How to Determine Sample Size
Sample size is one of the central methodological decisions in research and refers to how many participants, observations, cases, or analytical units should be included in a study.
An insufficient sample may prevent the detection of a genuine relationship, difference, or effect. An unnecessarily large sample may consume additional time, funding, and resources. Sample size should therefore be justified in relation to the research design, planned analysis, and expected effect whenever possible.
Are Sample Size and Sampling Method the Same?
No. Sample size concerns how many units will be included in the study, whereas the sampling method concerns how those units are selected.
A study may require 300 participants, for example, but whether those participants are selected through simple random, stratified, convenience, or another sampling method is a separate decision.
What Determines the Required Sample Size?
The required sample size varies according to the characteristics of the study. Important factors include:
- Research design
- Primary research question or hypothesis
- Planned statistical analysis
- Expected effect size
- Significance level
- Statistical power
- Number of groups
- Number of predictors or independent variables
- Population size
- Expected attrition, missing data, or nonresponse
- Sampling design
What Is Power Analysis?
Power analysis is a method used to estimate the sample size required to detect a specified statistical effect.
In hypothesis-driven quantitative research, an a priori power analysis may provide a stronger methodological justification than relying solely on generic sample-size tables or fixed rules of thumb.
What Is Statistical Power?
Statistical power is the probability that a study will detect an effect when that effect genuinely exists.
It is commonly expressed as:
1 − β
A power level of .80 is commonly used in many research settings, although an appropriate level may differ according to discipline, risk, and study purpose.
What Is Effect Size?
Effect size describes the magnitude of a relationship, difference, or intervention effect.
It is important for sample-size planning because smaller effects generally require larger samples to detect reliably.
Different analyses use different effect-size measures, including:
- Cohen's d: differences between two means
- r: correlation
- f: ANOVA-type analyses
- f²: regression analyses
- Odds ratio: selected categorical and epidemiological analyses
- Risk ratio: clinical and epidemiological research
How Should Effect Size Be Selected?
Whenever possible, the anticipated effect size should be based on evidence relevant to the research topic and analysis plan.
Possible sources include:
- Previous comparable studies
- Meta-analyses
- Pilot studies
- A minimum effect considered scientifically meaningful
- A clinically or practically important difference
Conventional small, medium, or large effect-size categories may be useful where evidence is unavailable, but they should not automatically be assumed to apply to every study.
What Is the Significance Level?
The significance level, or alpha, represents the threshold associated with the risk of concluding that an effect exists when it does not.
Many studies use:
α = .05
Different levels may be needed in settings involving multiple testing, high-risk decisions, or specialized research designs.
What Is G*Power?
G*Power is widely used software for statistical power analysis and sample-size calculation across several common statistical tests.
It can be used for analyses such as:
- t tests
- ANOVA
- Correlation
- Regression
- Chi-square tests
- Selected proportion and distribution tests
What Should Be Considered When Using G*Power?
Values should not be entered arbitrarily. Researchers should be able to justify:
- The selected test family
- The statistical test to be performed
- The chosen effect size
- The alpha and power levels
The statistical test selected in G*Power should correspond to the actual analysis planned for the study.
What Is an A Priori Power Analysis?
An a priori power analysis estimates the required sample size before data collection begins.
A simplified logic is:
Effect size + α + desired power + analysis characteristics → required sample size
Can Post Hoc Power Replace A Priori Sample Planning?
Post hoc power calculations based on observed results do not replace sample planning conducted before data collection.
Where possible, sample-size justification should therefore rely on prospective planning rather than retrospective calculations.
Sample Size for Comparing Two Groups
When two independent groups are compared, sample requirements depend on the expected group difference, allocation ratio, significance level, and statistical power.
For an independent-samples t test, the expected difference may be represented using Cohen's d.
Smaller expected differences generally require larger samples.
Sample Size in Correlation Studies
In correlation studies, the required sample size depends on the magnitude of the correlation that the study intends to detect.
Detecting a very small correlation reliably generally requires more participants than detecting a moderate correlation.
Sample Size for Regression Analysis
In regression models, the number of predictors and expected explained variance are important in addition to the total sample.
