Section 4.1
Sample
A sample is the part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population.
Table of Random Digits
A table of random digits is a long string of the digits 0-9 with the following properties: - Each entry in the table is equally likely to be any of the 10 digits 0 through 9. - The entries are independent of each other. That is, knowledge of one part of the table gives no information about any other part.
Convenience Sample
Choosing individuals who are easiest to reach results in a convenience sample.
Multistage Samples
Multistage samples are samples that combine two or more sampling methods.
Population
The population in a statistical study is the entire group of individuals about which we want information.
Stratified Random Sample & Strata
To select a stratified random sample, first classify the population into groups of similar individuals, called strata. Then choose a separate SRS in each stratum and combine these SRSs to form the full sample. - We want each stratum to contain similar individuals, and for there to be large differences between strata.
Undercoverage
Undercoverage occurs when some groups in the population are left out of the process of choosing the sample.
Inference
The process of drawing conclusions about a population on the basis of sample data is called inference because we infer information about the population what what we know about the sample. - The first reason to rely on random sampling is to eliminate bias in selecting samples from the list of available individuals. - Sample results, like the unemployment rate obtained from the monthly Current Population Survey, are only estimates of the truth about the population.
Sampling Frame
A sampling frame is a list of individuals from which we will draw our sample. - Ideally, the sampling frame should list every individual in the population.
Simple Random Sample
A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected. - An SRS not only gives each individual an equal chance to be chose but also gives every possible sample an equal chance to be chosen.
Nonresponse
Nonresponse occurs when an individual chosen for the sample can't be contacted or refuses to participate.
Sample Survey
Studies that use an organized plan to choose a sample that represents some specific population.
Wording of Questions
The most important influence on the answers given to a sample survey. Confusing or leading questions can introduce strong bias, and changes in wording can greatly change a survey's outcome. Even the order in which questions are asked matters.
Random Sampling
The use of chance to select a sample. The central principle of statistical sampling.
Response Bias
A systematic pattern of incorrect responses in a sample survey leads to response bias.
Voluntary Response Samples
A voluntary response sample consists of people who choose themselves by responding to a general appeal. Voluntary response samples show bias because people with strong opinions (often in the same directions) are most likely to respond.
Margin of Error
Results from random samples come with a margin of error that sets bounds on the size of the likely error. - The second reason to use random sampling is that the laws of probability allow trustworthy inference about the population. - Larger random samples give better information about the population than smaller samples.
Cluster Sample & Clusters
To take a cluster sample, first divide the population into smaller groups. Ideally, these clusters should mirror the characteristics of the population. Then choose an SRS of the clusters. All individuals in the chosen clusters are included in the sample. - For a cluster sample, we'd like each cluster to look just like the population, but on a smaller scale.
Bias
The design of a statistical study shows bias if it systematically favors certain outcomes.