Atlas
statminds
GLM (Sequential Block Model)The underlying model family class (e.g. GLM, linear model, categorical matrix, log-linear).Parametric ReferenceStatistical methods that assume a specific probability distribution family (typically normal).12-stage workflow

Hierarchical Regression

The engine for Incremental Discovery. Hierarchical Regression audits the additive power of predictors by entering them in sequential blocks, revealing exactly what each new layer adds to the 'Outcome Story'.

Model familyGLM (Sequential Block Model)
Hypothesisincremental
AliasesSequential Multiple Regression · Step-wise Block Analysis · Layered Predictive Modeling
G1
Incremental R² Audit
Determine if adding a new set of predictors meaningfully increases the model's predictive accuracy.
G2
Covariate Neutralization
Control for established demographic factors in Block 1 before testing the 'True Treatment' in Block 2.
G3
Model Parsimony Mapping
Identify the specific stage where adding more complexity yields 'Diminishing Returns' in explained variance.
1

What is it?

Hierarchical Regression compares nested regression models sequentially, measuring if adding target predictors significantly improves outcomes after controlling for covariate blocks.

2

When to use it

  • Covariate Adjustments: Control for age/gender before measuring primary variables.
  • Incremental Value: Evaluate Model 2 vs. Model 1 variance shifts.
Interactive Sandbox

Incremental Variance Live Laboratory

Adjust Model 1 base covariates R2 and the Model 2 target variable addition R2 to test significance.

Model 1 Covariates (R2)20%
Model 2 Target Addition (dR2)15%
Sample Size (N)30
Variance Partition Venn Diagram representationGreen circle indicates added variance portion
Model 1 (base)Model 2 (+target)
Hierarchical Comparison Table
MetricModel 1 (Base)Model 2 (Full)
Total R-squared0.20000.3500
F-change value-6.231
p-value Change-0.0181
The 12-Stage Precision Workflow
01The R² Change
Hypotheses
We test the null of zero incremental gain (ΔR² = 0) against the discovery of a significant 'Predictive Breakthrough' in the new block.
02Residual Stability
Assumptions
Ensuring that adding new blocks doesn't destabilize the OLS assumptions—normality and linearity must hold at every stage.
03Order Sensitivity
Diagnostics
Verifying that the sequence of entry is justified by theory—demographics first, then clinical markers, then the novel intervention.
04focus
Auditing FlowMotion recovery: Block 1 (Age/BMI) → Block 2 (Initial Severity) → Block 3 (FlowMotion Hours).
05Stepwise Pivot
Alternatives
Knowing when to abandon the theory-driven hierarchy for automated Stepwise Regression (if discovery is truly exploratory).
06F-Change Strike
Significance
Executing the 'F-Change' test to prove the new block's contribution is not a chance artifact of increased model complexity.
07ΔR²
Effect Size
Interpreting the 'R-Squared Change' as the unique percentage of the outcome uniquely captured by the new set of variables.
08The Block Buffer
Sample Size
Accounting for the N required to stabilize the final model, which now contains the cumulative total of all previous blocks.
09The Sequential Table
Reporting
Reporting Model 1 vs Model 2 side-by-side, tracking the evolution of coefficients and the growth of R².
10Block Syntax
Software
Executing 'lm' with sequential updates or specifying 'Method = Enter' for each discrete block in the command.
11focus
Identifying if earlier blocks 'soak up' so much variance that the novel predictor has no room left to show its true power.
12focus
Tracing the logic back to the theory-driven modeling traditions established by Cohen and Cohen (1983).
01Hypothesis test logic

Hypotheses

Pragmatic null and alternative hypotheses defined in mathematical notation.

We ask not just 'is there a link?', but 'how much does Y change for every unit of X?'
Logic Core
Null · H₀

H₀: ΔR² = 0 (new block of predictors does not improve model fit)

Alternative · Hₐ

Hₐ: ΔR² > 0 (new block significantly improves model fit beyond previous blocks)

Why it matters incremental

Each block is tested with F-change statistic. Focus is on whether adding new predictors explains significant additional variance beyond what is already explained by previous blocks.

02Model diagnostics

Assumptions

The core mathematical criteria needed to ensure that statistical testing remains unbiased and valid.

