Central Limit Theorem The central limit theorem (CLT) describes the theoretical char- acteristics of a sample population. The CLT is the theoretical backbone of survey research and is important in understanding the concepts of sampling error, statistical significance, and sample sizes. In brief, the theorem states that for almost all defined target populations, the sampling distribution of the mean or the percentage value ( ) derived from a simple random sample will be approximately normally distributed, provided the sample size is sufficiently large (i.e., when n is > or = 30). Moreover, the mean of the random sample with an estimated sampling error fluctuates around the true population mean () with a stan- dard error of and an approximately normal sampling distribution, regardless of the shape of the probability frequency distribution of the overall target population. In other words, there is a high probability that the mean of any sample taken from the target population will be a close approximation of the true target population mean (), as one increases the size of the sample

Sampling error Any type of bias that is attributable to mistakes in either drawing a sample or determining the sample size.

Nonsampling error A bias that occurs in a research study regardless of whether a sample or census is used.

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With an understanding of the basics of the CLT, the researcher can do the following:

1. Draw representative samples from any target population.
2. Obtain sample statistics from a random sample that serve as accurate estimates of the
3. target population's parameters.
4. Draw one random sample, instead of many, reducing the costs of data collection.
5. More accurately assess the reliability and validity of constructs and scale measurements.
6. Statistically analyze data and transform it into meaningful information about the target
7. population.