Unit 2 Comprehensive Vocab and relevant info

Statistical study

A process of collecting and analyzing data to answer a question.

Experiment

A study that deliberately imposes treatments on experimental units and measures their responses.

Observational study

A study that observes individuals and measures variables of interest without imposing treatments.

Retrospective observational study

An observational study in which individuals are selected at a point in time and data about the past are collected.

Prospective observational study

An observational study in which individuals are selected at a point in time and data are collected from that point into the future.

Survey

An observational study that collects data from people by asking them a common set of questions.

Population

The entire group of individuals or items we want information about.

Sample

The individuals or items from which data are actually collected.

Census

A study that collects data from every individual in the population.

Parameter

A numerical summary describing a population.

Statistic

A numerical summary describing a sample.

Explanatory variable

A variable that may help explain or predict changes in a response variable.

Response variable

The outcome measured in a study; it may change in response to the explanatory variable.

Categorical variable

A variable that places individuals into groups or categories.

Quantitative variable

A variable that takes numerical values for which arithmetic makes sense.

Confounding variable

A variable associated with both the explanatory and response variables that makes their relationship difficult to separate.

Cause-and-effect conclusion

A conclusion that changes in the explanatory variable caused changes in the response variable; this is supported by a well-designed randomized experiment.

Generalization

Applying sample results to a larger population.

Random sampling

A chance process used to select members of a population for a sample.

Random assignment

A chance process used to assign experimental units to treatment groups.

Simple random sample (SRS)

A sample of size n selected so that every possible sample of n individuals from the population has an equal chance of selection.

SRS using a random number generator

Label all N population members 1 through N; generate n distinct random integers from 1 through N; select the individuals with those labels.

Sampling without replacement

Once an individual is selected, that individual cannot be selected again.

Sampling with replacement

After an individual is selected, that individual is returned to the population and could be selected again.

Stratified random sample

Divide the population into non-overlapping groups called strata that are similar with respect to the variable of interest; take an SRS from every stratum and combine the selected individuals.

Stratum

One of the non-overlapping groups used in stratified random sampling; individuals within a stratum should be similar regarding the variable of interest.

Cluster random sample

Divide the population into non-overlapping clusters that each resemble the population in their composition; randomly select entire clusters and include all individuals in those clusters.

Cluster

One of the groups used in cluster sampling; ideally, each cluster is a small-scale version of the population.

Systematic random sample

Arrange the population in an order, randomly select one of the first k individuals, and then select every kth individual thereafter.

Sampling interval (k)

The fixed number of positions between selected individuals in a systematic sample.

Periodic pattern in systematic sampling

A repeating pattern in the population order that aligns with the sampling interval and can make a systematic sample unrepresentative.

Convenience sample

A sample made up of population members who are easiest to reach.

Voluntary response sample

A sample in which people choose themselves by responding to a general invitation.

Bias

A flaw in the data-collection design that makes a sample statistic likely to systematically overestimate or underestimate the population parameter.

Undercoverage bias

Occurs when some population members are less likely to be selected or cannot be selected.

Sampling frame

A list of population members from which a sample is selected.

Nonresponse bias

Occurs when selected individuals cannot be contacted or refuse to participate and differ from those who respond in ways relevant to the study.

Response bias

Occurs when survey responses consistently differ from the truth in the same direction.

Leading question

A question whose wording influences the answers people give.

Interviewer bias

When the interviewer's behavior or characteristics influence participants' answers.

Nonresponse

When an individual selected for a sample cannot be contacted or refuses to participate.

Voluntary response vs. nonresponse

Voluntary response means people choose to enter the sample; nonresponse means selected people do not provide data.

Four common random sampling methods

Simple random sampling, stratified random sampling, cluster random sampling, and systematic random sampling.

Factor

An explanatory variable that is deliberately manipulated in an experiment.

Level of a factor

A specific value or condition of an experimental factor.

Treatment

A specific condition imposed on experimental units; with multiple factors, a treatment is a combination of one level from each factor.

