Using Statulator: Sample Size for Estimating a Single Proportion

Mayta
May 2
2 min read

🎯 When to Use This Calculator

This calculator is built for descriptive study designs, where your goal is to estimate a single population proportion with a specific level of confidence and precision.

Think:

Prevalence of symptoms
Proportion of adherence
Uptake of a health behavior

No comparison groups, no hypothesis testing — just precise description of "how common is this?" in your population.

🧪 Formula Behind the Calculation

Statulator relies on this foundational equation:

This ensures your confidence interval is tight enough to support clinical or policy decisions.

🧾 How to Use Statulator’s Single Proportion Tool

Input on Statulator	What It Means	Example Entry
Level of Confidence	How sure you want to be in your estimate	0.95 (95% CI is standard)
Expected Proportion (p)	Your best estimate of the true population rate	0.40 (based on pilot/literature)
Margin of Error (d)	How precise you want your estimate (±d) to be	0.04 for ±4%

📊 Example Scenario

🏥 Clinical Context

You’re conducting a baseline needs assessment at a community mental health center. You want to estimate how many patients have unmet needs for psychotherapy, defined as screening positive for distress but not currently receiving treatment.

🎯 Study Objective (Descriptive)

"To estimate the proportion of patients with unmet psychotherapy needs among adults presenting to a community mental health center, with a 95% confidence level and ±4% margin of error."

🔢 Assumptions

Expected proportion of unmet need: 40%
Desired precision: ±4%
Confidence level: 95%

✅ Input into Statulator

Level of Confidence: 0.95
Expected Proportion: 0.40
Precision or Margin of Error: 0.04

Click "Calculate", and Statulator will provide the required sample size, likely somewhere around 577 participants (depending on final rounding).

🔁 Optional Adjustments

Click the “Adjust” button if you want to:

Add a design effect (e.g., if patients are clustered by provider)
Account for non-response (e.g., 80% expected response rate → multiply by 1.25)
Apply finite population correction (useful if your sampling frame is ≤1,000 people)

🧠 Key Concepts Recap

Higher confidence level (α) = wider Z = larger n
Smaller margin of error (d) = tighter CI = larger n
p = 0.5 yields the largest sample (most conservative)
Adjustment factors help tailor n to your field conditions

💡 What If You Don’t Know the Expected Proportion?

If no prior data exist:

Use 0.5 → maximizes required sample size
Safer if you want to avoid underpowering your descriptive analysis

📋 Summary Workflow

Define your descriptive aim — “what proportion are we estimating?”
Set your best-guess proportion based on existing data or expert consensus
Choose your desired margin of error (e.g., ±5% or ±3%)
Set the confidence level — default is 95%
Calculate using Statulator
Adjust for design effect or expected non-response