**SAMPLE SIZE CALCULATION**

To answer a specific research question, one critical parameter in designing an efficient experimental study is the sample size. The sample size, as the name reflects, is a group of experimental units that is large enough to give an applicable answer as if one had tested the entire population of interest, knowing that inclusion of the entire population would not be possible. In contrast, the sample size should not be too large, as reduction of experimental animals (units) is an important factor when complying with the 3R Principle by Russels and Burch.

Calculating the sample size, previous knowledge on important variables of the specific experimental design and outcome is important to gather in e.g. pilot studies or similar studies that were previously performed. These variables include a biological meaningful difference between treated and control groups with standard deviations. Together, these parameters are translated into a signal-to-noise ratio, which is a critical determinant of the sample size.

A high signal-to-noise ratio requires a smaller sample size than a low signal-to-noise ratio does.

**How to increase the Signal (Biological difference)**

- Increase the dose

- Using a more sensitive species or strain

**How to reduce the noise (Standard deviation)**

- Use a homogenous model across treatment groups e.g.

- Same sex

- Same strain

- Same age

- Disease free (strict quarantine and health monitoring)

Furthermore, using a cross-over study design when possible will reduce the noise as the experimental unit serves as its own control, thereby reducing the variance between subjects.

### Power calculation method

Experimental power translates into the “reliability” of the result. A desired power can be included in calculations when estimating sample sizes, or the power can be calculated post-experimentally by “Post-hoc power analysis” when exact standard deviation, mean and number of experimental units are known.

Experimental designs are set up to disprove the null hypothesis, i.e. Finding a difference between treatment and control group. If the sample size is too small and power is insufficient, there is a risk of falsely accepting or rejecting the null hypothesis.

For calculations, the risk of wrongly accepting the null hypothesis equals α and are also known as a “Type 1 Error”, which accepts the alternative hypothesis although it is not true. In contrast, wrongly rejecting the null hypothesis is denoted as β, a “Type 2 Error”.

Conclusively, the power of a study equals 1 - β, and indicates how many experimental units that should be included in the experiment to get a reliable answer with sufficient statistical power.

Several online calculators are readily available, that are useful when planning an upcoming experiment.:

http://clincalc.com/stats/samplesize.aspx

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

Lastly, if no previous experiments or pilot studies have been performed, resulting in unknown means and standard deviation, , an alternative method to calculate the sample size (number of experimental units to include) is the use of Meads resource equation, based on the law of diminishing returns.