What is it? Why is it important?

The aim of a Sample Size Calculation (SSC) is to determine the minimum number of participants needed to address a study question.


In order to calculate and decide on an applicable sample size, two main statistical frameworks are used:


  • The hypothesis testing: the primary outcome / endpoint is assessed with a statistical test (e.g. the difference between an intervention and control group). In a hypothesis testing framework, two competing hypotheses are formulated, the:
    • Null hypothesis (H0) (e.g. no effect)
    • Alternative hypothesis (Ha) - contradicts the null hypothesis (e.g. the occurrence of an effect)

The statistical test is significant when H0 is rejected in favour of Ha (e.g. intervention and control group are significantly different).


  • The Precision-based testing: The aim is to estimate a quantity with a certain accuracy. For example, the frequency of patients with a cardiac event (e.g. with a precision of +/- 2.5%), in other words with a certain width of the Confidence Interval (CI)


For hypothesis testing framework, see definition of type I error and power under more!


Type I error and power

In a hypothesis testing framework, you need to define the type I error and the power. The definition of these 2 parameters is usually done together with the statistician.


Definition Type I error: also known as a false positive, as it entails the rejection of the null hypothesis when it is actually true. It represents a situation where the researcher concludes that there is a significant effect when, in reality, there is no such effect (e.g. a cholesterol-lowering drug has an effect on cholesterol level when in reality there is no such effect). Type I error is often denoted by the symbol α (alpha). Type I error is classically set at 5%.


Defintion of Power: it is the probability of correctly rejecting the null hypothesis (e.g. a cholesterol-lowering drug has an effect on cholesterol levels). It is classically set at 80 or 90%.


Aspects to consider:

  • It is important for the study SP-INV to understand how important it is to do a proper sample size calculation, and the associated risks when sample size is underestimated (i.e. the study might lack the power to answer the study question, or a potential treatment effect might be missed)
  • The process to get to the number of participants needed for the study bears the risk of frustration for both, the SP-INV and the statistician. The SP-INV just wants to know the number that must be included in a proposal/protocol/grant application, while the statistician cannot provide a number before having received the required information form the SP-INV needed to perform a SSC. A good interdisciplinary collaboration and understanding between study SP-INV and statistician is crucial
  • The availability and ability to recruit the required number of study participants can be very challenging
  • Each additionally recruited participant increases work load and study budget

What do I need to do?

As a SP-INV, consult a statistician for the SSC of your study.


Provide the statistician with the following information:

  • The objective of your study, which will determine the statistical framework of your study
  • For a hypothesis testing, describe the planned comparison (e.g. mean values between intervention and control group)
  • The primary outcome/endpoint, including variable type (e.g. continuous, categorical, binary, count)
  • Time point of assessment (e.g. after x weeks of treatment or x weeks after surgery)
  • The variability of your study outcome/endpoint? (e.g. expected standard deviation of your continuous variables)
  • What effect do you expect to see?
    • Hypothesis testing: What change would be clinically important / meaningful?
    • Precision-based framework: The expected value of the quantity of interest (e.g. estimated proportion of deaths within 30 days of a MI = 36%)


Example of a hypothesis testing framework:

We are interested in a lab value (e.g. cholesterol concentration): we want to compare this value in two groups (e.g. intake of cholesterol-lowering drugs versus intake of placebo), and test the significance of this difference.

Thanks to your medical knowledge and previous work we know that:

  1. A difference of 20 (or more) between both groups is clinically relevant
  2. The standard deviation for this lab value can be assumed as equal to 12 in each group


We want to achieve a power of 90% with a two-sided alpha (type I error) of 5%

  • Framework: hypothesis testing
  • Comparison: mean comparison between intervention and control
  • Outcome: Continuous,
  • Effect we want to detect: difference of 20
  • SD = 12 in both groups


Example of a Precision based framework:

We want to estimate the proportion of deaths within 30 days of a Myocardial Infarction (MI). A previous study estimated that 36% (31% - 40%) of patients died within 30 days of an MI. We want to replicate their study with the same precision.

This short description contains the main information:

  • Framework: precision based,
  • Outcome: binary (i.e., occurrence of MI),
  • Expected value: 36%,
  • Precision we want to achieve: CI width = 9%

Where can I get help?

Your local CTU can support you with experienced staff regarding this topic

External Links



ICH Topic E9 statistical Principles for Clinical Trials – see in particular

  • 3.5 Sample size
  • 4.4 Sample size adjustment



SSTO Platforms: see: Sample Size Estimation with R

  • CI – Confidence Interval
  • ICH – International Council for Harmonisation
  • MI – Myocardial Infarction
  • SCTO – Swiss Clinical Trial Organisation
  • SD – Standard Deviation
  • SP-INV – Sponsor Investigator
  • SSC – Sample Size Calculation
Basic ↦ Statistic Methodology ↦ Study Design ↦ Sample Size Calculation

Provides some background knowledge and basic definitions

Basic Monitoring
Basic Drug or Device

Starts with a study idea

Ends after having assessed and evaluated study feasibility

Concept Statistic Methodology
Concept Drug or Device

Starts with confidence that the study is feasible

Ends after having received ethics and regulatory approval

Development Drug or Device

Starts with ethics and regulatory approval

Ends after successful study initiation

Set-Up Ethics and Laws
Set-Up Statistic Methodology
Set-Up Quality and Risk
Set-Up Drug or Device

Starts with participant recruitment

Ends after the last participant has completed the last study visit

Conduct Statistic Methodology
Conduct Drug or Device

Starts with last study visit completed

Ends after study publication and archiving

Completion Statistic Methodology
Completion Drug or Device
Current Path (click to copy): Basic ↦ Statistic Methodology ↦ Study Design ↦ Sample Size Calculation

Please note: the Easy-GCS tool is currently under construction.