Statistical Techniques

Sample size (n) can be determined using a statistical approach that considers the variability of the population and our requirements for precision. The formula to determine the number of samples needed to meet these statistical criteria is

Sample Size of n = (t squared x s squared) / k squared

The variability in the population is accounted for by s2, or the sample variance. A preliminary sample may be collected, or data from earlier studies in the same vegetation may be used to provide an indication of the expected variability in the population to be sampled. The formula shows the need for more sample units in a highly variable population (when s2 is large). Stratified sampling can help to reduce variability and decrease sample size requirements within a site. Variability may also be reduced by manipulating sample unit size and sample unit shape.

The t-value serves to weight the equation according to a probability level that reflects the probability that our conclusions are erroneous. If we are willing to accept a greater probability of incorrect assessments, the t-value will be smaller, meaning that fewer samples will be needed. The t-value can be obtained from the t-tables found in most statistics textbooks.

The k-value of the denominator is the difference between the sample mean and the population mean (mu plus or minus x-bar). Therefore, this component of the formula indicates how closely we want our sample mean to reflect the population mean. The formula shows that demanding a very small margin of error, insisting that the sample mean is very close to the population mean, will increase in the number of sample units that must be measured.

References and Further Reading

Bonham, C.D. 1989. Measurements for terrestrial vegetation. John Wiley Son, New York, NY. pp 65-67.