Chapter 12 and 13 Statistics Vocabulary

Representative

A sample is said to be representative if the statistics computed from it accurately reflect the corresponding population parameters.

Census

A sample that consists of the entire population is called a census.

Cluster Sample

A sampling design in which entire groups or clusters are chosen at random. Cluster sampling is usually selected as a matter of convenience, practicality, or cost. Each cluster should be heterogeneous (and representative of the population), so all the clusters should be similar to each other.

Stratified Random Sample

A sampling design in which the population is divided into several sub populations, or strata, and random samples are then drawn from each stratum. If the strata are homogeneous but are different from each other, a stratified sample may yield more consistent results.

Under-coverage

A sampling scheme that biases the sample in a way that gives a part of the population less representation than it has in the population, suffers from under-coverage.

Simple Random Sample (SRS)

A simple random sample of sample size n is one in which each set of n elements in the population has an equal chance of selection.

Observational Study

A study based on data in which no manipulation of factors has been employed.

Sample Survey

A study that asks questions of a sample drawn from some population in the hope of learning something about the entire population. Polls taken to assess voter preferences are common sample surveys.

Single Blind

There are two main classes of indiciduals who can affect the outcome of an experiment: Those who could influence the results (the subjects, treatment administrators, or technicians), and those who evaluate the results (judges, treating physicians, etc). When every individual in either of these classes is blinded an experiment is said to be single blind.

Double Blind

There are two main classes of indiciduals who can affect the outcome of an experiment: Those who could influence the results (the subjects, treatment administrators, or technicians), and those who evaluate the results (judges, treating physicians, etc). When everyone in both classes is blinded, we call the experiment double blind.

Statistically Significant

When an observed difference is too large for us to believe that it is likely to have occurred naturally, we consider the differences to be statistically significant. Subsequent chapters will show specific calculations and give rules, but the principle remains the same.

Block

When groups of experimental units are similar, it is often a good idea to gather them together into blocks. By blocking we isolate the variability attributable to the differences between the blocks so that we can see the differences caused by the treatments more clearly.

Confounding

When the levels of one factor are associated with the levels of another factor so their effects cannot be separated, we say that these two factors are confounded.

Convenience Sample

A convenience sample consists of the individuals who are conveniently available. Convenience samples often fail to be representative because every individual in the population is not equally convenient to sample.

Sampling Frame

A list of individuals from whom the sample is drawn is called the sampling frame. Individuals who may be in the population of interest but who are not in the sampling frame cannot be included in any sample.

Population Parameter

A numerically valued attribute of a model for a population. We rarely expect to know the true value of a population parameter, but we do hope to estimate it from sampled data. For example, the mean income of all employed people in the country is a population parameter.

Sample

A representative subset of a population, examined in hope of learning about the population.

Systematic Sample

A sample drawn by selecting individuals systematically from a sampling fame. When there is no relationship between the order of the sampling fame and the variables of interest, a systematic sample can be representative.

Placebo

A treatment known to have no effect, administered so that all groups experience the same conditions. Many subjects respond to such a treatment (a response known as placebo effect). Only by comparing with a placebo can we be sure that the observed effect of a treatment is not due simply to the placebo effect.

Response

A variable whose values are compared across different treatments. In a randomized experiment, large response differences can be attributed to the effect of differences in treatment level.

Factor

A variable whose values are compared across different treatments. In a randomized experiment, large response differences in factor levels may have on the responses of the experimental units.

Retrospective Study

An observational study in which subjects are selected and then their previous conditions or behaviors are determined. Because retrospective studies are not based on random samples they usually focus on estimating differences between groups or associations between variables.

Randomization

The best defense against bias is randomization in which each individual is given a fair, random chance of selection.

Experiment

An experiment manipulates factor levels to create treatments, randomly assigns subjects to these treatments

Prospective Study

An observational study in which subjects are followed to observe future outcomes. Because no treatments are deliberately applied, a prospective study is not an experiment. Nevertheless, prospective studies typically focus on estimating differences among groups that might appear as the groups are followed during the course of the study.

Matching

Any attempt to force a sample to resemble specified attributes of the population is a form of matching. Matching may help make better samples, but it is no substitute for randomizing.

Blinding

Any individual associated with an experiment who is not aware of how subjects have been allocated to treatment groups is said to be blind.

Bias

Any systematic failure of a sampling method to represent its population is bias. It is almost impossible to recover from bias, so efforts to avoid it are well spent. Common errors include relying on voluntary response, under-coverage of the population, non response bias, response bias

Response Bias

Anything in a survey design that influences responses falls under the heading of response bias. One typical response bias arises from the wording of questions, which may suggest a favored response. Voters, for example are more likely to express support of "the president" than support of the particular person holding that office at the moment.

Non-response Bias

Bias introduced to a sample when a large fraction of those sampled fails to respond. Those who do respond are likely to not represent the entire sample. Voluntary response bias is a form of non response bias, but non response may occur for other reasons. For example those who are at work during the day won't respond to a telephone survey conducted only during working hours.

Voluntary Response Bias

Bias introduced to a sample when individuals can choose on their own whether to participate in the sample. Samples based on voluntary response are always invalid and cannot be recovered no matter how large the sample size.

Principles of Experimental Design

Control aspects of the experiment that we know may have an effect on the response, but that are not the factors being studied. Randomize subjects to treatments to even out effects that we cannot control. Replicate over as many subjects as possible. Results for a single subject are just anecdotes. If, as often happens, the subjects of the experiment are not a representative sample from the population of interest, replicate the entire study with a different group of subjects, preferably from a different part of the population. Block to reduce the effects of identifiable attributes of the subjects that cannot be controlled.

Designs

In a randomized block design, the randomization occurs only within blocks. In a completely randomized design, all experimental units have an equal chance of receiving any treatment.

Matching

In a retrospective or prospective study, subjects who are similar in ways not under study may be matched and then compared with each other on the variables of interest. Matching, like blocking reduces unwanted variation.

Experimental Units

Individuals on whom an experiment is performed. Usually called subjects or participants when they are human.

Multistage Sample

Sampling schemes that combine several sampling methods are called multistage samples. For example, a national polling service may stratify the country by geographical regions, select a random sample of cities from each region, and then interview a cluster of residents in each city.

Statistic, Sample Statistic

Statistics are values calculated for sampled data. Those that correspond to, and thus estimate, a population parameter, are of particular interest. For example, the mean income of all employed people in a representative sample can provide a good estimate of the corresponding population parameter. The term "sample statistic" is sometimes used, usually to parallel the corresponding term, "population parameter".

Population

The entire group of individuals or instances about whom we hope to learn.

Control Group

The experimental units assigned to a baseline treatment level, typically either the default treatment, which is well understood, or a null, placebo treatment. Their responses provide a basis for comparison.

Sampling Variability

The natural tendency of randomly drawn samples to differ, one from another. Sometimes, unfortunately, called sampling error, sampling variability is no error at all, but just the natural result of random sampling.

Sample Size

The number of individuals in a sample. The sample size determines how well the sample represents the population not the fraction of the population sampled.

Treatment

The process, intervention, or other controlled circumstance applied to randomly assigned experimental units. Treatments are the different levels of a single factor or are made up of combinations of levels of two or more factors.

Level

The specific values that the experimenter chooses for a factor are called the levels of the factor.

Placebo Effect

The tendency of many human subjects (often 20% or more of experiment subjects) to show a response even when administered a placebo.

Random Assignment

To be valid, an experiment must assign experimental units to treatment groups at random. This is called random assignment.