Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Model. All tests are based on the regression
Y_is = α + β_P·P_s + β_V·V_s + β_PV·(P_s × V_s) + X_is'γ + ε_is,
where Y_is is the outcome of participant i in session s. P_s indicates live plants on the desks and V_s an open window view of a natural landscape. Both are assigned at the session level and coded −1/2 (absent) and +1/2 (present). X_is is a vector of pre-specified controls. Standard errors are clustered by session, and p-values are computed with the wild cluster bootstrap.
With this coding, the coefficients have a direct meaning in the units of the outcome:
α is the average of the four condition means.
β_P is the average difference in the outcome between sessions with and without plants, averaged over the two view conditions.
β_V is the average difference between sessions with the view open and covered, averaged over the two plant conditions.
β_PV is the difference-in-differences: how much the effect of plants changes when the view is open.
Hypotheses tested.
H1 (Plants and game behavior, two-tailed). Plants change cooperative and prosocial behavior in five economic games (Stag Hunt, Prisoner's Dilemma, Trust, Gift Exchange, Ultimatum) and in a summary index. Theory supports both a positive effect through stress reduction and a negative effect through more deliberative decision-making, so the test is two-tailed. H0: β_P = 0 versus H1: β_P ≠ 0.
H2 (View and game behavior, two-tailed). Same outcomes and reasoning as H1. H0: β_V = 0 versus H1: β_V ≠ 0.
H3 (Physiological stress, one-tailed). Plants and the view each lower physiological arousal, measured by skin conductance level and the frequency of skin conductance responses during the stress task and the games. H0: β_P ≥ 0 versus H1: β_P < 0; H0: β_V ≥ 0 versus H1: β_V < 0.
H5 (Plant exposure and valuation, one-tailed). Participants who had a plant on their desk state a higher willingness to accept (WTA) for the plant. H0: β_P ≤ 0 versus H1: β_P > 0.
H6 (View as a substitute, one-tailed). Participants who had the open view state a lower WTA for the plant. H0: β_V ≥ 0 versus H1: β_V < 0.
Interaction (exploratory, two-tailed). H0: β_PV = 0 versus H1: β_PV ≠ 0.
The mediation of the H1 and H2 effects by stress (H4) is estimated as supporting evidence and is not part of this power analysis.
Minimum detectable effect. For each test, the MDE is the smallest true |β| that rejects H0 with 80% power at α = 0.05, given 300 participants and the clustering assumptions below. MDEs are reported in standard deviations of the outcome (the SD in the Control condition) and converted to natural units where a reference SD is available. For one-tailed tests, the MDE applies only in the stated direction.
The calculation assumes α = 0.05 and 80% power, an intraclass correlation of 0.05 within sessions, and about [m] participants per session (design effect ≈ 1.2 for m ≈ 5). Effects of plants and view on game behavior (H1, H2) are tested two-tailed. Effects on physiological stress (H3) and plant valuation (H5, H6) are tested one-tailed, since the literature supports a direction for these. MDEs are in standard deviation units of each outcome.
Game behavior (H1, H2; two-tailed):
Outcomes every participant contributes (Stag Hunt, Prisoner's Dilemma, summary index; 150 vs 150): MDE = 0.32 SD without clustering and 0.35 SD with clustering. For a binary cooperation rate near 50%, this is about 18 percentage points.
Role-specific outcomes (Trust sent and returned, wage, effort, Ultimatum offer and acceptance; 75 vs 75): MDE = 0.46 SD without clustering and 0.50 SD with clustering. For example, with an SD of about $3 for amounts sent in a $10 Trust Game, this is about $1.50.
Physiological stress (H3; one-tailed): skin conductance level and skin conductance response frequency, relative to baseline; 150 vs 150. MDE = 0.29 SD without clustering and 0.31 SD with clustering. This assumes complete GSR data. Lost recordings will raise the MDE in proportion.
Plant valuation (H5, H6; one-tailed): WTA is elicited from all 300 participants, 150 vs 150 for each main effect. MDE = 0.29 SD without clustering and 0.31 SD with clustering.
Plants × View interaction (two-tailed): MDE ≈ 0.71 SD. The study is not powered to detect interactions of plausible size, so interaction estimates are exploratory.
The mediation analysis (H4) is not separately powered and is reported as supporting evidence on mechanism.