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Table of Contents
Year : 2021  |  Volume : 9  |  Issue : 3  |  Page : 90-92

Sample size determination simplified: A review

1 Department of Public Health Dentistry, Saraswati Dhanwantari Dental College, Parbhani, Maharashtra, India
2 Department of Community and Preventive Dentistry, UCMS-College of Dental Surgery, Bhairahawa, Nepal
3 Department of Community and Preventive Dentistry, People’s Dental Academy, Bhopal, Madhya Pradesh, India

Date of Submission18-May-2021
Date of Acceptance04-Jun-2021
Date of Web Publication27-Sep-2021

Correspondence Address:
Dr. Nilesh Arjun Torwane
Department of Public Health Dentistry, Saraswati Dhanwantari Dental College, Pathri Rd, Parbhani 431401, Maharashtra.
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/INJO.INJO_19_21

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Researchers active in clinical, epidemiological, or translational research have the aim to publish their outcomes so that they can generalize their findings to the population. The sample size decision should be based on the difference in the result between the two groups analyzed as in an analytical subject field. It should also be based on the acceptable P value for statistical significance and the expected statistical power to test a hypothesis. Therefore, the purpose of sample size planning is to calculate an appropriate number of subjects for a specified survey design. This article accounts the concepts in calculating the sample size.

Keywords: Alpha value, epidemiology, P value, power, sample size, statistics, type I error

How to cite this article:
Torwane NA, Singh VR, Dayma A. Sample size determination simplified: A review. Int J Oral Care Res 2021;9:90-2

How to cite this URL:
Torwane NA, Singh VR, Dayma A. Sample size determination simplified: A review. Int J Oral Care Res [serial online] 2021 [cited 2021 Nov 29];9:90-2. Available from: https://www.ijocr.org/text.asp?2021/9/3/90/326814

  Introduction Top

Possibly the most oftentimes demanded query regarding sampling is “How large a sample do I need?” The solution to this query is regulated by a number of factors, including the aim of the survey, population size, the risk of choosing a “bad” sample, anticipated outcome, and the permitted sampling error. The objective of the calculation is to determine a sufficient sample size to estimate the population prevalence with an effective precision. This paper reexamines criteria for determining a sample size and demonstrates various strategies for deciding the sample size.

  Strategies for Determining Sample Size Top

There are various approaches to specifying the sample size. These include applying:

  1. Applying a census for small populations

  2. Utilizing a sample size of a related survey

  3. Utilizing published tables

  4. Applying formulas to calculate a sample size (for simple random sampling)

  5. Computer software

  Utilizing Published Tables Top

There are several published tables that furnish the sample size for a fixed set of measures. Tables show sample sizes established on compounding of precision, confidence levels, and variability.[2],[3]

  Applying Formulas to Calculate a Sample Size (For Simple Random Sampling) Top

Descriptive surveys

Descriptive survey deals with calculation of population parameters. Two usually applied parameters are the proportion and the mean (measure of central tendency).

  • (a) Formula applied for sample size determination when population parameter is proportion: for population that are big, Cochran (1977) prepared the equation to generate a representative sample for proportions:[8]

where n is the desirable sample size (when the population>10,000), Z is standard normal deviate; normally fixed at 1.96 which represents 95% confidence level, P is the expected prevalence or proportion (in proportion of one; if 20%, P = 0.2), whenever there is no valid estimate, use 50% (i.e. 0.5),

and d is precision (in proportion of one; if 5%, d = 0.05) or in simple words the difference that is clinically significant.


A local health authority wants to estimates the prevalence of early childhood caries in children under 5 years. It is known that the true rate is unlikely to exceed 30%. To verify this figure within 5% of true value and 95% confidence how many children will be needed?

Now, in the above situation, z = confidence level at 95% (standard value of 1.96), P = 0.3, and d = 0.05 putting the values in the formula for sample size the value of n comes out to be

Design effect

The survey is designed as a cluster sample (a representative selection of villages), not a simple random sample. To correct for the difference in design, the sample size is multiplied by the design effect (D).

D = variance (cluster sample)/ variance (simple random sample).

The design effect for cluster random sampling is accepted as 1.5–2. For the purposive sampling, convenience or judgment sampling, design effect might get over 10.[7]


N = n x D

= 323 x 2

= 646 children of age under 5 years.

  • (b) Formula applied for sample size determination when population parameter is mean: the formula for the mean applies σ2 rather than [P (1–P)], as shown below:

where n is sample size, Z is standard normal deviate, e is desired level of precision, and σ2 is variance of an attribute in the population.

Clinical trial study

For clinical trials, power-based formula for sample size calculation given by Pocock is preferred. For clinical trials with qualitative outcome, 1:1 allocation ratio and a two-sided test sample can be calculated as follows:[6]

  • (a) Formula applied for sample size determination when population parameter is proportion:

where n is the sample size per group, π1 is expected percentage of proportion in one group, π2 is expected proportion in other group, and f(α, β) is the function of α and β derived from the standard normal distribution.

For instance, our objective is to compare failures of tooth restoration with chemically cured or a light-cured restorative material. Considering in earlier clinical trials, it was found that the proportion of failures for the chemically cured restorative material is 44% and proportion of failures for light-cured restorative material is 22%, and the desired significance is set at 5% and power is at 90%. Now using the above formula, the required sample size is as follows:

= 7/ each group

  • (b) Formula applied for sample size determination when population parameter is mean:

To compare the mean in one group to the mean in another, the sample size required in each group is given by

where µ1 – µ2 is the smallest difference in means and sd is the standard deviation (estimated from the previous study).

  Computer Software Top

Several software systems are accessible for executing power and sample size computing. These include nQuery Advisor, PASS, PS, Russ Lenth’s power, minitab, Stata, and SAS Power. PROC POWER and GLMPOWER are fresh add-ons to SAS version 9.0.[4],[5],[6],[7]

  Conclusion Top

Although it is not odd for investigators to have divergent opinions as to how sample size should be computed, the processes applied in this procedure should always be accounted, granting the reader to draw his or her personal opinions as to whether they consent the investigators presumptions and procedures. Generally, an investigator could apply the standard components described in this paper in the sample size finding procedure.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.

  References Top

Miaoulis G, Michener RD. An Introduction to Sampling. Dubuque, IA: Kendall/Hunt Publishing Company; 1976.  Back to cited text no. 1
Naing L, Winn T, Rusli BN. Practical issues in calculating the sample size for prevalence studies. Arch Orofac Sci 2006;1:9-14.  Back to cited text no. 2
Israel GD. Sampling the Evidence of Extension Program Impact. Program Evaluation and Organizational Development, Gainesville, FL: IFAS, University of Florida; 1992. PEOD-5. October.  Back to cited text no. 3
Macfarlane SB. Conducting a descriptive survey: 2. Choosing a sampling strategy. Trop Doct 1997;27:14-21.  Back to cited text no. 4
Krejcie RV, Morgan DW. Determining sample size for research activities. Educ Psychol Meas 1970;30:607-10.  Back to cited text no. 5
Phillips C. Sample size and power: What is enough? Semin Orthod 2002;8:67-76.  Back to cited text no. 6
Jain S, Gupta A, Jain D. Estimation of sample size in dental research. Int Dent Med J Adv Res 2015;1:1-6.  Back to cited text no. 7
Cochran WG. Sampling Techniques. 3rd ed.New York: John Wiley & Sons; 1977.  Back to cited text no. 8


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