Linearity is a strong claim. Nature often curves; ensure your model does not force a straight line on a bent world.
Integrity Shield
7
Assumptions
0
Critical / High Severity
How to check
Create scatterplots of each predictor against the outcome. Examine residual plots (residuals vs. fitted values); look for random scatter around zero. Use component-residual plots (partial regression plots) for each predictor.
If violated
Consider transforming variables (log, square root, polynomial terms). Use generalized additive models (GAM) for non-linear relationships. Add polynomial terms or splines if theoretically justified.
How to check
Examine Durbin-Watson statistic (values around 2 indicate independence; <1 or >3 suggest autocorrelation). Plot residuals in sequence order if data has temporal/spatial structure. Check for clustering in study design.
If violated
Use time series methods (ARIMA, autoregressive models) if temporal dependence exists. Consider multilevel/mixed models if hierarchical data structure (clustered observations). Add time lags or control variables.
How to check
Plot residuals vs. fitted values; look for funnel/cone shapes. Conduct Breusch-Pagan test or White test. Plot absolute/squared residuals against fitted values. Examine scale-location plot.
If violated
Transform the dependent variable (log, square root). Use weighted least squares (WLS) regression. Apply robust standard errors (HC3, HC4). Consider generalized linear models if variance relates to mean structure.
How to check
Create Q-Q plot (quantile-quantile plot) of residuals; points should follow diagonal line. Use Shapiro-Wilk test (n<50) or Kolmogorov-Smirnov test (n>50). Examine histogram of residuals. Note: Less critical with large samples (n>30-40) due to Central Limit Theorem.
If violated
Transform the dependent variable (log, Box-Cox transformation). Remove or down-weight outliers (after investigation). Use bootstrapping for inference. Consider robust regression methods. Note: Violation is less problematic with large samples.
How to check
Calculate Variance Inflation Factor (VIF) for each predictor; VIF > 10 indicates severe multicollinearity, VIF > 5 suggests concern. Examine correlation matrix of predictors (|r| > 0.8-0.9 problematic). Check condition index (>30 indicates collinearity).
If violated
Remove highly correlated predictors (keep theoretically most important). Combine correlated predictors into composite scores (mean, factor analysis, PCA). Use ridge regression or LASSO. Center predictors, especially if using interaction terms.
How to check
Review research literature and theory supporting the hypothesized causal or temporal ordering. Ensure earlier blocks represent established relationships or control variables. Verify that later blocks contain focal predictors or theoretical extensions. Document rationale clearly.
If violated
Do not proceed with hierarchical regression if ordering is arbitrary or solely data-driven (use stepwise regression instead, though with caution). Reconsider theoretical model. Use simultaneous multiple regression if no clear theoretical ordering exists. Consider structural equation modeling (SEM) for complex theoretical models.
How to check
Quick
Apply Green's (1991) rules: N ≥ 50 + 8k for testing overall R² (where k = total predictors in final model), and N ≥ 104 + k for testing individual predictors. For hierarchical tests, ensure N provides power ≥ .80 to detect expected ΔR² for each block.
Rigorous
Conduct a priori power analysis using G*Power or pwr package in R. Specify: (1) expected ΔR² for focal block (small = .02, medium = .13, large = .26), (2) number of predictors in that block, (3) number of predictors already in model, (4) desired power (.80 or .90), (5) alpha (.05). Calculate required N. Power to detect ΔR² is lower than power for overall R², so sample size requirements are often larger than expected.
If violated
Underpowered studies risk: (1) Type II errors (failing to detect real block effects), (2) unstable coefficient estimates (coefficients change substantially across samples), (3) inflated effect sizes when significant results obtained (winner's curse). If sample size is limited: (1) reduce number of blocks or predictors based on theory, (2) combine correlated predictors into composites, (3) report power analysis and interpret non-significant results cautiously, (4) replicate findings before making strong claims, (5) report observed power and effect sizes even for null results to inform meta-analysis and future research.
03Residual Forensics

Diagnostics

Checking residual plots and indices to examine model deviations and ensure standard error integrity.

