Design-based learning is commonly evaluated through teacher-rated achievement, although previous research’s often omit the covariance information required to reproduce adjusted comparisons. This study asks which conclusions about an instructional achievement contrast remain identifiable when that information is unavailable and when numerical precision, collaborative work, and assessment offsets are considered explicitly. The materials used statistics for 207 university students undertaking stage-costume design available online. A common-slope analysis of covariance is retained, and Cauchy–Schwarz constraints are used to bound its group coefficient. Additional calculations examine differences in mean change, rounding intervals, three-person team dependence, and fixed additive shifts in assessment. The posttest contrast is 0.480 points, with an independent-student 95% confidence interval of 0.368–0.592 and Hedges’ \(g=1.166\). Every covariance-compatible adjusted coefficient lies between 0.458 and 0.502 points. The difference in mean changes is 0.510 points, but its uncertainty varies substantially with the unavailable within-person correlations. Under an illustrative maximum team design effect of three, the posttest interval is 0.283–0.677 points; an additive displacement of 0.283 points would move its lower limit to zero. Incompatible gender and motivation summaries prevent their use as corroborating adjusted evidence. The instructional contrast is therefore stable to covariance choices and printed precision, while its causal and educational interpretation remains contingent on allocation, assessment, and dependence assumptions. Aggregate ratings support a bounded statistical contrast, but do not independently establish individual improvement, equal outcomes across genders, motivational mechanisms, or transfer to unfamiliar design tasks.
