Ensure your research has statistical significance with our comprehensive sample size calculator and detailed methodology guide. Perfect for student researchers and academic projects.
This is the minimum number of respondents needed for your research to be statistically significant at the selected confidence level.
Sample size refers to the number of individual samples measured or observations used in a survey or experiment. In research, it's the number of subjects, respondents, or observations included in your study.
Choosing an appropriate sample size is crucial because:
The sample size is a balance between practical constraints (time, budget) and statistical requirements (precision, confidence). The goal is to select the smallest sample that will provide the most accurate results.
A "good" sample size depends on several factors:
While definitions vary by field:
A sample is "large" when adding more participants doesn't significantly change your results.
The basic formula for calculating sample size (for infinite populations) is:
Where:
When you know the population size (N), the adjusted formula is:
Common confidence levels and their corresponding Z-scores:
How confident you need to be that your results reflect the true population value. Higher confidence requires larger samples.
The acceptable amount of error in your results. Smaller margins require larger samples.
Total size of the group you're studying. Only matters for small populations.
Expected distribution of responses. 50% is most conservative (requires largest sample).
| Confidence Level | Z-Score | Relative Sample Size |
|---|---|---|
| 99% | 2.576 | Largest |
| 95% | 1.96 | Medium (standard) |
| 90% | 1.645 | Smaller |
| 80% | 1.282 | Smallest |
Scenario: Surveying voter preferences for a national election
Calculation: (1.96² × 0.5 × 0.5) / 0.03² = 1,067 respondents
Scenario: Studying student satisfaction at a university
Calculation: First calculate infinite population size: (1.96² × 0.5 × 0.5) / 0.05² = 384. Then adjust for finite population: 384 / (1 + (383/10000)) ≈ 370 students
Scenario: Clinical trial for a new medication
Calculation: (2.576² × 0.5 × 0.5) / 0.02² = 4,147 participants
Results may not be statistically significant or generalizable. Increases risk of Type II errors (false negatives).
Choosing sample sizes based on convenience rather than statistical calculation leads to unreliable results.
For small populations (under 5,000), failing to adjust sample size calculations can lead to oversampling.
In comparative studies, unequal group sizes reduce statistical power and can bias results.
Sample size is determined by theoretical saturation (when no new information is obtained) rather than statistical power. Typically 15-50 participants.
Focus on statistical power (typically 80% or higher) to detect meaningful effects. Power analysis is essential.