Trust, but verify. The outliers often hold more truth than the averages.
System Health
Essential checks
  1. R² change significance tests (F-test for ΔR²) for each block
  2. VIF for multicollinearity (final model, all VIF < 10, ideally < 5)
  3. Residual plots: residuals vs. fitted values (check homoscedasticity and linearity)
  4. Q-Q plot of residuals (check normality)
  5. Scale-location plot (check homoscedasticity)
Recommended checks
  1. Durbin-Watson test for independence (values 1.5-2.5 acceptable)
  2. Cook's distance for influential cases (Cook's D > 4/n problematic)
  3. Leverage values (hat values > 3k/n where k=predictors, n=sample size)
  4. DFBETAS for influence on individual coefficients (|DFBETAS| > 2/√n concerning)
  5. Partial regression plots (added-variable plots) for each predictor
  6. Component-residual plots to detect non-linearity
  7. Breusch-Pagan test for heteroscedasticity (p > .05 desired)
  8. Shapiro-Wilk test for normality of residuals (p > .05 desired; less critical with n > 50)
  9. Bootstrap confidence intervals for ΔR² (1000-2000 iterations) to assess stability
04Live Instances

Applied Minds

Review concrete study examples, data layout guidelines, and copy executable syntax scripts.

Theory is the map. Practice is the terrain. Simulation bridges the gap.
Applied Wisdom
Example 01

Testing Incremental Contribution of Motivation Beyond Demographics and SES

Research question: Does student motivation explain significant variance in academic achievement beyond demographic and socioeconomic factors? Block 1: Demographics (age, gender), Block 2: SES (parental education, family income), Block 3: Motivation (intrinsic motivation, academic self-efficacy).

05Tactical Pivots

Alternatives

Structured fallback pathways for choosing alternative tests when normality or slopes requirements fail.

When the path is blocked, pivot. Rigor is not rigidity; it is the intelligent adaptation to reality.
Adaptive Strategy
Measurement Precision Ladder Ideal · Ratio / Interval
Ratio
Maintain Hierarchical logic. Optimal for auditing the unique incremental gain of high-fidelity clinical markers.
Peak Signal
Interval
Ideal for Block-wise Modeling. Ensure Block 1 (Covariates) are centered to simplify interpreting the Intercept.
Standard Precision
Ordinal
Pivot to Hierarchical Ordinal Regression to preserve threshold integrity across blocks.
Precision Loss
Nominal
Abandon Sequential OLS. Use Hierarchical Multinomial models if the outcome is unordered.
Information Suicide
Temporal Trajectory Audit Static Incremental Snapshot
Static Layers
Sequential model audit.
Stay with Hierarchical Regression. Isolate the ΔR² of your primary discovery factor.
Longitudinal Layers
Trajectory growth.
Pivot to Multilevel Modeling (LMM) with sequential block-entry for both fixed and random effects.
Adaptive Technical Safeguards · adaptive safeguards
multicollinearity between blocks
  • Ridge-Augmented Hierarchy — Apply L2 penalties to Block 1 to stabilize the path for Block 2 discovery.
  • PCA Pre-Reduction — Collapse redundant covariates into a single 'Baseline Control' factor.
theory violated
  • Stepwise Regression — Abandon the manual hierarchy for automated statistical selection if theory is absent.
  • All-Subsets Strike — Audit every possible model combination to find the most parsimonious fit.
normality violated
  • Bootstrap ΔR² — Generate significance for the incremental gain using 1,000 resamples.
06Adjusted Comparisons

Post-hoc

Group mean comparisons and correction controls (e.g. Tukey HSD, Bonferroni) to protect against Family-Wise Error Rates.

The omnibus test opens the door; post-hoc analysis explores the room.
Forensic Detail
Adjusted Comparisons
  • Vary order of variable entry to assess robustness
  • Compare with simultaneous (standard) regression
  • Examine tolerance/VIF for multicollinearity at each step
  • Bootstrap confidence intervals for incremental R²
  • Cross-validation to assess predictive improvement
Interpretation Guidelines

Hierarchical regression compares nested models. Post-hoc focuses on model comparison.

07Standardized scale impact

Effect Size

Understanding effect sizes (e.g., Cohen's d, Partial Eta-Squared) and clinical impact benchmarks.

Significance is noise. Magnitude is the signal. Measure the impact, not just the probability.
Impact Magnitude

Proportion of additional variance explained by new block beyond previous blocks. ΔR² = 0.02 (small), 0.13 (medium), 0.26 (large) based on Cohen (1988) guidelines. Always report with 95% CI using bootstrap (1000-2000 iterations) or analytical methods. Example: ΔR² = .15, 95% CI [.08, .24].

