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# Krejcie and Morgan 1970

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DETERMINING SAMPLE SIZE FOR RESEARCH ACTIVITIES ROBERT V. KREJCIE University of Minnesota, Duluth DARYLE W. MORGAN Texas A. & M. University The ever increasing demand for research has created a need for an efficient method of determining the sample size needed to be representative of a given population. In the article “Small Sample Techniques,” the research division of the National Education Association has published a formula for determining sample size. Regrettably a table has not bee available for ready, easy reference which could have been constructed using the following formula. s = X 2 NP (1 − P) ÷ d 2 ( N − 1) + X 2 P(1 − P). s = required sample size. X2 = the table value of chi-square for 1 degree of freedom at the desired confidence level (3.841). N = the population size. P = the population proportion (assumed to be .50 since this would provide the maximum sample size). d = the degree of accuracy expressed as a proportion (.05).

No calculations are needed to use Table 1. For example, one may wish to know the sample size required to be representative of the opinions of 9000 high school teachers relative to merit pay increases. To obtain the required sample size enter Table 1 at N = 9000. The sample size representative of the teachers in this example is 368. Table 1 is applicable to any defined population. The relationship between sample size and total population is illustrated in Figure 1. It should be noted that as the population increases the sample size increases at a diminishing rate and remains relatively constant at slightly more than 380 cases. REFERENCE Small-Sample Techniques. The NEA Research Bulletin, Vol. 38 (December, 1960), p. 99.

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