unit 1b stats

Census

Records information from every single item or individual in a population.

Observational study

Treatments are not imposed; the researcher simply measures existing variables (cannot prove causation).

Prospective study

An observational study where units are selected in the present and tracked into the future.

Retrospective study

An observational study where units are selected in the present and past data is collected.

Survey

An observational study collecting data from human respondents using a standard set of questions.

Experiment

The researcher intentionally assigns treatment conditions to units to test a cause-and-effect relationship.

Experimental unit

The smallest unit to which a treatment is assigned (called subjects or participants when humans).

Explanatory variable (factor)

The variable whose categories or levels are intentionally imposed on units.

Response variable

The outcome variable measured on each unit after treatment is applied.

Confounding variable

A variable associated with BOTH the explanatory and response variables, offering an alternative explanation for the results.

Random selection

Units are chosen from the population using a random mechanism (e.g., random number generator).

Generalization

Allowed to the entire population ONLY if units were randomly selected; otherwise, applies only to similar individuals.

Sampling without replacement

Selected units are not returned to the population, so they cannot be picked again.

Sampling with replacement

Selected units are returned to the population, so they can potentially be chosen again.

Simple random sample (SRS)

Sample size n where every possible combination of size n has an equal chance of selection.

Stratified random sample

Population is split into homogeneous groups (strata) by a trait, then an SRS is taken from EVERY stratum.

Cluster random sample

Population is split into heterogeneous mini-groups (clusters), an SRS of clusters is chosen, and EVERY unit in selected clusters is measured.

Systematic random sample

Choosing units at a fixed periodic interval after a random starting point.

Bias

Systematic error in sampling that consistently over- or underestimates a parameter; describes the method and is NOT fixed by larger samples.

Voluntary response bias

Occurs when sample consists of self-selected volunteers who often hold strong, extreme views.

Undercoverage bias

Occurs when certain groups in the population are left out or less likely to be chosen by the sampling frame.

Nonresponse bias

Occurs when chosen individuals fail or refuse to respond, and their traits differ from respondents.

Response bias

Occurs when confusing questions, interviewer behavior, or self-reporting leads to inaccurate/misleading answers.

Nonrandom sampling methods

Methods like convenience or voluntary response sampling that lack chance and introduce bias.

Convenience sample

Selecting individuals who are easiest to reach; highly susceptible to bias.

Well-designed experiment

Includes comparison of treatments, random assignment, replication, and direct control of extraneous variables.

Control group

Baseline group receiving an inactive treatment or no treatment for comparison.

Placebo

An inactive treatment disguised to look and feel like the active treatment.

Placebo effect

The response improvement seen from taking a placebo compared to no treatment.

Single-blind

Experiment where subjects do not know their assigned treatment, but evaluators do (or vice versa).

Double-blind

Experiment where neither subjects nor evaluators interacting with them know who receives which treatment.

Extraneous variable

Any variable other than the explanatory variable that might affect the response variable.

Purpose of random assignment

Balances extraneous variables across treatment groups so differences in response can be attributed to the treatment.

Replication

Assigning multiple experimental units to each treatment group to reduce chance variation.

Direct control

Keeping potential extraneous variables at a constant setting across all experimental units.

Completely randomized design

Treatments are assigned to all experimental units entirely by chance.

Blocking variable

A known source of extraneous variation used to group similar subjects before assigning treatments. (Ex. Demographics, time, environment)

Randomized block design

Units are split into homogeneous blocks based on a trait, then randomly assigned treatments within each block.

Purpose of blocking

Reduces variability in response variables caused by the blocking trait, making treatment comparison more precise.

Matched pairs design

Subjects are paired based on similar traits (or act as their own control in a pre-test/post-test setup), with one treatment randomly assigned to each member of the pair, or each unit may receive both treatments with the order randomized

Cause-and-effect conclusion

Justified ONLY when treatments are randomly assigned to experimental units.

FRQ Tip - Selection vs. Assignment

Random SELECTION allows generalization to population; Random ASSIGNMENT allows cause-and-effect conclusions.

FRQ Tip - Writing SRS steps

Label every unit 1 to N, use RNG to generate n unique numbers ignoring repeats, and match numbers to individuals.

FRQ Tip - Describing Bias

State the bias type, name the group over/underrepresented, and explain how the statistic will systematically differ from the truth.