How to calculate sample size formula

Written by michael keenan
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How to calculate sample size formula
The formula for calculating sample sizes involves several variables. (Calculator image by Alla Podkopaeva from

Sample sizes are vital for conducting research. If your sample size is too small, you may not have a wide enough range of participants to see results, or your results may be dismissed as the result of chance. If your sample size is too large, the costs of your research will make it necessary for you to obtain more funding.

Skill level:

Things you need

  • Calculator
  • Z-score table

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  1. 1

    Determine the confidence interval of your study. The confidence interval is the number of percentage points above or below the proportion that you find in your study that the true proportion should be within. For example, if your confidence interval is 3.5 per cent and your study reveals a proportion of 57 per cent, the true proportion is likely between 53.5 per cent and 60.5 per cent.

  2. 2

    Determine the confidence level of your study. The confidence level is how certain your need to be that the true proportion lies within your confidence interval. For example, if you use a confidence level of 95 per cent, you can predict with 95 per cent certainty that the true proportion lies within your confidence interval.

  3. 3

    Convert your confidence level to a Z-score by using a Z-score table. For example, a 98.5 per cent confidence level results in a 2.43 Z-score.

  4. 4

    Predict the proportion of the study. For example, if you expect 53 per cent of respondents to respond affirmatively, 0.53 would be your proportion.

  5. 5

    Compute the needed sample size by plugging your values into the following formula, where Z is the Z-score, P is the proportion and I is the confidence interval.

    Sample Sized Needed = Z² --- P (1 -- P) / I²

    For example, if your Z-score is 2.43, your proportion is 0.53 and your interval is 3.5 per cent, you would need a sample size of 1,201 subjects.

Tips and warnings

  • Err on the side of a more balanced result when calculating sample size. For example, if you predict an 80 per cent result and you get a 54 per cent result, you will not have enough people in your study.

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