It is important to note that a larger sample size will reduce the size of the confidence interval. Although the size of the interval is determined by several factors, the most important is sample size. Larger samples are more likely to yield data that accurately reflect the true population value. This statement should make intuitive sense to you; a sample of 200 people from your school should yield more accurate data about your school than a sample of 25 people.
TABLE 7.2 Sample size and precision of population estimates (95% confidence level)
How large should the sample be? The sample size can be determined using a mathematical formula that takes into account the size of the confidence interval and the size of the population you are studying. Table 7.2 shows the sample size needed for a sample percentage to be accurate within plus or minus 3%, 5%, and 10%, given a 95% level of confidence. Note first that you need a larger sample size for increased accuracy. With a population size of 10,000, you need a sample of 370 for accuracy within ±5%; the needed sample size increases to 964 for accuracy within ±3%. Note that sample size is not a constant percentage of the population size. Many people believe that proper sampling requires a certain percentage of the population; these people often complain about survey results when they discover that a survey of an entire state was done with “only” 700 or 1,000 people. However, you can see in the table that the needed sample size does not change much, even as the population size increases from 5,000 to 100,000 or more. As Fowler (2014) notes, “a sample of 150 people will describe a population of 1,500 or 15 million with virtually the same degree of accuracy …” (p. 38).
There are two basic techniques for sampling individuals from a population: probability sampling and nonprobability sampling.
Page 150Probability sampling is required when you want to make precise statements about a specific population on the basis of the results of your survey. Although nonprobability sampling is not as sophisticated as probability sampling, we shall see that nonprobability sampling is quite common and useful in many circumstances.