## Sample Size Determination

### To calculate the number of samples needed

To calculate the number of samples needed for a given error level use:

$$n = \left( \frac{t_{\alpha}s}{d} \right)^2$$

where d = the desired absolute error in plus or minus of the units of measure, s = the standard deviation, tα = Student's t value for n - 1 degrees of freedom for the 1 - α level of confidence, and n = the sample size.

### To calculate the error for a given number of samples

If you have a set number of samples and want to know the absolute error use:

$$d = \frac{t_{\alpha}s}{\sqrt{n}}$$

where the variables are the same as above.

### To calculate the number of plots in relative terms

To calculate the number of plots in relative terms use the following formula:

$$n = \left( \frac{t_{\alpha}cv}{E\%} \right)^2$$

where the t and n variables are the same as above. c is the coefficient of variation in the percent form and E% is the desired error as a percent.

Also See:

Chapter 5 - Sample Size Determination pages 173-178 in:

Krebs, C. J. 1998. Ecological Methodology. Harper and Row, Publishers. New York. 620 pp.
or

Chapter 8 - One-Sample Hypotheses pages 108-112 in:

Zar, J. H. 2007. Biostatistical Analysis. Prentice-Hall, Inc. Englewood Cliffs, New Jersey. 718 pp.