Notes

Population and Sample

The population in a statistical study is the entire group of individuals about which we want information.

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.

Convenience Sample

Choosing individuals who are easiest to reach results in a convenience sample.

Bias

The design of a statistical study shows bias if it systematically favors certain outcomes.

Voluntary Response Sample

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 direction) are most likely to respond.

Simple Random Sample

A simple random sample (SRS) of size n consists of 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.

Table of Random Digits

A table of random digits is a long string of digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with these 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.


Stratified Random Sample and 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.

Cluster Sample and 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.

Undercoverage

Undercoverage occurs when some groups in the population are left out of the process of choosing the sample.

Nonresponse

Nonresponse occurs when an individual chosen for the sample can't be contacted or refuses to participate.



Observational Study and Experiment

An observational study observes individuals and measures variables of interest but does not attempt to influence the responses.

An experiment deliberately imposes some treatment on individuals to measure their responses.

Lurking Variable

A lurking variable is a variable that is not among the explanatory or response variables in a study that may influence the response variable.

Confounding

Confounding occurs when two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other.

Random Assignment

In an experiment, random assignment means that experimental units are assigned to treatments at random, that is, using some sort of chance process.

Completely Randomized Design

In a completely randomized design, the treatments are assigned to all the experimental units completely by chance.

Double-blind

In a double-blind experiment, neither the subjects nor those who interact with them and measure the response variable know which treatment a subject received.

Statistically Significant

An observed effect so large that it would rarely occur by chance is called statistically significant.

Block and Randomized Block Design

A block is a group of experimental units that are known before the experiment to be similar in some way that is expected to affect the response to the treatments.

In a randomized block design, the random assignment of experimental units to treatments is carried out separately within each block.



Most statistical studies aim to make inferences that go beyond the data actually produced. Inference about the population requires that the individuals taking part in a study be randomly selected from the larger population. A well-designed experiment that randomly assigns treatments to experimental units allows inference about cause and effect.

Lack of realism in an experiment can prevent us from generalizing its results.

In the absence of an experiment, good evidence of causation requires a strong association that appear consistently in many studies, a clear explanation for the alleged causal link, and careful examination of possible lurking variables.

Studies involving humans must be screened in advance by an institutional review board. All participants must give their informed consent before taking part. Any information about the individuals in the study must be kept confidential.

Remember that randomized comparative experiments can answer questions that can't be answered without them. Also remember that "the interests of the subject must always prevail over the interests of science and society."