Journal of Human Reproductive Science
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Year : 2014  |  Volume : 7  |  Issue : 2  |  Page : 155-156

Error in sample size formula

Department of Psychiatry; Centre for Genomic Sciences, University of Hong Kong, Hong Kong, China

Date of Web Publication16-Aug-2014

Correspondence Address:
Desmond Dedalus Campbell
L10-64 Lab Block, Faculty of Medicine, 21 Sassoon Road, Central and Western, Hong Kong
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/0974-1208.138878

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How to cite this article:
Campbell DD. Error in sample size formula. J Hum Reprod Sci 2014;7:155-6

How to cite this URL:
Campbell DD. Error in sample size formula. J Hum Reprod Sci [serial online] 2014 [cited 2022 Dec 1];7:155-6. Available from:


Re: Suresh K, Chandrashekara S. Sample size estimation and power analysis for clinical research studies. J Hum Reprod Sci 2012;5:7-13.

Although informative and useful Suresh and Chandrashekara's article on sample size estimation and power analysis contains a serious error (Suresh and Chandrashekara, 2012). In the section titled "sample size estimation with two means" they state the minimum required sample size for detecting a mean difference between two groups is:


α is the false positive rate

β is the false negative rate

N is the sample size required to detect an inter-group mean difference of d with specified α and power of 1−β

δ2 is the variance in each group (both groups having the same variance)

r is the ratio of size (n1 and n2 ) of the two groups, that is, r = n1 /n2

Z is the standard normal distribution deviate, note this is the absolute of the z-score, as in (Suresh and Chandrashekara, 2012) [Table 2] and [Table 3].

The formula as stated cannot be correct as relabeling of the two groups results in different values of N.


The original erroneous formula could result in studies seriously underestimating their required sample size. For instance, the required sample size (as calculated by the current formula) is half that truly required, given equal numbers in the two groups. I therefore draw this error to your attention. The illustrative examples that follow the formula presentation are also in error.[1]

   References Top

1.Wittes J. Sample size calculations for randomized controlled trials. Epidemiol Rev 2002;24:39-53  Back to cited text no. 1


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