Specialized Tools
Beyond the general means/proportions/correlation calculators, the module includes specialised sample-size tools for designs with their own distinct methodology: animal experiments, prevalence surveys, survival analysis, ROC curves, and repeated-measures ANOVA.
Mead's Method for Animal Experiments
For animal and preclinical studies where ethical and cost constraints make minimising animal numbers a priority. Uses Mead's resource equation rather than conventional effect-size power calculation.
The resource equation:
E = N - B - T
df_error (E) = total - 1 - df_treatment - df_blocking
df_treatment = number of groups - 1
The optimal range: searches per-group size (n from 2 upward) for smallest design with error df between 10 and 20:
| Error df (E) | Verdict |
|---|---|
| 10-20 | Optimal |
| > 20 (or >= 10 when 10-20 can't be hit) | Sufficient |
| < 10 | Potentially insufficient |
Fallback: smallest design with E >= 10, or per group = ceil((10 + 1 + df_treatment + df_blocking) / number of groups).
When a reliable effect size is unavailable (common in early preclinical work), the resource equation provides a defensible sample size based on achieving adequate error degrees of freedom.
Survey Sample Size (Prevalence Studies)
For prevalence and survey studies -- estimating proportion of a population with some characteristic to within a target precision.
Inputs: expected prevalence (p), margin of error, confidence level, optionally population size.
Formula (infinite population):
d = margin of error / 100
z = normal quantile at (1 - (1 - confidence/100)/2)
n = ceil( z^2 * p * (1-p) / d^2 )
Finite population correction (when population size N supplied):
n_adjusted = ceil( (n * N) / (n + N - 1) )
Reduces required sample when population is small relative to sample. Labels precision based on margin of error (< 5% = high, < 10% = moderate).
Sample Size for Survival Analysis (Hazard Ratio)
For time-to-event/survival studies comparing two groups via hazard ratio, using the event-driven Schoenfeld approach.
Inputs: target hazard ratio, probability of event occurring, power, alpha.
Formula:
events needed = (z_alpha + z_beta)^2 * 4 / (ln(HR))^2
total sample size = ceil( events needed / event probability )
per group = ceil( total sample size / 2 )
Power depends on number of events, not number of participants. A study with few events (low event probability) needs many participants.
Interpretation:
| Hazard ratio | Label |
|---|---|
| < 0.5 | Strong treatment effect (large hazard reduction) |
| 0.5 - 0.75 | Moderate treatment effect |
| 0.75 - 1.0 | Small treatment effect |
| > 1.5 | Strong increased risk |
| 1.0 - 1.5 | Increased risk |
Sample Size for ROC Curve (AUC)
For diagnostic-accuracy studies estimating or testing area under the ROC curve, using Hanley and McNeil variance method.
Inputs: null AUC, alternative (target) AUC, ratio of controls to cases, power, alpha.
Method (Hanley-McNeil AUC variance):
Q1 = AUC / (2 - AUC)
Q2 = 2*AUC^2 / (1 + AUC)
variance = [AUC(1-AUC) + (ratio-1)(Q1-AUC^2) + (ratio-1)(Q2-AUC^2)] / ratio
Variances under null and alternative AUC feed sample-size formula, yielding cases needed with controls = ceil(cases * ratio).
Correctly accounts for non-normal sampling distribution of AUC and correlation structure from using same cases/controls across the curve.
Repeated Measures ANOVA
For within-subject designs where same subjects are measured under multiple conditions or time points.
Method: computes repeated-measures ANOVA from supplied measurements:
df_between = k - 1 (k = number of measurements/conditions)
eta2 = SS_between / SS_total
Includes sphericity assessment -- when violated, degrees of freedom are corrected before computing p-value. Reports F-value, corrected p-value, and eta-squared as effect size.
Summary of specialized methods
| Tool | Core method |
|---|---|
| Mead's Method | Resource equation (error df in 10-20) |
| Prevalence Survey | Proportion precision + finite population correction |
| Survival (HR) | Schoenfeld event-driven formula |
| ROC (AUC) | Hanley-McNeil AUC variance |
| Repeated Measures ANOVA | Within-subject ANOVA with sphericity correction |
Choosing the methodology matching your design is essential -- a general means or proportions calculator would not correctly size an animal experiment, survival study, or diagnostic-accuracy study.