# Calculating Sample Size

The amount of samples required is dependent on a few factors:

1. The desired detection difference you want. Do you want to see any difference or do want to detect a certain amount of difference and in which direction?
2. The Confidence Level (or 1 - alpha-risk, ∝). Typically 95% is used (or 5% alpha-risk)
3. The desired level of Power (or 1 - beta-risk, β)
4. The level of variability (variance) or standard deviation

## Calculating Sample Size - Variables Data Most commonly assumed confidence level is 95% which is an alpha-risk of 0.05. Also in most cases the question is two-tailed so shown below is the corresponding z value. Practice Question:

What sample size (n), is needed to specify a 95% confidence interval of +/- 1.5 units from the mean?

Assuming a normal distribution, the set of data of widget lengths has a historical variance of 13.4.

In this case it is two-tailed and Z = 1.96

The variance is 13.4 mm (which is the standard deviation squared).

Substituting:

n = (1.962 * 13.4) / 1.52

n = 3.8416 * 13.4 / 16 = 51.477 / 2.25 = 22.87

n = 23 samples (always round up to next sample to ensure enough Power)

## Calculating Sample Size - Poisson Data

Use the sample size shown above with the exception of substituting the Poisson average in place of the standard deviation

Poisson average = n*p-hat = mean (from the attribute c chart of the data)

## Calculating Sample Size - Binomial Data  ## Other sources

There are many tutorials and calculators on the web. A few links/videos are shown below:

https://www.surveysystem.com/sscalc.htm

https://www.calculator.net/sample-size-calculator.html

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