Inferential Statistics

Inferential statistics allow researchers to make generalizations about how well results from samples match those for populations. Because samples are parts of populations, samples do not include all of the population information. Thus, no inference can be perfect because samples cannot represent completely their parent populations.

Imagine that a population is defined as all students enrolled in U.S. schools. Suppose researchers want to study how well students in that population enjoy school. A survey is developed, and researchers prepare to collect response data. Researchers estimate the target population consists of 3 million students. Because the population encompasses the entire United States, the team of researchers must include all geographic areas from Maine to Hawaii. However, actually collecting data for all U.S. students is too massive, so a sample is selected. Ideally, this sample would be randomly selected, which means that all U.S. students have the same chance of being selected. This makes the sample representative of the population. Essentially, this means that although the sample may represent only a small percentage of the students who comprise the complete population, that sample is assumed to reflect the characteristics of all U.S. students, including those not selected.