Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
The study is powered to detect moderate-to-large effects in self-placement bias using a standardized sample of N=100 per experimental cell, resulting in a total sample of N=1,000 across both waves. This sample size is chosen to address specific methodological requirements.
The choice of N=100 per arm is calibrated against findings in the better-than-average (BTAE) literature, most notably Svenson (1981), which demonstrated that in subjective domains like driving, up to 80–90% of participants place themselves in the top 50% of the distribution. These high expected proportions provide the signal baseline for the study. A sample of N=100 per group allows for 80% power (1-β = 0.80) at a 5% significance level (α = 0.05) to detect a Minimum Detectable Effect of approximately 14 percentage points between treatment arms. This precision is necessary to determine if experimental manipulations, such as scale granularity (Quartile vs. Median), significantly shift these established baselines.
A critique of self-assessment data in the literature is that observed overplacement may be a statistical artifact of random noise or regression to the mean, particularly at the boundaries of a response scale, as argued by Burson, Larrick, & Klayman (2006). By maintaining N=100 per cell, the study ensures that individual random errors cancel out, resulting in a stable and reliable estimate of the group's mean self-placement. This sample size provides the robustness needed to distinguish true error from the statistical artifacts identified in the literature, especially when comparing the Easy IQ and Subjective IQ tasks in Wave 2, where task difficulty is known to influence response variance.
The study is designed to test the primary hypothesis that overplacement is driven by a desire to avoid the bottom of the distribution. In a uniform, unbiased distribution, 25% of participants are expected to place themselves in each quartile. With N=100, the study is sufficiently powered to detect if the proportion of participants in the bottom quartile (Q1) is significantly lower than this 25% benchmark (e.g., an observation of 11% or lower is significant at p < 0.05). Similarly, for the median condition, N=100 is sufficient to detect if "Above Median" placement significantly exceeds the 50% null hypothesis benchmark. This ensures that any detected deviations from the expected distribution represent meaningful biases rather than marginal shifts.