Cohen's f² measures local effect size for each block: f² = ΔR²/(1-R²_full) where R²_full is final model R². Interpretation: f² = 0.02 (small effect), 0.15 (medium effect), 0.35 (large effect). f² represents variance explained by focal block relative to unexplained variance. Less influenced by overall model R² than ΔR² alone.

Standardized regression coefficient (β) represents effect of one SD change in predictor on DV in SD units, holding all other predictors constant. |β| = 0.10 (small), 0.30 (medium), 0.50 (large). Report with 95% CI. β coefficients can change substantially across blocks as new predictors are added—this is informative for understanding mediation and redundancy.

Semi-partial correlation squared (sr²) represents unique variance explained by a predictor beyond all other predictors. Sum of all sr² values ≤ R². sr² is always ≤ standardized β². Useful for partitioning variance contributions among predictors within a block.

Partial R² represents variance explained by a predictor after controlling for all other predictors. Larger than sr² because it doesn't include variance shared with other predictors. Answers: 'How much would R² drop if this predictor were removed from the full model?'

Recommended Metric: Report both ΔR² (with 95% CI) and Cohen's f² for each block; report standardized β (with 95% CI) for all predictors in final model
Small
0.2
Medium
0.5
Large
0.8
0.50
Report both ΔR² (with 95% CI) and Cohen's f² for each block; report standardized β (with 95% CI) for all predictors in final model
Recommended Measure
5
Available Metrics
ReportUse Report both ΔR² (with 95% CI) and Cohen's f² for each block; report standardized β (with 95% CI) for all predictors in final model to represent clinical impact magnitude.
08Statistical Power

Sample Size

Guidelines for minimum sample requirements and power analysis parameters.

An underpowered study is an ethical failure. Respect the data by collecting enough of it.
Power Protocol
Floor Requirements

The 'Incremental Mandate': A minimum of 15 participants per predictor in the *final* block is essential. Adding new layers to an underpowered model will only hide the signal in the noise of the previous blocks.

Effect SizeParametersRequired n
Small EffectΔR² = .02 (Small)n ≈ 600 total
Medium EffectΔR² = .10 (Medium)n ≈ 110 total
Large EffectΔR² = .25 (Large)n ≈ 45 total
Key considerations

The 'Covariate Soak': If Block 1 already explains 80% of the variance, Block 2 will struggle to achieve power even if it contains a powerful predictor. Audit the 'Unique Contribution' before committing to a massive recruitment plan.

G*Power StrategyBenchmark: F-tests → Linear Regression: R² change. Parameters: Block 1 predictors (k1), Block 2 predictors (k2), Incremental ΔR², α = .05, Power = .80. Note: Power is defined as the detection of the 'Predictive Breakthrough' in the new layer.
09APA narrative blueprint

Reporting

How to compile statistical results into publication prose matching APA and journal style guides.

The Beta coefficient is the currency of change. Interpret it in real-world units, not just standardized abstractions.
Narrative Arc
10Exhibit Builder

Manuscript Lab

Copy standard summary tables and forensic reporting grids to outline analysis details.

Table 1: Hierarchical Regression: Predicting Performance
Model StepR²Adj R²ΔR² (Change)F Changep (Change)
Step 1: Demographics.12.10.125.42.006
Step 2: + Intervention.35.31.2318.50< .001
Note. Step 1: Controls. Step 2: Main Predictors. N = 120.
ΔR² = .23Crucial finding. The Intervention added 23% explanatory power over and above demographics, proving its unique contribution.
Header glossary

The Value Add. The specific percentage of variance explained by the NEW variables added in this step.

The Gatekeeper. Tests if the improvement in model fit is statistically significant.

11Algorithmic Logic

Command Center

Syntax libraries and function parameters for executing calculations in stats packages.

Code your model to handle residuals. The errors tell you what your model missed.
Execution Engine
# 1. Fit Nested Models
m1 <- lm(y ~ age + gender, data=df)
m2 <- lm(y ~ age + gender + intervention, data=df)

# 2. Compare Models (F-test for R2 Change)
anova(m1, m2)
Library stack
R
statsolsrr
Python
statsmodels
Elite Forensic Strike

Hierarchical regression assumes a theoretical order of entry. Do not use 'Stepwise' (automated) selection unless you want to be rejected by top journals.