Sample-size planning may consider:
- Number of predictors
- Expected f² effect size
- Alpha
- Statistical power
Simple rules such as “10 participants per predictor” should not be treated as universal substitutes for appropriate power analysis.
Sample Size for Mediation Analysis
Sample requirements for mediation depend on the magnitude of the indirect effect, the structure of the model, and the analytical method used.
Small indirect effects may require substantially larger samples.
Where bootstrap-based mediation is planned, sample size should reflect the expected paths and indirect effect within the model.
Sample Size for Moderation Analysis
Moderation analysis tests an interaction effect.
Interaction effects may be smaller than main effects, making adequate sample size particularly important in moderation studies.
Sample Size for Structural Equation Modeling
There is no universal minimum sample size for every structural equation model.
Requirements depend on factors such as:
- Model complexity
- Number of observed and latent variables
- Number of indicators
- Expected effect sizes
- Missing data
- Distributional characteristics
- Estimation method
Statements such as “SEM always requires at least 200 participants” should therefore not be treated as universal rules.
Sample Size for Confirmatory Factor Analysis
Sample requirements for CFA may vary according to the number of factors and items, factor loadings, model complexity, and data characteristics.
Rules based only on a fixed number of participants per item should not replace a design-specific sample justification.
Sample Size in Scale Development
Scale development studies should not determine sample size solely from the number of items.
Exploratory factor analysis, confirmatory factor analysis, reliability assessment, criterion validity, and other analyses may each have different data requirements.
Where feasible, conducting EFA and CFA in independent samples may provide a stronger methodological design.
Sample Size in Scale Adaptation
Sample planning for scale adaptation should consider factor-structure testing, reliability analysis, language-related validation, and relevant convergent or criterion validity analyses.
Sample Size Based on Population Size
Some descriptive studies estimate proportions or prevalence within a defined population.
Such calculations may involve:
- Population size
- Confidence level
- Margin of error
- Expected proportion or prevalence
What Is a Confidence Level?
Confidence level is related to the uncertainty represented by a confidence interval.
A 95% confidence level is widely used, but it is not an automatic requirement for every study.
What Is Margin of Error?
Margin of error represents the degree of difference that is accepted between a sample estimate and the corresponding population value.
For example, a survey estimating a proportion may be planned with a margin of error of ±5%.
Smaller margins of error generally require larger samples.
Does a Finite Population Affect Sample Size?
Yes. When a population is relatively small and its size is known, a finite population correction may influence the required sample.
For very large populations, the effect of additional population size on required sample size becomes relatively limited after a certain point.
Why Is “How Many Participants for a Population of 1,000?” Not Enough?
Because population size alone does not determine sample size.
The same population of 1,000 could require different samples for:
- A prevalence estimate
- A two-group comparison
- A regression model
- A mediation analysis
Should Additional Participants Be Added for Missing Data and Attrition?
Yes. If nonresponse, dropout, or missing data are expected, recruitment targets may need to exceed the calculated minimum.
For example, if the minimum analytical sample is 300 and approximately 10% data loss is expected, targeting exactly 300 participants may be insufficient.
The additional allowance should reflect the likely loss pattern in the specific study.
Attrition in Experimental Research
Longitudinal and intervention studies may experience greater follow-up loss.
An expected dropout rate should therefore be considered during sample planning.
Design Effect in Cluster Samples
Participants selected within schools, hospitals, neighborhoods, or other clusters may be more similar to one another than independently selected individuals.
A sample size calculated for simple random sampling may therefore be inadequate for a clustered design.
Where relevant, design effect and intracluster correlation should be considered.
Complex and Multistage Sampling Designs
Stratified, clustered, and multistage sampling designs should not be planned solely around a simple total sample size.
Sampling weights, design effects, and intended subgroup analyses may need to be considered prospectively.
Sample Size for Subgroup Analyses
When analyses are planned separately by age, sex, profession, disease group, or other subgroups, researchers should determine whether each subgroup will contain sufficient observations.
A large total sample may still contain subgroups that are too small for reliable analysis.
Do Multiple Hypotheses Affect Sample Requirements?
A large number of primary statistical tests can increase the risk of false-positive findings.
