Comprehensive Key Terms in Statistical Inference and Experimental Design

statistical Inference

The process of using sample statistics to answer questions about population parameters

experiment

deliberately imposes treatments on items or individuals to measure their responses.

response variable

measures an outcome of a study

explanatory variable

A variable that helps explain or predict changes in a response variable.

treatment

a specific condition applied to the individuals in an experiment

experimental unit

the object or individual to which a treatment is assigned

Factors

explanatory variables that are manipulated and may cause a

change in the response variable.

levels

different values of the factor

observational study

observes items or individuals and measures variables of interest but

does not impose treatments.

retrospective observational study

when the observational units are selected at a point in time

and data about them are gathered from the past.

prospective observational study

when the observational units are selected at a point in time

and data about them are gathered both at that time and into the future.

survey

the collection of data by having people answer a series of questions

confounding variable

a factor other than the factor being studied that might influence a study's results

Random Sampling

a chance process to determine which members of a

population are chosen for the sample.

When the goal is to understand cause and effect,

___________________________________ are the only source of fully convincing data.

cause and effect

confidence interval

the range of values within which a population parameter is estimated to lie

Hypothesis Test

a statistical method designed to assess claims that uses sample data to evaluate a hypothesis about a population

Simple Random Sample (SRS)

of size n consists of n individuals from the population chosen in such a way that every set of n items or individuals has an equal chance to be the sample actually selected

How to choose an SRS with technology

Label: "Assign each individual an integer 1 to r."

o r is the number of individuals in the population

2. Randomize: "Use a RNG to select q unique

integers from 1 to r."

o q is the desired sample size.

3. Select: "Choose the individuals corresponding to those integers for the sample."

Strata

groups of items or individuals in a population that share characteristics thought to be associated with the variables being measured in a study.

stratified random sample

a sampling design in which the population is divided into several subpopulations, and random samples are then drawn from each stratum and combined into one overall sample

Stratified random sampling works best when the items or individuals within each stratum are

similar (homogeneous) with respect to what is being measured and when there are large differences between strata.

to keep

the sample size within each stratum roughly _________________________________ to the size of the strata in the population.

proportional

cluster

groups of items or individuals in the population that are located near each other.

primary criterion for forming clusters

location and heterogenous groups

For a cluster random sample, we would like each cluster to

look just like the population, but on a smaller scale.

Systematic Random Sampling

A method of sampling in which sample elements are selected from a list or from sequential files, with every nth element being selected after the first element is selected randomly within the first interval

most large-scale surveys use

multistage sampling, which combines two or more sampling methods.

Convenience Sampling

choosing individuals who are easiest to reach

The design of a statistical study shows bias if the resulting sample statistic is

very likely to underestimate or very likely to overestimate the population parameter due to a @law in the data collection

process.

voluntary response sample

consists of people who choose to be in the sample by responding to a general appeal

Undercoverage

when some members of the population are less likely to be chosen or cannot be chosen for a sample.

Nonresponse

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

response bias

when responses to a survey question consistently differ from the

truth in the same way.

question wording bias

bias created by the wording of the survey questions

control group

used to provide a baseline for comparing the effects of

other treatments.

Placebo

treatment that has no active ingredient but is otherwise like the other treatments.

placebo effect

the fact that some subjects in an experiment will respond favorably to any treatment, even an inactive treatment.

double-blind procedure

an experimental procedure in which both the research participants and the research staff are ignorant (blind) about whether the research participants have received the treatment or a placebo.

single-blind experiment

either the subjects or the people who interact with them and

measure the response variable don't know which treatment a subject is receiving.

random assignment

treatments are assigned to experimental units (or

experimental units are assigned to treatments) using a chance process.

if random assignment is successful, the distribution of any extraneous variables will be

about the same

for all treatment groups, whether or not we identi@ied the variable in advance.

completely randomized design

the treatments are assigned to all the experimental units completely at random

Replication

multiple experimental units are assigned to each treatment.

Direct Control

keeping the values of some extraneous variables the same for all experimental

block

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

randomized block design

the random assignment of experimental units to treatments is carried out separately within each block

matched pairs design

two similar experimental units

are paired and the two treatments are randomly assigned within each pair. In others, each experimental unit receives both treatments in a random order.

When an observed difference in responses between the groups in an experiment is so large that it is unlikely to be explained by chance variation in the random assignment, the results are called

statistically significant