## Statistical Analysis of Frequency Data

Frequency data may be analyzed by several different techniques, depending upon how the sample units were located and how the data was collected.

Values collected from randomly located quadrats to determine frequency follow a binomial distribution. In this case, the comparison of sample means (evaluating significant differences between years or among sites, should be based on binomial statistics). In this situation, binomial confidence intervals are used to assess if two sample means are significantly different. The binomial confidence interval for a given frequency remains constant, according to sample size and the level of probability. Tables listing the width of confidence intervals have been developed for commonly used sample sizes (typically *n*=100 and *n*=200) and probability levels. If the confidence intervals (for the correct sample size and probability level) for the sample means being compared overlap, it is concluded that these values are not significantly different.

However, if the design is based on quadrats arranged as a group of subsamples to determine frequency, the data set of transect sample means follows a normal distribution. In this case, evaluating significant differences between years or sites can be based on conventional inferential statistics, whereby two sample means can be compared by considering the possibility that their respective confidence intervals overlap.

### References and Further Reading:

(Note: *pdf* files require Adobe Acrobat (free) to view)

Despain, D.W., Ogden, P.R., and E.L. Smith. 1991. Plant frequency sampling for monitoring rangelands. In: G.B. Ruyle. (ed). *Some methods for monitoring rangelands and other natural area vegetation.* University of Arizona, College of Agriculture, Extension Report 9043. pp. 16-18.

Greig-Smith, P. 1983. *Quantitative plant ecology.* Blackwell Scientific Publications, Oxford. 3rd ed. pp. 36-41.

Hironaka, M. 1985. Frequency approaches to monitor rangeland vegetation. In: W.C. Krueger. (chairman). *Proceeding 38th Annual Meeting, Society for Range Management,* Salt Lake City, UT, February 1985. p. 85.

Whysong, G.L., and W.W. Brady. 1987. Frequency sampling and type II errors. *Journal of Range Management* 40:472-474. (*pdf*)

Whysong, G.L., and W.H. Miller. An evaluation of random and systematic plot placement for estimating frequency. *Journal of Range Management* 40:475-479. (*pdf*)