Fewer questions.
How much precision?
Short-Form Precision & Statistical Power Loss Simulator
Explore the tradeoff between respondent burden and precision where your decisions happen. An illustrative planning model, using hypothetical five-category items.
━ Full scale┄ Mean-clustered━ Target-zone
| Form | Precision proxy ρ | Mean SEM | Power at N | Total N for 80% |
|---|
Build a short form around your research question.
DASS can evaluate your item data, content constraints, and target population.
What this model assumes
All curves use a five-category graded response model, with four thresholds offset by −0.9, −0.3, 0.3, and 0.9 from each item center. Full-scale centers span −2.2 to 2.2; mean-clustered centers span −0.4 to 0.4; target-zone centers span the lower bound minus 0.3 to the upper bound minus 0.1. These are separate hypothetical item sets, not subsets selected from a calibrated bank. No IRT fitting, alpha-based selection, Q3 analysis, or MILP optimization is performed.
Information is evaluated on θ = −3 to 3 in 0.1 increments. The table averages I/(I+1) within the target zone as a precision proxy, and averages SEM = 1/√I. This proxy is not empirical reliability or a validated population reliability estimate. Greater precision in one zone may come at the expense of other trait levels.
Under a classical independent measurement-error approximation, d observed = d latent × √ρ. Power is the exact two-sided (α = .05) noncentral t power for two equal groups of N/2, with df = N − 2 and noncentrality d observed × √(N/4), the same calculation as R’s pwr.t.test. Required total N is twice the smallest whole per-group n that reaches 80% power, so it is always even. Odd planned totals use an equal-allocation continuous approximation. The measurement-error step above is an approximation, and none of this is a simulated trial result. Item-count reduction approximates burden reduction; it does not measure completion time.
Actual short-form performance requires calibration data, content review, local-dependence assessment, and validation in the intended population. The target-zone form is not guaranteed to outperform another selection strategy.
From planning scenarios to constrained assembly
Read the technical methodology: IRT and constrained test assembly →. The tutorial includes runnable R and Python examples that select items from a supplied information matrix. This simulator uses separate hypothetical forms and does not perform that optimization.
Reproduce locally
Download the annotated Python implementation or R implementation. Both use the same assumptions and even-N rounding as this page.