How to Calculate Sample Size for Your Research Study

One of the most common questions researchers face is: "How many participants do I need?" Too few participants and your study lacks the power to detect real effects. Too many and you waste time and resources. Sample size calculation — also called power analysis — gives you the answer before you collect any data.

Why Sample Size Matters

An underpowered study is a wasted study. If your sample is too small:

Real effects may go undetected (Type II error)
Confidence intervals will be too wide to be useful
Results will be unreliable and difficult to replicate
Your thesis committee or journal reviewers will flag it

An overpowered study (too large) is less common but also problematic — it detects trivially small effects that have no practical significance, and it wastes resources.

Key Concepts

Before calculating sample size, understand these four interconnected components:

1. Effect Size

How large is the difference or relationship you expect to find?

Small: A subtle effect (e.g., Cohen's d = 0.2, r = .10)
Medium: A noticeable effect (e.g., Cohen's d = 0.5, r = .30)
Large: A substantial effect (e.g., Cohen's d = 0.8, r = .50)

Where do you get the expected effect size?

From previous studies in your field (the best source)
From pilot data you collected
Using Cohen's conventions as defaults (d = 0.5 is a common starting point)

2. Statistical Power (1 - β)

The probability of detecting an effect if it truly exists.

Standard target: 80% (β = .20)
Stricter target: 90% or 95% for clinical or high-stakes research
80% power means a 20% chance of missing a real effect

3. Significance Level (α)

The probability of a false positive (Type I error).

Standard: α = .05 (5% risk of false positive)
Stricter: α = .01 for multiple comparisons or confirmatory research

4. Sample Size (N)

This is what you are solving for, given the other three components.

The relationship: Larger effect sizes need fewer participants. Higher power or stricter alpha require more participants.

Sample Size for Common Statistical Tests

Independent Samples T-Test

Comparing two group means.

Effect Size (d)	Power 80%	Power 90%	Power 95%
0.2 (small)	394 per group	526 per group	651 per group
0.5 (medium)	64 per group	86 per group	105 per group
0.8 (large)	26 per group	34 per group	42 per group

One-Way ANOVA (3 groups)

Comparing three or more group means.

Effect Size (f)	Power 80%	Power 90%
0.10 (small)	969 total	1,299 total
0.25 (medium)	159 total	213 total
0.40 (large)	66 total	87 total

Pearson Correlation

Testing the relationship between two continuous variables.

Effect Size (r)	Power 80%	Power 90%
.10 (small)	782	1,046
.30 (medium)	85	112
.50 (large)	29	37

Multiple Regression

Predicting an outcome from multiple predictors.

The required sample size depends on the number of predictors. Common rules of thumb:

Minimum: N ≥ 50 + 8 × (number of predictors) — for testing the overall model (Green, 1991)
For individual predictors: N ≥ 104 + (number of predictors)
Conservative: N ≥ 20 × (number of predictors)

For 5 predictors: minimum ~90 participants, ideally 100–120.

Chi-Square Test

Testing association between categorical variables.

Effect Size (w)	Power 80% (df=1)	Power 80% (df=2)
0.1 (small)	785	964
0.3 (medium)	88	108
0.5 (large)	32	39

Sample Size for Surveys

For descriptive surveys (estimating a population proportion or mean), the formula is:

n = (Z² × p × (1-p)) / E²

Where:

Z = Z-score for your confidence level (1.96 for 95%, 2.576 for 99%)
p = Expected proportion (use 0.5 if unknown — gives the largest sample)
E = Margin of error you can tolerate (e.g., 0.05 = ±5%)

Quick Reference

Confidence Level	Margin of Error	Sample Size
95%	±5%	385
95%	±3%	1,068
99%	±5%	664
95%	±10%	97

These assume an infinite (or very large) population. For small populations, apply the finite population correction.

Free Tools for Sample Size Calculation

You do not need to calculate these by hand. Use these free tools:

G*Power (free software) — The gold standard for power analysis. Supports t-tests, ANOVA, regression, correlation, chi-square, and more. Download from the HHU Düsseldorf website
ClinCalc — Simple web calculator for common tests
OpenEpi — Web-based epidemiological calculator
R (pwr package) — For programmatic calculation

G*Power Quick Guide

Open G*Power
Select Test family (e.g., t-tests)
Select Statistical test (e.g., Means: Difference between two independent means)
Set Type of power analysis to A priori (compute required sample size)
Enter: Effect size (d), α (0.05), Power (0.80), Allocation ratio (1 for equal groups)
Click Calculate

Reporting Sample Size Justification

For your thesis or research proposal, report the power analysis:

An a priori power analysis was conducted using G*Power 3.1 (Faul et al., 2009) to determine the minimum sample size required for an independent samples t-test. With a medium effect size (d = 0.50), α = .05, and power = .80, the required sample size was 128 (64 per group). To account for potential attrition of approximately 10%, a target of 142 participants was set.

Always include:

The software used
The statistical test
The expected effect size (and its source)
Alpha level
Target power
The resulting sample size
Any adjustment for attrition or non-response

Common Mistakes

Calculating sample size after data collection — Power analysis must be done before collecting data. Post-hoc power analysis is widely criticized and tells you nothing useful
Using rules of thumb instead of formal calculation — "30 per group is enough" is not a valid justification. Always run a power analysis
Ignoring attrition — Plan for 10–20% dropout/non-response by recruiting extra participants
Using a large effect size to minimize sample size — Unless prior research supports a large effect, use a medium or small effect. Reviewers will catch this
Forgetting to report the power analysis — Many thesis committees now require it in the methodology chapter

Need help with sample size calculation or research design? Our team can run the power analysis and plan your entire data analysis. Get a free consultation.