One of the most critical aspects of planning a clinical study is the calculation of the sample size. As it is not possible to study the whole population in the study, a set of participants is selected (“sample”) from the population, which, although less in size, adequately represents the population from which it is drawn. Thus, the results of the study in this sample can be considered that truly reflect the results of the study in the total population.

Generally, the sample size for any study depends on the:

- Acceptable level of significance
- Power of the study
- Expected effect size
- Underlying event rate in the population
- Standard deviation in the population

#### Sample size calculation

The sample size is calculated using the following formula:

where *n* is the required sample size.

Z_{α} is a constant (set by convention according to the accepted α error and whether it is a one-sided or two-sided effect) as shown below:

α-error | 5% | 1% | 0.1% |

2-sided | 1.96 | 2.5758 | 3.2905 |

1-sided | 1.65 | 2.33 |

Z_{1-β} is a constant set by convention according to the power of the study as shown below:

Power | 80% | 85% | 90% | 95% |

Value | 0.8416 | 1.0364 | 1.2816 | 1.6449 |

In the above-mentioned formula σ is the standard deviation (estimated) and Δ the difference in the effect of two interventions which is required (estimated effect size).

#### Online sample size calculators

- https://clincalc.com/stats/samplesize.aspx
- https://www.surveymonkey.com/mp/sample-size-calculator/
- https://www.calculator.net/sample-size-calculator.html
- http://www.raosoft.com/samplesize.html

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