Purpose

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This workflow turns a dissertation question into a transparent sample-size and recruitment plan. It combines prospective power, minimum detectable effects, precision, attrition adjustment, clustered and longitudinal designs, and simulation-based planning. The goal is not one authoritative number. The goal is a defensible set of scenarios whose assumptions can be examined, revised, and reported.

Plan the analysis you will run. A power calculation is only as relevant as the estimand, model, decision rule, outcome scale, dependence structure, missing-data process, and effect assumptions it represents. Generic conventions and software defaults are not substitutes for design reasoning.

Learning outcomes

After completing the workflow, users should be able to:

  • distinguish prospective power, design sensitivity, and precision planning;
  • express a smallest effect of interest in original and standardized units;
  • document evidence and uncertainty for every planning assumption;
  • translate analyzable sample size into a staged recruitment target;
  • plan individual-level, clustered, longitudinal, and indirect-effect analyses;
  • create power, precision, and sensitivity displays rather than report one number;
  • quantify Monte Carlo uncertainty in simulation-based power; and
  • generate dissertation-ready planning language with explicit limitations.

User settings

Planning intake and assumptions register

Define the target

Before calculating sample size, complete Templates/planning-intake.csv. The focal parameter should match the planned dissertation claim. An omnibus test does not plan a specific interaction, indirect effect, simple contrast, or subgroup comparison.

Assumptions register for the worked examples
assumption value plausible_low plausible_high source rationale status
Primary effect 3.00 NA NA User supplied Define in original outcome units before standardizing Required
Outcome SD 10.00 NA NA Prior study or pilot Use a range when the estimate is uncertain Required
Alpha 0.05 0.01 0.05 Analysis plan Allocate across confirmatory tests if needed Required
Target power 0.80 0.80 0.90 Analysis plan Not a universal adequacy threshold Required
Attrition rate 0.15 0.05 0.30 Feasibility evidence Model stages separately where possible Required
Intraclass correlation 0.08 NA NA Comparable studies Required for clustered designs Conditional

Choose a planning mode

Mode Known Solves for Appropriate interpretation
Prospective power Effect, alpha, design Sample size or power Probability of the prespecified decision under the assumed alternative
Sensitivity Feasible sample, alpha, power Minimum detectable effect Effects the proposed design is calibrated to detect
Precision Variability and target interval width Sample size Expected estimation precision
Simulation Full data-generating and analysis process Power, bias, failures Operating characteristics under explicit scenarios
Recruitment Analyzable requirement and loss stages Invitations or clusters Operational target under staged retention assumptions

Do not calculate “observed power” from the final sample estimate. Once results exist, report estimates and confidence intervals. A completed design can be described using a prespecified sensitivity analysis, but the result should not be used to rescue a nonsignificant finding.

Basic-design reference scenarios

Illustrative basic-design calculations
design planning_effect required_analyzable_n notes
Correlation r = .20 194 Two-sided test
Two independent proportions 60% versus 50% 776 Equal group sizes
Balanced four-group ANOVA Cohen f = .25 180 Omnibus effect; plan focal contrasts separately

These reference scenarios demonstrate the common analytic calculators. Replace their conventional-looking values with a smallest effect of interest and plausible nuisance parameters. For ANOVA, a focal contrast or interaction normally deserves its own calculation or simulation.

Example 1: Two-group intervention

Primary calculation

The first example plans a continuous posttest comparison adjusted for baseline. The baseline-outcome correlation reduces residual variance only when the planned analysis actually includes baseline appropriately and the assumed relationship is realistic.

Two-group analyzable sample-size plan
design estimand effect effect_scale alpha target_power n_group1 n_group2 analyzable_n details
Two-group ANCOVA approximation Adjusted mean difference 3 Outcome units 0.05 0.8 123 123 246 Residual SD=8.352; standardized effect=0.359

Sensitivity curve

Precision comparison

Precision-based comparison
target planning_value half_width required_n
Mean in outcome units 10.0 1.50 171
Proportion near .50 0.5 0.05 385
Correlation near .30 0.3 0.10 320

Power and precision answer different questions. When both a hypothesis test and an estimate must be useful, plan for the larger requirement or explain the compromise.

Recruitment waterfall

Recruitment assumptions and expected counts
stage expected_n stage_rate cumulative_rate
Invited 539 NA 1.000
Eligible 458 0.85 0.850
Consented 321 0.70 0.595
Baseline complete 305 0.95 0.565
Retained 259 0.85 0.480
Analytically usable 246 0.95 0.456

A single unexplained attrition inflation hides important operational assumptions. Eligibility, consent, baseline completion, retention, and analytic usability should be supported separately.

Example 2: Incremental regression

Focal change in explained variance

Power plan for a focal predictor added after covariates
design estimand effect effect_scale alpha target_power analyzable_n details
Multiple regression Incremental R-squared 0.035 Delta R-squared 0.05 0.8 178 Total R2=0.25; f2=0.047; predictors=8

Detectable-effect curve

Collinearity, measurement reliability, missing predictors, nonlinear terms, interactions, and data-dependent variable selection can all reduce effective information. A coefficient-level simulation is preferable when the predictor distribution and covariance structure are central.

Factorial interaction planning

Simulation-based factorial interaction power
n_per_cell total_n power mcse replications
20 80 0.070 0.018 200
40 160 0.145 0.025 200
60 240 0.160 0.026 200
80 320 0.305 0.033 200
100 400 0.325 0.033 200

Factorial plans should use plausible cell means or contrasts, within-person correlations for repeated factors, allocation ratios, multiplicity rules, and the exact interaction or planned contrast that supports the dissertation claim.

