## Mathguy.us

**Chapter 12: Sample Surveys **
**Terms and Notes **
**Sample: **a subset of a population that is examined in order to determine information about the entire

population.

**Types of Samples: **Note that all statistical sampling approaches have the common goal that chance,

rather than human choice, is used to select the sample.

•

**Cluster Sample: ** a sampling approach in which entire groups (i.e., clusters) are chosen at

random; a census is taken of each cluster.

*Each cluster should be representative of the entire *
*population. *All clusters should be heterogeneous and similar to each other. The problem with cluster samples is that the clusters are often not homogeneous and representative.
•

**Convenience Sample:** a sample of individuals who are conveniently available. Convenience

samples often fail to be representative.
•

**Multistage Sample:** a sampling approach that combines several sampling methods. Example:

stratify the country by geographic region; randomly select cities from each region; interview a cluster of residents from each city. Care should be taken at each step not to introduce bias.
•

**Simple Random Sample (SRS): **a sample of size 𝑛 in which each set of 𝑛 elements has an equal

chance of being selected. This is the standard against which other sampling methods are measured.
•

**Stratified Random Sample:** the population is divided into subgroups (i.e., strata), and random

samples are taken from each subgroup. This is better than a simple random sample if the strata are relatively homogeneous and different from each other. It results in reduced sampling variability, and can point out differences in responses among groups.
•

**Systematic Sample:** individuals are selected systematically from a sampling frame (e.g., every

10th person). Can be representative if there is no relationship between the order of the sampling frame and the variables of interest.

** **

Randomization: each member of a population is given a fair, random chance of selection in the sample.

This reduces bias in a sample.

**Biased Sample:** one that over- or under-emphasizes some characteristics of the population. It is caused

by poor design and is not reduced as sample size increases.

**Types of Bias **
•

**Voluntary Response Bias:** occurs when sample participants are self-selected volunteers (i.e.,

•

**Undercoverage Bias**: occurs when some members of the population are inadequately covered

•

**Nonresponse Bias**: occurs when respondents to a survey differ in meaningful ways from non-

•

**Response Bias**: occurs when the question is asked in such a way that it influences the response.

**Sample Size: **the number of individuals in a sample.

**Required sample size** does

**NOT** depend on the size of the population (as long as the population is large

enough and our sample is less than 10% of the population).

**Representative Sample:** A sample whose statistics accurately reflect the corresponding population

parameters.

**Sampling Frame:** a list of individuals from which the sample is drawn.

**Sampling Variability:** the natural tendency of randomly drawn samples to differ from one another.

Note: sampling variability is not a problem.

**Pilot:** A small trial run of a survey used to determine if the questions are clear.

** **

Population: the entire group of individuals that we hope to learn about.

**Census:** examination of information about every member of a population. This is the best approach

when the population is small and accessible.

Why not do a census al the time? • Difficult or expensive to complete. • Populations rarely stand stil . A census takes time and the population changes during it. • A census is more complex than a sample.

**Parameter:** a descriptive measure (using a numerical value) of the population, e.g., 𝜇, 𝜎. Also called a

**population parameter**.

**Statistic:** a descriptive measure (using a numerical value) of a sample, e.g., 𝑥̅, 𝑠. Also called a

**sample **
**statistic**.

**Key Statistics and Parameters **
**Sample Statistic **
**Population Parameter **
** **

The Valid Survey
• What do I want to know? • Am I asking the right respondents (i.e., do I have the right sampling frame)? • Am I asking the right questions? Ask only questions that help you learn what you want to know.
Be specific. In each question, either give a set of alternative answers (i.e., multiple choice) or ask for a numerical response, if possible. Ask questions in a neutral way (i.e., avoid bias).
• What will I do with the answers: will they address what I want to know?

Source: http://www.mathguy.us/BySubject/Statistics/Chapter_12_(Part3)_Notes.pdf

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