# Generate Full APA Table with Blocks
apaTables::apa.reg.table(m1, m2, filename = 'hierarchical.doc')
12The Over-adjustment Trap

Common Mistakes

Analytical caveats and corrections to maintain modeling integrity.

Wisdom is learning from the failures of others. Anticipate the error before it occurs.
Defensive Logic
Why it's wrong
Hierarchical regression requires theoretical justification for the ordering of blocks. Entering predictors based on which produces the largest R² increment is capitalizing on chance and invalidates the theoretical interpretation. If you test multiple orderings and choose the 'best' one based on the data, you're engaging in p-hacking—inflating Type I error and producing non-replicable results.
The correction
Establish block order a priori based on theory, temporal sequence, or established relationships. Document the rationale clearly in your pre-registration or methods section. Common orderings: (1) Demographics → SES → Psychological, (2) Established predictors → Novel predictors, (3) Distal factors → Proximal factors, (4) Time-ordered (earlier variables → later variables). If no theoretical ordering exists, use simultaneous multiple regression instead.
Why it's wrong
The key question in hierarchical regression is whether each new block adds significant variance beyond previous blocks. Reporting only final model R² obscures the incremental contributions that motivated the hierarchical approach. Reviewers and readers cannot evaluate whether your focal predictors truly add value beyond controls. This also prevents meta-analysis of your findings.
The correction
Report R², ΔR², and F-change (with df and p-value) for each block entry. Provide effect sizes (f²) for theoretically important blocks. Create a summary table showing the progression across blocks: Block | Predictors | R² | ΔR² | F-change | df | p-value. Include 95% CIs for ΔR² when possible. Report whether each F-change meets your alpha threshold.
Why it's wrong
A non-significant F-change means the new block does not explain significant additional variance beyond previous blocks. Some researchers incorrectly focus only on whether individual predictors in that block are significant in the final model, ignoring the block test. This confuses omnibus tests (does the block contribute as a whole?) with individual predictor tests (is each predictor uniquely significant?).
The correction
When F-change is non-significant, conclude that the block as a whole does not contribute meaningfully, regardless of individual predictor p-values. Individual coefficients test unique effects controlling for all other predictors (including those within the same block), not block contributions. If your focal block shows non-significant F-change, report this honestly rather than cherry-picking significant individual predictors. Discuss power and effect size (f²) to distinguish 'no effect' from 'insufficient power.'
Why it's wrong
Coefficients of predictors in earlier blocks often change (sometimes becoming non-significant or even reversing sign) when later blocks are added. This pattern provides important information about mediation, suppression, or confounding, but is often overlooked. Failing to examine coefficient changes misses key insights into mechanism and causal structure.
The correction
Compare coefficients across models systematically. Create a coefficient comparison table showing how each predictor's β, SE, t, and p-value change across blocks. Discuss substantive meaning: (1) If control variables' effects diminish substantially (>30-50% reduction) after adding focal predictors → suggests mediation or redundancy, (2) If coefficients increase → suggests suppression, (3) If signs reverse → indicates confounding or multicollinearity. Report percentage changes in standardized coefficients. Consider formal mediation analysis if substantial reductions observed.
Why it's wrong
When blocks share substantial variance (e.g., two different measures of SES entered in separate blocks, or highly overlapping constructs), the incremental variance explained by the second block will be artificially small, not because it's unimportant theoretically, but because multicollinearity has absorbed the shared variance. This can lead to Type II errors (missing genuine effects) and unstable coefficients (inflated standard errors).
The correction
Check VIF values and correlations between predictors across blocks before finalizing block structure. If VIF > 10 or inter-block correlations r > .70-.80, consider: (1) Combining highly correlated predictors into composites (factor scores, mean scores), (2) Dropping redundant predictors based on theory, (3) Using structural equation modeling (SEM) to explicitly model shared and unique variance, (4) Reporting that multicollinearity limits ability to distinguish block contributions. Never enter nearly identical measures in separate blocks.
Why it's wrong
Hierarchical regression establishes incremental prediction, not causation. Even with theoretically motivated ordering based on causal assumptions, cross-sectional designs cannot establish temporal precedence or rule out alternative explanations (reverse causation, third variables, bidirectional effects). Using causal language ('X affects Y,' 'X influences Y,' 'X produces changes in Y') misrepresents what the analysis can establish.
The correction
Use causal language carefully and accurately. Frame findings in terms of: 'explains additional variance,' 'predicts beyond,' 'contributes uniquely to,' 'is associated with incremental,' or 'accounts for variance beyond.' Acknowledge observational limitations explicitly. For stronger causal claims: (1) Use longitudinal designs measuring predictors before outcomes, (2) Employ experimental manipulation for focal predictors, (3) Use matching or propensity scores to address confounding, (4) Conduct sensitivity analyses for unmeasured confounders. Always include limitations section discussing alternative causal interpretations.
Why it's wrong
Assumption violations in the final model (non-linearity, heteroscedasticity, multicollinearity, influential outliers) compromise all model comparisons and effect estimates, yet many analysts only check assumptions after noting problems or skip diagnostics entirely. All F-change tests, coefficient estimates, and p-values are invalid if assumptions are violated. Multicollinearity is especially common in hierarchical models as predictors accumulate.
The correction
Conduct full assumption diagnostics on the final model BEFORE interpreting any block comparisons: (1) Linearity: component-residual plots for each predictor, (2) Independence: Durbin-Watson test (should be ~2.0), check for clustering, (3) Homoscedasticity: Breusch-Pagan test, residuals vs. fitted plot (no funnel shapes), (4) Normality: Q-Q plot, Shapiro-Wilk test (less critical if n > 50), (5) Multicollinearity: VIF < 10 for all predictors, (6) Influential cases: Cook's D < 4/n. Report all diagnostic results. If violations found, address them (transformations, robust SEs, remove outliers with justification) and rerun analyses before interpreting.
Why it's wrong
Hierarchical regression requires adequate power to detect meaningful ΔR² values, not just overall R². Small samples may have sufficient power for overall model R² but insufficient power to detect incremental contributions of later blocks, especially if ΔR² is small (e.g., .02-.05). Non-significant F-change may reflect low power rather than true absence of effect. Researchers often conclude 'no effect' when underpowered.
The correction
Conduct a priori power analysis specifically for ΔR² (not just overall R²). Use G*Power or pwr package in R: specify expected ΔR² for focal block, number of predictors in that block, number of predictors in previous blocks, desired power (.80-.90), and alpha (.05). Rule of thumb: N > 104 + k (k = total predictors) for medium ΔR² at 80% power. If post-hoc power is low (<.60) and F-change is non-significant, report: 'F-change was non-significant, but power to detect a small-to-medium effect was limited (post-hoc power = X). The null finding should be interpreted cautiously.' Report observed ΔR² and f² even if non-significant to inform meta-analysis.
13Academic Lineage

