The JavaScript source code used for sample size calculation is open source and is published here.
You can also run our tests for the source code to confirm that the calculators work correctly in your browser.
6 Mar 2011 and updated 7 Nov 2011 with binary equivalence results. 12 Oct 2012 checked after switch to JavaScript calculators.
The results from Sealed Envelope's power calculators were compared to published sample size calculations. The results are shown in the table below.
Trial | Outcome | Reference | Parameters | Reference n | Calculator result |
---|---|---|---|---|---|
Superiority | Continuous | Julious 2004, 2.1.1 | d = 8, σ = 40, α = 5%, β = 10% | 527 | 526 |
Superiority | Continuous | Pocock 1983 | d = 0.5, σ = 1.8, α = 5%, β = 5% | 337 | 337 |
Equivalence | Continuous | Julious 2004, 3.4.3 | d = 10, σ = 50, α = 2.5%, β = 10% | 651 | 650 |
Non-inferiority | Continuous | Julious 2004, 4.1.1 | d = 10, σ = 40, α = 2.5%, β = 10% | 338 | 337 |
Superiority | Binary | Pocock 1983 | p _{1} = 90%, p _{2} = 95%, α = 5%, β = 10% | 578 | 579 |
Equivalence | Binary | Julious 2009, 12.1 | p = 70%, d = 10%, α = 2.5%, β = 10% | 546 | 546 |
Equivalence | Binary | Julious 2009, 12.1 | p = 70%, d = 20%, α = 2.5%, β = 10% | 137 | 137 |
Equivalence | Binary | Julious 2009, 12.1 | p = 90%, d = 5%, α = 2.5%, β = 10% | 936 | 936 |
Non-inferiority | Binary | Donner, Example 3 | p = 80%, d = 10%, α = 10%, β = 20% | 145 | 145 |
Non-inferiority | Binary | Blackwelder, Table 3 | p = 90%, d = 20%, α = 5%, β = 10% | 39 | 39 |
Non-inferiority | Binary | Blackwelder, Table 3 | p _{s} = 60%, p _{e} = 50%, d = 20%, α = 5%, β = 10% | 420 | 420 |
Non-inferiority | Binary | Pocock 1983 | p = 70%, d = 10%, α* = 5%, β = 20% | 332 | 330 |
Non-inferiority | Binary | Pocock 2003 | p = 85%, d = 15%, α* = 5%, β = 10% | 120 | 120 |
* Note: Pocock assumes a 2-sided confidence interval will be produced, so α should be set to 2.5% in the calculator
Blackwelder WC. "Proving the Null Hypothesis" in Clinical Trials. Control. Clin. Trials 1982; 3:345-353
Donner A. Approaches to Sample Size Estimation in the Design of Clinical Trials - A Review. Statist. Med. 1984; 3:199-214
Julious SA. Sample sizes for clinical trials with Normal data. Statist. Med. 2004; 23:1921-1986
Julious SA. Estimating Samples Sizes in Clinical Trials. CRC; 2009
Pocock SJ. Clinical Trials: A Practical Approach. Wiley; 1983.
Pocock SJ. The pros and cons of noninferiority trials. Fundam Clin Pharmacol 2003; 17: 483–490