AP Stats: Unit 4 (experiments)

Observational Study

A study that does not attempt to alter the behaviors of participates. Outcomes are simply measured (observed)

Experimental Study

Study in which a treatment (or multiple treatments) is applied. The explanatory variable is manipulated in order to measure a response.

Convenience Sample

A researcher gathers data that is easy to obtain

Systematic Sample

A researcher collects data from every n^th individual available

Stratified Sampling

A researcher collects data randomly from different categories (or “strata”) for equal or proportional representation

Clustered Sampling

A researcher randomly selects several “clusters” of individuals, and all members of the selected clusters are in the sample. 

Simple-Random Sample (best in most cases)

All members of the population are equally likely to be included in the sale and all groupings are possible

Bias in stats

A systematic over or under estimation of the value of a parameter

Parameter

Population value → Standard dev, mean, etc

Undercoverage Bias

Certain indiduals or groups are excluded from the sampling methodi

Non-response Bias

Individuals are selected for a sample but do not (or cannot) produce a response

Voluntary-response Bias

Members of a population selected themselves to contribute a response

Response bias

A response given by a member of the sample, but it is incorrect in some way (a lie, influenced by interaction, misunderstanding, etc.)

Experimental Unit

The smallest “group” to which a treatment is applied. It is usually an individual (who/what got the treatment)

Factors are…

explanatory variables

Factors are explanatory variables that may be…

combined to form a treatment

Principals of Experimental Design

What makes a good experiment?

What are the four factors in Prinipals’s of Experimental Design?

Comparison, Control, Random Assignment, Replication

Comparison

2 or more groups should be compared

Control

Hold certain variables constants to reduce variability (and confounding)

Random Assignment

Use a chance process to assign experimental units to treatment groups (this allows us to conclude cause and effect)

Replication

Use enough units (large n) to show a consistent change in the response variable

Confounding

Occurs when a third variable (a confounding variable) affects both the independent and dependent variables, distorting the observed relationship between them.

Types of experiments

Completely Randomized, Randomized Block, (and matched pairs: but don’t worry about this as much)

Completely Randomized

The first division to groups is random

Randomized Block

The first division to groups is non-random (based on a categorical variable)

Matched pairs

Special case of randomized block in which each “block” contains only 2 individuals (or some individual)

To do matched pairs, we compare treatments on…

identical twins, “twin-like” pairs → 2 individuals are matched on multiple measures, one individual is its own “clone” (2 measures from 1 individual.

Double-Blind

Neither the participant(s) nor the researcher* know which treatment is which (*lead researcher keeps track)