Sample Size
• Topics: Agricultural Education and Communication | Program Evaluation | Sampling | Israel, Glenn D
Determining Sample Size1
Glenn D. Israel2
Perhaps the most frequently asked question concerning sampling is, "What size sample do I need?" The answer to this question is influenced by a number of factors, including the purpose of the study, population size, the risk of selecting a "bad" sample, and the allowable sampling error. Interested readers may obtain a more detailed discussion of the purpose of the study and population size in Sampling The Evidence Of Extension Program Impact, PEOD-5 (Israel, 1992). This paper reviews criteria for specifying a sample size and presents several strategies for determining the sample size.
SAMPLE SIZE CRITERIA
In addition to the purpose of the study and population size, three criteria usually will need to be specified to determine the appropriate sample size: the level of precision, the level of confidence or risk, and the degree of variability in the attributes being measured (Miaoulis and Michener, 1976). Each of these is reviewed below.
The Level Of Precision
The level of precision, sometimes called sampling error, is the range in which the true value of the population is estimated to be. This range is often expressed in percentage points, (e.g., ±5 percent), in the same way that results for political campaign polls are reported by the media. Thus, if a researcher finds that 60% of farmers in the sample have adopted a recommended practice with a precision rate of ±5%, then he or she can conclude that between 55% and 65% of farmers in the population have adopted the practice.
The Confidence Level
The confidence or risk level is based on ideas encompassed under the Central Limit Theorem. The key idea encompassed in the Central Limit Theorem is that when a population is repeatedly sampled, the average value of the attribute obtained by those samples is equal to the true population value. Furthermore, the values
Determining Sample Size1
Glenn D. Israel2
Perhaps the most frequently asked question concerning sampling is, "What size sample do I need?" The answer to this question is influenced by a number of factors, including the purpose of the study, population size, the risk of selecting a "bad" sample, and the allowable sampling error. Interested readers may obtain a more detailed discussion of the purpose of the study and population size in Sampling The Evidence Of Extension Program Impact, PEOD-5 (Israel, 1992). This paper reviews criteria for specifying a sample size and presents several strategies for determining the sample size.
SAMPLE SIZE CRITERIA
In addition to the purpose of the study and population size, three criteria usually will need to be specified to determine the appropriate sample size: the level of precision, the level of confidence or risk, and the degree of variability in the attributes being measured (Miaoulis and Michener, 1976). Each of these is reviewed below.
The Level Of Precision
The level of precision, sometimes called sampling error, is the range in which the true value of the population is estimated to be. This range is often expressed in percentage points, (e.g., ±5 percent), in the same way that results for political campaign polls are reported by the media. Thus, if a researcher finds that 60% of farmers in the sample have adopted a recommended practice with a precision rate of ±5%, then he or she can conclude that between 55% and 65% of farmers in the population have adopted the practice.
The Confidence Level
The confidence or risk level is based on ideas encompassed under the Central Limit Theorem. The key idea encompassed in the Central Limit Theorem is that when a population is repeatedly sampled, the average value of the attribute obtained by those samples is equal to the true population value. Furthermore, the values
References: Cochran, W. G. 1963. Sampling Techniques, 2nd Ed., New York: John Wiley and Sons, Inc. Israel, Glenn D. 1992. Sampling The Evidence Of Extension Program Impact. Program Evaluation and Organizational Development, IFAS, University of Florida. PEOD-5. October. Kish, Leslie. 1965. Survey Sampling. New York: John Wiley and Sons, Inc. Miaoulis, George, and R. D. Michener. 1976. An Introduction to Sampling. Dubuque, Iowa: Kendall/Hunt Publishing Company. Smith, M. F. 1983. Sampling Considerations In Evaluating Cooperative Extension Programs. Florida Cooperative Extension Service Bulletin PE-1. Institute of Food and Agricultural Sciences. University of Florida. Sudman, Seymour. 1976. Applied Sampling. New York: Academic Press. Yamane, Taro. 1967. Statistics, An Introductory Analysis, 2nd Ed., New York: Harper and Row. >100,000 1,111 400 204 100 a = Assumption of normal population is poor (Yamane, 1967)