Home About us Editorial board Ahead of print Current issue Search Archives Submit article Instructions Subscribe Contacts Login 
  • Users Online: 2677
  • Home
  • Print this page
  • Email this page

   Table of Contents      
Year : 2012  |  Volume : 60  |  Issue : 6  |  Page : 582

Sample size calculation

Department of Biostatistics and Medical Informatics, University College of Medical Sciences, Delhi -110 095, India

Date of Web Publication26-Nov-2012

Correspondence Address:
Rajeev Kumar
Department of Biostatistics and Medical Informatics, University College of Medical Sciences, Delhi -110 095
Login to access the Email id

Source of Support: None, Conflict of Interest: None

DOI: 10.4103/0301-4738.103809

Rights and Permissions

How to cite this article:
Kumar R. Sample size calculation. Indian J Ophthalmol 2012;60:582

How to cite this URL:
Kumar R. Sample size calculation. Indian J Ophthalmol [serial online] 2012 [cited 2020 Jul 2];60:582. Available from: http://www.ijo.in/text.asp?2012/60/6/582/103809

Dear Editor,

Thanks for writing a nice editorial on the importance of sample size and calculation in medical research. [1] The principle of sample size calculation and formulas to determine adequate sample have been explained for testing the hypothesis for single mean, two means and two proportions. [2] The author has given the definition of important key terms used in the calculation of sample size but left out the distinction between one-tailed and two-tailed situations, which is an important issue: also, standardized difference (generally called effect size) compares two populations, and it is equal to the clinically important difference between the populations divided by the standard deviation (SD) of the population, assuming both the populations SD are equal. In addition, there are many lapses in formulas and their description given by the author.

The author has used standardized difference in the solution of Problem B given in the article to calculate the sample size per group for comparing the two population means: however, formula given by the author did not include standardized difference. Correct formulas for comparing the two means assuming a two-tailed situation and similar variance in both populations or pooled variance and for comparing the two proportions are in [Table 1]. [3],[4]
Table 1: Corrected formulas with and without standardized difference

Click here to view

Note: α is the level of significance, β is probability of Type II error and (1-β) is power. For α = 0.05, Zα/2 = 1.96, and Zα = 1.645. For β = 0.10, Zβ = 1.28; for β = 0.20, Zα/2 = 0.845

In problems B and C in the article, the author mentioned 90% power but in the description of data the author wrote "the probability of failing to reject a false null hypothesis (β)" as 0.80. It should be 0.10 not 0.80. Similarly, in Problem A, the author wrote 0.80 which should be 0.20. In the description of problems B and C, d is the size of the effect which is simply the difference between two population parameters while in the solutions the author considered d as standardized difference and the value of p1 + p2/2 is not same as

This type of articles would certainly provide basic inputs to the researchers and the clinicians. [1],[2],[5]

Editor's Comments

The article by Gogate[2] was written with the purpose of initiating interest amongst the readers and was not exhaustive.

  References Top

Nayak BK. Understanding the relevance of sample size calculation. Indian J Opthalmol 2010;58:469-70.  Back to cited text no. 1
Gogate N. Principles of sample size calculation. Indian J Opthalmol 2010;58:517-8.  Back to cited text no. 2
Indrayan A. Confidence Interval, Principles of Tests of Significance, and Sample size. In: Medical Biostatistics. 2 nd ed. Boca Raton: Chapman and Hall/CRC Press: 2008. p. 389.  Back to cited text no. 3
Whitley E, Ball J. Statistics review 4: Sample size calculations. Crit Care 2002;6:335-41.  Back to cited text no. 4
Malhotra RK, Indrayan A. Simple nomogram for estimating sample size for sensitivity and specificity of medical tests. Indian J Ophthalmol 2010;58:519-22.  Back to cited text no. 5
[PUBMED]  Medknow Journal  


  [Table 1]


    Similar in PUBMED
   Search Pubmed for
   Search in Google Scholar for
    Access Statistics
    Email Alert *
    Add to My List *
* Registration required (free)  

  In this article
Article Tables

 Article Access Statistics
    PDF Downloaded487    
    Comments [Add]    

Recommend this journal