References

Scholarly lineage and citation keys grounding the statistical framework.

We stand on the shoulders of giants. Honor the source of the method.
Academic Lineage
[1]
Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Routledge.
Comprehensive treatment of hierarchical regression, effect sizes, and model building strategies.
doi: 10.4324/9780203774441
[2]
Petrocelli, J. V. (2003). Hierarchical multiple regression in counseling research: Common problems and possible remedies. Measurement and Evaluation in Counseling and Development, 36(1), 9-22.
Discusses common mistakes and best practices in hierarchical regression applications.
doi: 10.1080/07481756.2003.11909717
[3]
Wampold, B. E., & Freund, R. D. (1987). Use of multiple regression in counseling psychology research: A flexible data-analytic strategy. Journal of Counseling Psychology, 34(4), 372-382.
Early influential paper on hierarchical model building and interpretation.
doi: 10.1037/0022-0167.34.4.372
[4]
Green, S. B. (1991). How many subjects does it take to do a regression analysis? Multivariate Behavioral Research, 26(3), 499-510.
Essential reference for sample size planning in regression analyses.
doi: 10.1207/s15327906mbr2603_7
[5]
Pedhazur, E. J. (1997). Multiple regression in behavioral research: Explanation and prediction (3rd ed.). Thomson Learning.
Classic comprehensive text covering hierarchical regression theory and applications.
A significant predictor is good; a significant R² change is elite. Prove that your discovery adds something that the world didn't already know.
The Interpretive Rigor Directive
statminds · HierarchicalMind reference · v2.2 · updated 2026-01-1715 of 15 sections