Sample size calculation: A general rule of thumb

Is it possible to estimate the size of the required sample without using statistical formulae?

Yes, if a general rule of thumb is employed.

The rule of thumb: Add 20 subjects for each additional variable.


A study has the following variables in the questionnaire/ Data collection Form:

Age; Sex; Heart Rate; BMI; Socio-Economic Status (SES)

What would the minimum sample size requirement be for this study?

Employing the rule of thumb, we obtain the minimum sample size required as:

Total number of variables: 5.

Therefore, minimum sample size required is

5 x 20 = 100 subjects

Why take 20 subjects per additional variable? Why not 10 or 15?

I’m guessing it has to do with the Chi-square test.

The Chi-square test employs a 2×2 contingency table. Thus, there are 4 cells. One of the guidelines states that the number of observations/ value of any cell should not be less than 5. This means that we should have at least 5 in each cell. Multiplying, we get the minimum number of total observations as 5 x 4 = 20.

Sample size obtained by the rule of thumb will be adequate for any situation involving the Chi-square test during analysis. In addition, it is unlikely that one would under-estimate the required sample size using this approach.

Bottomline: Adding 20 subjects for each additional variable will yield a reasonable estimate of the required sample size.

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4 thoughts on “Sample size calculation: A general rule of thumb

  1. Anonymous

    Great idea. But the justification for 20 is oversimplified because, with the number 20, the chance of any cell in 2×2 table being less than 5 is more than 90%.


    1. drroopesh Post author

      Dear Someone,

      Thanks for the feedback. I was guessing the justification for 20, but it seems my guess was off-track. Would you please elaborate on the justification for everyone’s benefit?

      Thanks in advance.


    1. drroopesh Post author

      Dear Mujaheed,

      The sample size would depend on several factors such as prevalence of the condition under investigation, desired precision, level of significance, and study design. As mentioned in the article, it would also depend on the number of variables under study.

      Dr. Roopesh



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