AP Stats- Chapter 11

• Census

• Random Sample

• Simple Random Sample (SRS)

• Cluster Random Sample

• Stratified Random Sample

• Systematic Random Sample

• Multistage Sample

• Convenience Sample

• collects data from all individuals in a population

  • best way to measure median household income

  • very hard to do

    • the US only attempts to pull it off once every 10 years :0

• Easier than census

• Should be representative of the general population if done well

• tends to provide unbiased estimates

• easy to explain

• can be easy to perform or not

• may not be as precise as other methods

• Every group of a given size (“n”) has an equal chance of being chosen/of selection

  • 1) Number all blank from blank to blank

  • 2) random number generator to select #’s between blank and blank, without replacement (no repeats)

• Samples are representative but it is very difficult to collect this data

ex: List of all students at my school

In a random sample: each member of the entire population has an equal chance of being selected.

In a Simple Random Sample: a group of size n is selected and every possible group has the same chance of being selected.

• Population is divided into clusters of individuals that are near one another

• SRS of clusters is taken

• All individuals within each cluster are sampled (entire groups)

• Much easier to collect sample data than with census or SRS

• There has to be difference BETWEEN the groups

Heterogenous subgroup → sample all

• Sampling is effective when clusters are heterogeneous and similar to one another

• Unbiased, high variability

• Bad if clusters are homogenous but are very different between clusters because that would lead to high variability and may get statisticians an estimate that is very far from the “truth” aka the true mean

ex: Randomly pick a cafeteria at school and ask everyone (aka all individuals are sampled!) there your question

1. this would be heterogenous because there are all different grade levels in one lunchroom

2. the clusters would be North A,B,C, South A,B,C cafeterias

3. then label them 1-6 and randomly select from those #’s

• Population is divided into strata based on a similar characteristic (homogeneous grouping)

• SRS within each stratum is taken

• Selected individuals are combined into a larger sample and then the median is found of this group

• It is very difficult to collect this data/implement, even more so than with SRS

• unbiased and low variability

  ex: homogenous within regions, each possible sample has a similar mix of inomes

ex: Split the school by grade and randomly select 50 students from within each group

• Cluster

  • Heterogeneous grouping

  • SRS of groups

  • Sample all individuals aka entire groups

• Stratified

  • Homogeneous grouping

  • SRS within each group

  • Sample selected individuals from each strata into one larger group

think:

cluster those bad guys (the bad guys movie because all the bad guys are dif animals but work together as a team so they are sampled as a team ;))

stratified: think ecology, all those same trees together but median found separately as they are all their own but same at the same time.

• Randomly choose a start point, then sample at a fixed periodic interval

• It is easy to collect the sample especially if the individuals in the population are “lined up”

• ex: assign people numbers 1-20 and then every 20th person is sampled afterwards

to remember:

Start at a randomly selected point, Yield samples at fixed intervals, and Stick to this system until you're done

yass 3rd syster

ex: Pick every 20th person in the list of students at my school

• Combination of multiple sampling methods

• you draw a sample from a population using smaller and smaller groups at each stage

• used when the population is very large

commonly

startified → systematic

clustered → systematic

• Those sampled are those conveniently available

• Often fails to be representative of the population

• can result in biased results

• for ease of the researchers

• Accuracy

• are you centered at the true value (ex: the median) you want to be estimating?

• A systematic tendency to favor certain responses over other

• Something researchers ant to get rid of

• It is deliberately or accidentally introduced to samples when we use bad surveys or experiments

• Bias is bad, error is normal

• unbiased(low bias)=accurate

• biased (high bias)=inaccurate

• Precision

• How much distance is there between the different estimates you may have gotten?

• Low variation/variability=precise

• High variation/variability = imprecise

is this error? if so..

Error comes from randomness, it is an expected change/deviation from the mean that can be measured

Bias is bad, error is normal

Unbiased and low variatation/variability

• Undercoverage

• Non response

• Voluntary response

• Response

When part of the population has a reduced chance of being included in a sample

ex: landline survey, younger people don’t use landline phones so they have a reduced chance of being included in the sample and more old people will be sampled which will lead to an overestimate of the age of the population

When individuals chosen for a sample don’t respond

Leads to bias if these individuals differ from the respondents

ex: Homework email, all students have a chance to respond but they refuse to respond because they don’t want their teachers to know they didnt do their homework

1. Identify the population and the sample and describe the bias

2. Explain how the sampled individuals might differ from the general population aka what is wrong with the survey, how this bias arises

   1. ONLY talk about bias, not error (aka sampling variability)

   2. (ex: why people did not respond to the survey)

3. Explain how this will lead to an overestimate or underestimate of the population

ex: What is wrong with this survey?

Do you think the Mayor will over or underestimate the true mean age of people in Springfield? Why?

When an invitation is sent to all individuals in a population to participate.

Those who choose to participate (volunteers) may differ from individuals who do not choose to participate

ex: voluntary would be filling out a survey afterschool in main office, only those with strong positive or negative views will respond to the survey and actually go to the main office

• How the question is worded or who asks the question

• Anything in a surgery design that influences responses

ex: boy scouts, the boyscout is wearing his unfirom so of course someone wont say they hate boyscouts

• Question Wording Bias

• Self-reported response bias

When survey questions are confusing or leading

When individuals inaccurately report their own traits

ex: I can deadlift 10000 pounds

List of individuals from whom the sample is drawn

note that: those in the population of interest but not in the sampling frame cannot be included in the sample

• Piece of a population

• Has statistics

• Have both error and bias

• Never take more than 10% of the population as a sample

  • as long as your sample is representative of the population you do not need to sample more.

  • If you go above 10% of the population there is a greater chance of the sample having similar opinions and the same ideas

ex: Sample size (ex: 100 students at my school) is NOT connected to the population size (every student at my school

Have parameters but

• although we rarely talk about them because they are from censuses which we know are extremely hard to conduct

show how stratified sampling can reduce the variability in the response variable (which in this case is the proportion of students in the sample who like the mandatory pep rallies) compared to a simple random sample.