# 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.

Illustration:

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.

## 2 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%.

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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.
Best,
Roopesh

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