Sample Size CalculatorStatistical Methods Guide
Concepts, procedure selection, required inputs, and formulae for planning sample size and statistical power
Core Concepts
Review the statistical choices and assumptions that shape a defensible sample-size plan.
Common Planning Pitfalls
- Using unrealistic effect sizes (too optimistic)
- Ignoring dropout/attrition rates
- Not accounting for unequal group sizes
- Forgetting to adjust for multiple comparisons
- Using wrong test for study design
- Inadequate pilot data for parameter estimates
Statistical Analysis Framework
Understanding the fundamentals of statistical analysis and sample size determination
Sample Size Determinants
Questions to be answered to know how to calculate the sample size:
Type of statistical analysis:
Type of analytical statistics:
Type of the Outcome variable and the risk factor:
Areas of Statistics
There are two main areas of Statistics:
Descriptive statistics
Provides tabular and graphical techniques and numerical measures for describing data.
Analytical (Inferential) statistics
Provides procedures for analyzing data and making decisions. Using the sample to infer about the population (parameter).
Types of Inferential Statistics
Estimation
The answer for the research question is a value or a range of values (Confidence interval)
Example:
"What is the prevalence of Diabetes in a certain population?"
Hypothesis testing
The data may provide enough evidence to reject the null hypothesis; otherwise, fail to reject it. A non-significant result does not prove the null is true.
Example:
"Is there a significant difference in the prevalence of Diabetes between males and females in a certain population?"
Types of Variables
Understanding variable types is crucial for selecting the appropriate statistical test
Variables can be classified into two main categories:
Qualitative (Categorical)
Labels or names used to identify attributes of the sample elements. The labels can be numbers with no real numerical meaning.
It has only two categories or levels
Appropriate Tests:
- • Chi-Square Test
- • Fisher's Exact Test
- • McNemar's Test (paired)
- • One/Two-Proportion Z-Test
- • Logistic Regression
- • Odds Ratio (case-control)
- • Relative Risk (cohort)
The order of the categories is not essential (no ranking)
Appropriate Tests:
- • Chi-Square Test of Independence
- • Chi-Square Goodness of Fit
- • Multinomial Logistic Regression
- • Fisher's Exact Test (small samples)
The categories can be ordered
Appropriate Tests:
- • Mann-Whitney U Test
- • Wilcoxon Signed-Rank Test
- • Kruskal-Wallis Test
- • Spearman Correlation
- • Ordinal Logistic Regression
- • Cochran-Armitage Trend Test
- • Jonckheere-Terpstra Test
Quantitative (Numerical)
Numbers (with real meaning), representing measurements, obtained from the sample elements.
Is measured on a numeric or a quantitative scale and can take countable values (how many)
Appropriate Tests:
- • Poisson Regression
- • Negative Binomial Regression
- • Chi-Square Test (when grouped)
- • Mann-Whitney U (non-parametric)
- • Kruskal-Wallis (non-parametric)
- • Can also use tests for continuous data if assumptions met
Is measured on a numeric or a quantitative scale and can take uncountable real values (how much)
Appropriate Tests:
- • One-Sample t-Test
- • Two-Sample t-Test
- • Paired t-Test
- • ANOVA (One-Way, Two-Way)
- • Linear Regression
- • Pearson Correlation
- • ANCOVA
- • Time-to-event outcomes require survival methods that account for censoring
- • Outcomes counted over time — exacerbations, falls, admissions — are compared as rates over person-time, not as single measurements
Sampling designs: simple, stratified and clustered
How the people in a survey are chosen changes how many are needed. Stratification and clustering are separate choices, and a survey can use either, both or neither.
Simple random sample
Everyone in the population has the same chance of selection, independently.
n = z² × variance / E²
The baseline every other design is compared with.
Stratified sample
The population is divided into strata, such as regions or urban and rural areas, and every stratum is sampled.
DE_w = Σ W_h² / a_h
Sampling in proportion to the population costs nothing (DE_w = 1). Giving small strata more than their share, to report on them, weights respondents unequally and costs the combined estimate DE_w > 1.
Cluster sample
Groups such as villages, schools or clinics are sampled first, then people within them.
DE = 1 + (m − 1) × ICC
People in the same cluster resemble each other, so each adds less information: the sample grows by the design effect, more so for large clusters.
- Both together: clusters sampled inside every stratum, as most national surveys do. The two design effects multiply, and each stratum needs at least two clusters.
- A figure for every stratum, not just the national one, means sizing each stratum as its own survey. It usually costs far more people; the national estimate then comes out more precise than needed.
- Finite populations: with strata, each stratum carries its own finite-population correction. With clusters, the correction belongs to the clusters (1 − c/C), and matters only when a large share of all clusters is sampled.
- Stratified randomisation in a trial is a different idea: it balances the arms and barely changes the sample size.
In the calculator, open “Estimate precisely”, choose one mean, proportion, median, paired difference or category proportions, and tick “Stratified sampling”, “cluster sampling”, or both. The formulas and worked examples are in Sample size for a stratified survey
Find a Suitable Statistical Procedure
Tell us what you want to measure and compare. We suggest a starting method and explain what to check.
Step 1
1Planning goal
Estimate a value, such as prevalence or an ICC, or test a hypothesis, such as a difference between groups or that reliability exceeds a benchmark.
The shortlist will narrow the options. Pairing, repeated measurements, clustering, censoring, sampling, and model assumptions can still change the appropriate method.