Where multiple-comparison adjustments are planned, the effective significance threshold and required sample size may change.
Can a Pilot Study Be Used for Sample-Size Planning?
Pilot studies may provide preliminary estimates of variance or effect size for the main study.
However, effect-size estimates from small pilot samples can be unstable. Pilot findings should therefore be considered together with existing literature and scientific expectations.
How Is Sample Size Determined in Qualitative Research?
Qualitative sample size is generally not determined through conventional statistical power analysis.
Sample adequacy may depend on:
- Research aim
- Qualitative design
- Characteristics of the participant group
- Depth and richness of data
- Variation in the phenomenon
- Analytical approach
- Saturation or information power
How Many Participants Are Needed in Phenomenology?
There is no fixed participant number appropriate for every phenomenological study.
The relevance of participants' lived experience and the richness of the data they provide may be more important than a universal numerical threshold.
How Many Participants Are Needed in Grounded Theory?
In grounded theory, sample size may develop alongside emerging categories and theoretical sampling.
A final sample size therefore may not always be fixed before data collection begins.
Sample Size in Focus Group Research
In focus group research, the number of groups and the composition of each group are important in addition to the total number of participants.
The required number of groups should reflect the research question, participant diversity, and adequacy of the resulting data.
Is There a Sample Size in Systematic Reviews?
Systematic reviews do not use participant sampling in the conventional sense. Instead, they include studies meeting predefined eligibility criteria and the participants represented within those studies.
Researchers should not set an arbitrary target number of studies merely to reach a preferred sample size.
Number of Studies in Meta-Analysis
Very small numbers of studies may limit heterogeneity assessment, publication-bias evaluation, and some advanced analyses.
However, unsuitable studies should never be included merely to increase the number of studies in a meta-analysis.
How Should Sample Size Be Reported in a Manuscript?
A statement such as “the sample consisted of 300 participants” is often insufficient by itself.
Where appropriate, report:
- How the sample size was calculated
- The primary analysis or outcome used for the calculation
- Effect size
- Alpha level
- Statistical power
- Required minimum sample
- Allowance for attrition or missing data
- Final analytical sample
Example of Reporting a Power Analysis
Example: The minimum sample size was determined before data collection using G*Power. An a priori calculation based on a medium effect size, α = .05, and statistical power of .80 indicated that at least 128 participants were required. The recruitment target was increased to allow for potential data loss.
This example illustrates reporting structure only. Effect size and all other parameters should be scientifically justified for the specific study.
Example of Population-Based Sample Reporting
Example: The accessible population consisted of 2,450 individuals. Sample size was estimated using a 95% confidence level and a ±5% margin of error, and the recruitment target was increased to account for potential nonresponse.
Common Sample-Size Mistakes
- Selecting a sample size without justification
- Using the same generic sample-size table for every study design
- Assuming population size is the only determinant
- Selecting a G*Power test that does not match the planned analysis
- Assuming a “medium” effect without justification
- Ignoring expected missing data or attrition
- Presenting post hoc power as though it were a priori sample planning
- Assuming one fixed minimum sample size applies to all SEM models
- Treating participants-per-item rules as universal requirements
- Ignoring sample adequacy for subgroup analyses
- Justifying qualitative samples only with a fixed numerical rule
- Failing to state which hypothesis or analysis the power calculation addressed
A Practical Sample-Size Planning Sequence
For hypothesis-testing studies:
Research question → Primary analysis → Expected effect → α → Power → Minimum sample → Attrition allowance → Recruitment target
For descriptive proportion estimates:
Population → Expected proportion → Confidence level → Margin of error → Minimum sample → Nonresponse allowance
Check Before Submission
- Is it clear how sample size was determined?
- Does the calculation correspond to the primary analysis?
- Is the effect-size source or justification stated?
- Are alpha and power levels reported?
- If G*Power was used, was the appropriate test selected?
- Was additional recruitment planned for missing data or attrition?
- Was design effect considered for clustered sampling?
- Are planned subgroup analyses adequately powered?
- Was sample planning conducted before data collection where appropriate?
- Is the final analytical sample clearly reported?
- For qualitative studies, is sample adequacy justified according to the methodological design?
