065. Determining the Sample Size

The size of the sample has an important impact on the probability of error and the precision of the estimate, as well as on other important factors associated with the research effort. Determination of the appropriate sample size is crucial. Given a desired confidence level, two factors are particularly instrumental in influencing the necessary sample size:

(1) The variability of the population, 2.

(2) The size of the error that can be tolerated.

While the first factor is beyond the control of the researcher, the size of the tolerable error should be examined at this point.

The extent of error a researcher can tolerate depends on how critical the work must be. Some tasks are extremely delicate and require exacting results: Vital medical procedures upon which lives may depend, or the production of machine parts that must meet precise measurements, can tolerate only a small error. In other instances, larger errors may be of lesser consequence.

Example 6.6. Presume that in manufacturing a part for compact disk players, an error of 2 centimeters (cm) in diameter will cause no problem. Any error in excess of 2 cm will, however, result in a defective disk player. If the part can vary above and below some desired mean diameter by 2 cm, an interval of 4 cm is allowed. Any given interval is twice the tolerable error. See Figure 6.7 for an illustration.

Figure 6.7 – The Tolerable Error is One-Half the Interval

Thus, The confidence interval can extend above and below the mean by the amount of the tolerable error.

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