unit 2 exam

Contingency Table

A table that shows how individuals are distributed along each variable.

Marginal Distribution

The row total or column total in a contingency table.

Conditional Distribution

The distribution of one variable for cases that satisfy a condition on another variable.

Population

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

Sample

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

Sample Survey

A study that asks questions of a sample drawn from some population in the hope of learning something about the entire population.

Randomization

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

Census

A sample that consists of the entire population.

Population Parameter

A numerically valued attribute of a model for a population.

Sample Statistic

Values that are calculated for sample data.

Sampling Frame

A list of individuals from whom the sample is drawn.

Simple Random Sample (SRS)

A sample in which each set of elements in the population has an equal chance of selection.

Stratified Random Sampling

A sampling design in which the population is divided into several subpopulations and random samples are drawn from each stratum.

Cluster Sampling

Entire groups, or clusters, are chosen at random.

Multistage Sampling

Sampling schemes that combine several sampling methods.

Systematic Sample

A sample drawn by selecting individuals systematically from a sampling frame.

Voluntary Response Bias

Bias introduced to a sample when individuals can choose whether to participate.

Undercoverage Bias

Biases the sample by giving a part of the population less representation.

Nonresponse Bias

Bias introduced when a large fraction of those sampled fails to respond.

Response Bias

Anything in a survey design that influences responses.

Observational Study

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

Retrospective Study

An observational study in which subjects are selected and their previous conditions or behaviors are determined.

Prospective Study

An observational study in which subjects are followed to observe future outcomes.

Matching in Studies

Participants who are similar in ways not under study may be matched and then compared on the variables of interest.

Experiment

Manipulates factor levels to create treatments, randomly assigns subjects to these treatment levels, and then compares the responses of the subject groups.

Factor

A variable whose levels are manipulated by the experimenter.

Response Variable

A variable whose values are compared across different treatments.

Levels

Specific values that the experimenter chooses for a factor.

Treatment

Process, intervention, or other controlled circumstance applied to randomly assigned experimental units.

Block

When groups of experimental units are similar in a way that is not a factor under study, it is often a good idea to gather them together into blocks and then randomize the assignment of treatments within each block.

Randomization through Random Assignment

An experiment must assign experimental units to treatment groups using some form of randomization.

Control

Control aspects of the experiment that may have an effect on the response, but are not the factors being studied.

Replicate

Replicate over as many subjects as possible.

Statistically Significant

When an observed difference is too large to have occurred naturally, it is considered statistically significant.

Completely Randomized Design (CRD)

All experimental units have an equal chance of receiving any treatment.

Randomized Block Design (RBD)

Participants are randomly assigned to treatments within each block.

Matched Pair Design

Participants are paired with similar subjects, and the difference in response variables is compared.

Control Treatment

Experimental units assigned to a baseline treatment level.

Control Group

Experimental units assigned to a baseline treatment level, providing a basis for comparison.

Blinding

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

Single Blind

When either those who could influence the results or those who evaluate the results are blinded.

Double Blind

When both those who could influence the results and those who evaluate the results are blinded.

Placebo

A treatment known to have no effect.

Placebo Effect

The tendency of human subjects to show a response even when administered a placebo.

Confounding

When the levels of one factor are associated with the levels of another factor in such a way that their effects cannot be separated.

Lurking Variable

A variable associated with both y and x that makes it appear that x may be causing y.

Random Phenomenon

A phenomenon is random if we know what outcomes could happen, but not which particular values will happen.

Trial

A single attempt or realization of a random phenomenon.

Outcome

The value measured, observed, or reported for an individual instance of a trial.

Event

A collection of outcomes.

Sample Space

The collection of all possible outcome values.

Law of Large Numbers (LLN)

The long-run relative frequency of an event's occurrence gets closer to the true relative frequency as the number of trials increases.

Independence

Two events are independent if learning that one event occurs does not change the probability that the other event occurs.

Probability

A number between 0 and 1 that reports the likelihood of an event's occurrence.

Empirical Probability

The probability that comes from the long-run relative frequency of an event's occurrence.

Theoretical Probability

The probability that comes from a model, such as equally likely outcomes.

Personal (or subjective) Probability

The probability that is subjective and represents personal belief.

Legitimate Assignment of Probabilities

An assignment of probabilities to outcomes is legitimate if each probability is between 0 and 1, and the sum of the probabilities is 1.

Probability Assignment Rule

The probability of the sample space must be 1.

Complement Rule

The probability of an event not occurring is 1 minus the probability that it occurs.

Addition Rule

The probability that one or the other of two disjoint events occurs is the sum of their individual probabilities.

Multiplication Rule

The probability that both of two independent events occur is the product of their individual probabilities.

General Addition Rule

The probability of the union of any two events is the sum of their individual probabilities minus the probability of their intersection.

Conditional Probability

The probability of an event given that another event has occurred.

General Multiplication Rule

The probability of the intersection of two events is the product of their individual probabilities.

Independent Events

Events are independent if the probability of one event occurring does not affect the probability of the other event occurring.

Tree Diagram

A display of conditional events or probabilities that is helpful in thinking through conditioning.

Bayes Rule

A rule that calculates the conditional probability of an event given another event using the probabilities of the two events and their complements.

Binomial Distribution

A sequence of trials with exactly 2 possible outcomes (success and failure), where the probability of success is constant and the trials are independent. There are a fixed number of trials, n.

Success/Failure Condition

A condition for a Binomial Model to be approximately Normal, where there are at least 10 successes and 10 failures, i.e. np ≥ 10 and n(1 - p) ≥ 10.

P(A | B)

The probability of event A given event B, which is calculated using Bayes Rule:P(A | B) = P(B | A) P(A) / (P(B | A) P(A) + P(B | Not A) P(Not A)).

P(B)

The probability of event B, which can be calculated using the Multiplication Rule:P(B and A) = P(B) P(A | B).

Binomial Model

A probability model used for binomial distributions, where the probability of exactly k successes in n trials is given by P(X = k) = n! / (k! (n - k)!) p^k (1 - p)^(n - k). The mean is μ = np and the standard deviation is σ = sqrt(np(1 - p)), where n! represents n factorial.