) in the baseline treatment (without influence/observability).
In sum we will have the following sample sizes for our Wave 1 treatments:
Baseline: 300; Influence 1-1: 240; Influence 1-20: 60; Influence 20-1: 240; Influence 20-20: 240
Observability 1-1: 240; Observability 1-20: 60; Observability 20-1: 240; Observability 20-20: 240, where Influence x-y denotes an influence treatment where each Wave 1 participant is observed by x others who each observe y others in total.
Sample sizes in Wave 2 then directly follow from these.
Update June 2024: After conducting the study the effect size for OBS(1,1) was slightly bigger than conjectured and as a result the difference between INF(1,1) and OBS(1,1) not statistically significant at conventional levels (p=0.1219). We propose to increase the sample size by 500 participants (100 participants each in baseline, INF(1,1) and OBS(1,1) and as a consequence also an additional 200 Wave-2 participants) to be able to detect also this slightly smaller effect size.
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