Experimental unit

The item or individual to which a treatment is assigned.

Subject

An experimental unit that is a human being.

Treatment group

A group of experimental units that receives the same treatment.

Control group

A group used as a baseline for comparison; it may receive a placebo, an active treatment, or no treatment.

Placebo

A treatment with no active ingredient that is otherwise like the active treatment.

Placebo effect

When subjects respond favorably because they believe they are receiving a treatment, rather than because of the treatment's active ingredient.

Blinding

Keeping subjects and/or people who interact with them or measure responses unaware of which treatment subjects receive.

Single-blind experiment

An experiment in which either the subjects or the people interacting with them/measuring responses do not know which treatment each subject receives.

Double-blind experiment

An experiment in which neither the subjects nor the people interacting with them/measuring responses know which treatment each subject receives.

Completely randomized design

An experimental design in which all experimental units are assigned to treatments completely at random.

Randomized block design

An experiment that first divides experimental units into blocks of similar units, then randomly assigns units to treatments separately within each block.

Block

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

Matched pairs design

A randomized block design for two treatments in which experimental units are paired by similarity, or the same unit receives both treatments in random order.

Matched pairs using the same subjects

Each experimental unit receives both treatments, with the order randomized.

Replication

Using multiple experimental units in each treatment group; it helps distinguish treatment effects from chance variation.

Direct control

Keeping the values of some variables the same for all experimental units to prevent those variables from confounding the results.

Four components of a well-designed experiment

Comparison/control, random assignment, replication, and direct control of extraneous variables.

Comparison

Using two or more treatments so their responses can be compared fairly.

Purpose of random assignment

To create treatment groups that are roughly equivalent at the beginning, balancing lurking variables on average and supporting cause-and-effect conclusions when results are statistically significant.

Purpose of replication

Using enough experimental units in each treatment group to make treatment differences easier to distinguish from chance variation.

Purpose of direct control

Keeping relevant conditions the same across groups so they do not provide alternative explanations for observed differences.

Purpose of a control group

To provide a baseline for comparison, helping determine whether outcomes are due to the treatment rather than other factors or changes over time.

Statistically significant result

An observed difference so large that it would be unlikely to occur from chance variation in random assignment alone if the treatments had no effect.

Simulation for statistical significance

A chance model that shows what differences could occur from random assignment alone under the assumption that the treatment has no effect.

5% significance guideline

If fewer than about 5% of simulated differences are at least as extreme as the observed difference, the result is commonly considered statistically significant.

Random sampling and inference

Random sampling supports generalizing results to the population from which the sample was randomly selected.

Random assignment and inference

Random assignment in a well-designed experiment supports cause-and-effect conclusions if the results are statistically significant.

Scope of inference

The conclusions a study can support: random sampling supports population generalization; random assignment supports cause and effect.

Why observational studies cannot establish causation reliably

Researchers do not impose treatments or randomly assign explanatory-variable conditions, so confounding variables may explain the association.

Data ethics: IRB

An institutional review board reviews planned studies to help protect participants' rights and welfare.

Informed consent

Participants agree to take part after being given relevant information about the study.

Confidentiality

Individual data are kept private; public reports should generally present statistical summaries rather than identifiable individual data.

Four components of sampling methods

Identify the population/frame, use a chance-based selection method when required, select the sample according to the method, and recognize how the method affects representativeness and inference.

Three major experimental designs

Completely randomized design, randomized block design, and matched pairs design.

Stratified vs. cluster sampling

Stratified sampling selects some individuals from every stratum; cluster sampling randomly selects entire clusters and usually includes every individual in chosen clusters.

When stratified sampling is effective

When individuals within each stratum are similar on the variable of interest and strata differ from one another.

When cluster sampling is useful

When the population is large or spread out and selecting whole groups saves time or money.

How bias affects an estimate

Bias can systematically push a sample statistic above or below the true population parameter; a larger sample does not necessarily remove bias.

Sampling variability

The natural variation in sample statistics from sample to sample, even when the same method and sample size are used.