Example 3: Students nested within schools

Primary clustered plan

Clustered design plan
design estimand effect effect_scale alpha target_power clusters_per_arm total_clusters cluster_size analyzable_n design_effect details
Two-arm cluster trial Marginal mean difference 3 Outcome units 0.05 0.8 16 32 24 768 3.013 ICC=0.08; cluster-size CV=0.3

Cluster and student tradeoff

The design-effect approximation is a transparent starting point, not the final word for few clusters, random slopes, binary outcomes, treatment-by-context effects, informative cluster sizes, or complex small-sample corrections. Those designs require a model-matched simulation and a credible minimum number of clusters.

Example 4: Longitudinal and daily-diary planning

Repeated change

Approximate longitudinal change plan
design estimand effect effect_scale alpha target_power analyzable_n waves details
Two-group longitudinal change Difference in change 2.5 Outcome units 0.05 0.8 328 4 SD change=8.05; within-person r=0.6

Correlation and attrition sensitivity

For daily diary studies, total records are not independent sample size. The full simulation should vary people, planned days, compliance, time-varying predictor variance, random slopes, serial dependence, missing lags, and the exact mixed model. The included module is a planning bridge to the existing Daily Diary product.

Daily-diary demonstration

Daily-diary simulation with Monte Carlo uncertainty
participants planned_days power mcse replications failures
50 14 0.983 0.017 60 0
80 14 1.000 0.000 60 0
110 14 1.000 0.000 60 0
140 14 1.000 0.000 60 0

Example 5: Indirect effect by simulation

Simulation power curve

Simulation-based indirect-effect power
n power mcse replications failures
100 0.184 0.025 250 0
200 0.748 0.027 250 0
300 0.948 0.014 250 0
400 0.992 0.006 250 0
500 1.000 0.000 250 0

This runnable demonstration uses a normal-theory indirect-effect decision rule to keep rendering time practical. A final study-specific plan should simulate the intended estimator and confidence interval, measurement reliability, covariates, nonnormality, missingness, and temporal design. The report must include replications, Monte Carlo uncertainty, convergence failures, and the seed.

SEM global-fit planning

Illustrative SEM RMSEA-based planning scenarios
df rmsea_alternative required_n implied_power
12 0.05 579 0.800
24 0.05 375 0.799
48 0.05 249 0.801

Global-fit power is not coefficient power. A dissertation whose claim concerns a path, indirect effect, factor loading, invariance restriction, or latent mean difference should plan that focal parameter directly. SEM simulations should report convergence, improper solutions, estimator, nonnormality, missingness, reliability, and model misspecification.

Combined scenario summary

Primary planning scenarios
scenario_id design estimand effect effect_scale alpha target_power analyzable_n timestamp n_group1 n_group2 details clusters_per_arm total_clusters cluster_size design_effect waves
S001 Two-group ANCOVA approximation Adjusted mean difference 3.000 Outcome units 0.05 0.8 246 2026-09-25 14:55:56.589281 123 123 Residual SD=8.352; standardized effect=0.359 NA NA NA NA NA
S002 Multiple regression Incremental R-squared 0.035 Delta R-squared 0.05 0.8 178 2026-09-25 14:55:56.589281 NA NA Total R2=0.25; f2=0.047; predictors=8 NA NA NA NA NA
S003 Two-arm cluster trial Marginal mean difference 3.000 Outcome units 0.05 0.8 768 2026-09-25 14:55:56.589281 NA NA ICC=0.08; cluster-size CV=0.3 16 32 24 3.013 NA
S004 Two-group longitudinal change Difference in change 2.500 Outcome units 0.05 0.8 328 2026-09-25 14:55:56.589281 NA NA SD change=8.05; within-person r=0.6 NA NA NA NA 4

Dynamic dissertation-ready text

The planned two-group analysis tests an adjusted mean difference of 3 outcome points. Assuming an outcome standard deviation of 10, a baseline-outcome correlation of 0.55, a two-sided alpha of 0.05, equal allocation, and target power of 0.8, the analytic approximation requires 246 analyzable participants (123 per group). Under the staged eligibility, consent, baseline-completion, retention, and usability assumptions, the operational target is approximately 539 invitations. The sensitivity analysis shows that this recommendation depends most strongly on the smallest effect of interest and the baseline-adjusted residual variance.

For the clustered education example, a mean difference of 3 points, outcome standard deviation of 12, ICC of 0.08, average cluster size of 24, and cluster-size coefficient of variation of 0.3 produced a planning requirement of 32 schools and 768 students. This approximation should be replaced by a model-specific simulation when the final cluster structure and analysis are known.

Reporting checklist

  • Identify the focal estimand, model, decision rule, alpha, sidedness, and confirmatory status.
  • Define the smallest effect of interest in original units before translating it to a standardized effect.
  • Cite or document the source and plausible range for every effect and nuisance parameter.
  • Present low, expected, and high scenarios rather than one exact sample size.
  • Separate analyzable sample size from invitations, consent, retention, and usable-data targets.
  • Respect clustering, repeated observations, allocation imbalance, missingness, and multiplicity.
  • Report simulation replications, seed, Monte Carlo uncertainty, convergence failures, and inadmissible solutions.
  • Explain whether the plan targets hypothesis-test power, effect precision, or both.
  • Recalculate the plan if the design, primary outcome, analysis model, or decision rule changes.
  • After data collection, report estimates and confidence intervals rather than observed power.

When this workflow is not enough

Seek design-specific support for adaptive, sequential, noninferiority, equivalence, diagnostic-accuracy, high-stakes regulatory, rare-event, complex-survey, network, spatial, intensive-time-series, mixture, or highly parameterized latent-variable designs. Statistical power does not repair poor measurement, confounding, selection bias, treatment contamination, weak manipulation, or an analysis that does not answer the research question.

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