Census: a survey which measures an entire population. Example: The United States conducts a census of the American population every ten years. A census is very tedious and takes a long time to complete. Therefore, we use samples of a population to make inferences about that population.

Sample a small number of individuals representing a larger group. Population Sample

Population Whether a researcher is drawing a sample or is studying an entire population, the population needs to be defined. This helps focus the research. Example: If I want to know what type of candy 7th grade students prefer, then my population is defined as the set of all 7th grade students. Population Sample

Types of Sampling Simple Random Sample Stratified Random Sample Cluster sampling Systematic Convenience Math Alliance Project

Simple Random Sample Every subset of a specified size n from the population has an equal chance of being selected Math Alliance Project

Stratified Random Sample The population is divided into two or more groups called strata, according to some criterion, such as geographic location, grade level, age, or income, and subsamples are randomly selected from each strata. Math Alliance Project

Cluster Sample The population is divided into subgroups (clusters) like families. A simple random sample is taken of the subgroups and then all members of the cluster selected are surveyed. Math Alliance Project

Systematic Sample Every kth member ( for example: every 10th person) is selected from a list of all population members. Math Alliance Project

Convenience Sample Selection of whichever individuals are easiest to reach It is done at the “convenience” of the researcher Math Alliance Project

Errors in Sampling Non-Observation Errors Sampling error: naturally occurs Coverage error: people sampled do not match the population of interest Underrepresentation Non-response: won’t or can’t participate Math Alliance Project

Errors of Observation Interview error- interaction between interviewer and person being surveyed Respondent error: respondents have difficult time answering the question Measurement error: inaccurate responses when person doesn’t understand question or poorly worded question Errors in data collection Math Alliance Project