AP Statistics Unit 3

sample

a subset of a population used to estimate characteristics of the whole population.

It’s only appropriate to make generalizations about a population based on samples that:

• Are randomly selected or otherwise representative of that pop.

• Were selected from that pop. specifically

Confounding factors

hard to parse out if the cause is one of these factors, a combo, or none of these

observational study

• survey that was taken without imposing treatments on individuals

• cannot infer cause + effect relationships

There are two types of observational studies:

Prospective and retrospective

Retrospective

Examine current or past data for a set of individuals

Prospective

follow a sample of individuals into the future for collecting data

Experiment

Different conditions(treatments) are imposed upon subjects

Census

• Collects data from all individuals in a pop.

• Very hard to do

Random sample

• Much easier than measuring everyone

• If done well, is an accurate data collection method

We are going to go over types of random samples

yay so skibbidi

Simple Random Sample (SRS)

• Every group of a given size has an equal chance of being chosen

• Representative of sample, unbiased, not as precise as other methods

• Hard to collect data

Cluster Random Sample

• Population is divided into groups

• SRS of groups is taken

• All indivs within the groups selected are sampled

• Unbiased, clusters must be heterogenous in order to have less variability

• Easier to collect data

Stratified Random Sample

• Pop. is divided into strata, based on a similar characteristics

• SRS within each strata is taken

• A few indivs from each strata are chosen and combined into larger sample

• Unbiased, very precise (low variability)

• Very difficult to implement

Cluster and Stratified are most effective with what conditions?

Cluster - heterogenous

Stratified - Homogenous

Systematic Random Sample

• Randomly choose a starting point and then sample at a fixed periodic interval

• Easy to collect sample (primary advantage)

Bias is a measure of

accuracy

undercoverage bias

when part of the pop. has a reduced chance of being included in a sample

ex: excluding students who didn’t graduate

nonresponse bias

when indivs chosen for a sample don’t respond

(leads to bias if these indivs differ from respondents)

voluntary response bias

occurs when an invitation is sent to all indivs in a pop. to participate. Those wo choose to participate (volunteers) may differ from indivs who don’t choose to participate

FRQ Bias tip

On an FRQ, if you’re unsure, don’t try to use one of these vocab terms, instead, just describe the bias, how it arises, and whether it leads to an underestimate or overestimate

we will go over survey-specific bias

okidoki

question wording bias

when survey questions are confusing or misleading

self-reported response bias

when indivs inaccurately report their own traits

confounding variable

another var that is related to the explanatory var and influences the response var and may create a false perception of association between the two

One issue with observational studies is that there is a possibility of

having a confounding variable

Observational studies cannot determine….

causation

A well-designed experiment contains

• Comparisons of at least two treatment groups (one of which could be a control group)

• Random assignment of treatments to experimental units

• Replication (use enough experimental units in each treatment group)

• Control of possible confounding vars where appropriate

For designing experiments in FRQs you must…

Explain the method of random assignment

A method of random assignment

• number something 1 to n

• the 1st random # selected corresponds to a cow that will be assigned to the 1st group

• continue until the desired # of cows have been assigned to each experimental group

benefit of random assignment

tends to balance the effects of potential confounding vars so that differences in responses can be attributed to the treatments

randomized block design

• ensures that units within each block are similar with a regard to blocking var

• helps separate natural variability from differences due to the blocking var

blocking

non-randomly splitting a group into two separate groups in a way that reduces bias and gives more accurate results

Placebo

fake treatment that is similar to the treatments being tested

Placebo effect

when experimental units have a response to a placebo

Single-blind experiment

subjects don’t know which treatment they are receiving. but researchers do (or vice versa)

Double-blind

Neither the subjects nor the researchers who interact with subjects are aware of the treatments being administered

Matched pairs design

Special type of block design where blocks are made between pairs of things that are closely aligned. Within each block, both treatments are randomly assigned.

The use of a placebo helps determine if an effect is truly due to the treatment and not simply cuz of the …

placebo effect

treatments

what you are manipulating in a study

Random assignment allows us to conclude that very large observed changes are not merely by…

chance (or are statistically significant)

Decisions from the sample can be attributed to the _______ from which the sample was drawn

population

If experimental units are representative of the pop, then the results can be generalized to the …

pop of subjects like the ones in the study

Random selection of indivs gives a better chance that the sample will be representative of the…

population

If asked to describe how design of a sample survey leads to bias, you’re expected to do two things:

1. describe how members of the sample might respond differently than rest of pop

2. explain how difference would lead to an underestimate or overestimate of value you want to know

Response bias

occurs when there is a consistent pattern of inaccurate responses to a survey question

When asked to identify a possible confounding var, your expected to explain how the var you chose is associated with

the explanatory var and the response var

factor

an x var that is manipulated and may cause a change in the y var

levels

different values of a factor

If experimental units were not randomly selected, so the largest population to which we can generalize the results of this study is eus like the eus in the study, but if randomly selected, we can generalize the results to

the population where the sample came from!