AP Stats Unit 1 Part 2

experiment

hands on - researchers manipulate the variables

response variable

variable that measures the OUTCOME of a statistical study

explanatory variable

variable that predicts/explains a change in the response variable

factors

the variables that are manipulated in an experiment

levels

the values of the factors

treatments

the combination of the levels and the factors applied to an experimental unit

experimental units

non-human individuals in an experiment

subjects

human individuals in an experiment

observational study

hands off - researchers just collect data

retrospective

gathering data from the past

prospective

data gathered in real time, going forward as well

survey

collect data by asking questions of a sample

extraneous variable

variable other than the explanatory variable that may affect the response variable

confounding variable

a variable associated with both the explanatory and response variables (subset of extraneous)

census

collecting data by asking questions of a population

randomly assigned treatments shows

cause and effect

randomly sampled group of target population shows

generalization

components of an investigative question

guides the data collection process, guides the choice of data analysis

methods, and indicates the types of conclusions that can be made.

1st component of an investigative question

identify the variable(s)

2nd component of an investigative question

identify type of inference, including parameters

what are the two types of inferences

1: estimate a population parameter. 2: test a claim about the population

3rd component of an investigative question

indicate the type of conclusion that can be made, including the population to which results can be generalized, and the possibility of a cause and effect conclusion

Investigative Question for causation

For (population of interest), does (explanatory variable) CAUSE (direction of outcome) in (response variable) compared to (comparison group)?

investigative questions for association

For (population of interest), is (explanatory variable) ASSOCIATED WITH (direction of outcome) in (response variable) compared to (comparison group)?

Simple Random Sample

every possible group of individuals in the population has an equally likely chance of being selected

How to carry out an SRS

1: Label - all of the individuals to choose from. 2: Randomize - selection must be random (calc, numbers in a hat, number table). 3: Select items based on numbers generated

Stratified Random Sample

Split people/items into strata or groups that share characteristics that may be associated with one of the variables being measured. Then choose an SRS from each stratum to create a sample

Cluster Random Sample

Split people/items up into clusters, or groups of the population that are located near each other. Take an SRS of clusters and perform a census of each selected group.

Systematic Random Sample

Survey every nth person/item on a list of all possible participants/items in the sample frame. Be sure the list is not ordered.

Sampling Variability

Sampling variability shows how random samples differ from each other, sample-to-sample differences.

What are bad sampling methods

Voluntary response sample and convenience sample. Due to researcher issues

What are biases

Non-response, undercoverage, and response bias. Due to respondents issue

What is non-response bias

Anything where you don’t get 100% responses. We don’t know why the others didn’t respond.

What is undercoverage bias?

Missing out on part of the population

What is response bias?

Biased by how the question was asked or who was asking it

How to write about the impact of a bias on a sample

1: Identify the population of interest and the sample selected. 2: Identify the observational units that may be excluded from the sample and how they differ. 3: Explain how the exclusion leads to an over or underestimate (impact) of the parameter.

4 Principles of Experimental Design

1. Comparison of at least two treatments.

2. Random assignment of treatments to experimental units.

3. Replication - many experimental units in each treatment group.

4. Control of extraneous variables.

optional elements of an experimental design

control group, placebo, placebo effect, single-blind study, double-blind study

Control group

group with no treatment for comparison purposes

placebo

fake/inactive treatment given to experimental units

placebo effect

change in response variable despite no active treatment

single-blind study

one group (subjects or researchers) don’t know which group is which

double-blind study

both groups (subjects and researchers) don’t know which group is which

statistically significant

large enough to be unlikely to happen by chance

Completely Randomized Design

experimental units are assigned to treatments completely at random

how to describe a completely randomized design

number all experimental units 1-n. split into as many groups as treatments. assign each group to a treatment. run the experiment. compare response variables between groups.

Randomized Block Design

experimental units are grouped in blocks, based on an extraneous variable. then response variables are compared within blocks.

how to describe a randomized Block Design

create blocks based on extraneous variable. split into as many groups as treatments and assign each group to a treatment. run the experiment. compare response variable within blocks.

Randomized Block Design purpose

gives us control over the impact of the blocking variable in the response variable

Matched Pairs Design

1. Each block is composed of 2 similar experimental units (matched pair)

2. The same experimental unit receives both treatments and the order of treatments is randomized.

how to describe Matched Pairs Design

have one person act as their matched pair. randomize the two treatments. give the two treatments, then compare within matched pair.

Matched Pairs Design purpose

to give us EXTREME control