AP Statistics 4.1-4.3

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56 Terms

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Population

A parameter, true mean

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Simple Random Sample steps

1. Label individuals

-assign numbers, write names on strips of paper

2. Randomize

-Random number generator(no repeats)

-Random digit table

-Names in hat (shuffled)

3. Select

-BS results, corresponding name with #

4. Repeat process

-until total sample size

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Explain clearly how you would use your calculator to choose a sample of 75 students for this study.

You should assign numbers 1-3478 to the students, making sure each student has a unique number. Using your calculator you can generate 75 random numbers 1-3478. If a number repeats you can reenter the operation (1, 3478, 75). Do this until 75 random numbers are selected. Then you can use random assignment again to split the students into groups.

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simple random sample

A sample of size n selected from the population in such a way that each possible sample of size n has an equal chance of being selected.

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simple random sample example

In an effort to identify whether an advertising campaign has been effective, a marketing firm conducts a nationwide poll by randomly selecting individuals from a list of known users of the product

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systematic sampling

Every nth item in the target population is selected.

Pros: Easy to gather data if pop units are lined up, and unbiased

Cons: only useful in certain scenarios

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systematic sampling example

Starting with a randomly chosen ice cream customer, every 5th customer was chosen and that customer was asked to fill out a survey.

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cluster sampling

Randomly choose 1 or more cluster and sample everyone in that cluster.

Pros: Easiest to implement, unbiased, accurate

Cons: If large variation in between clusters it's imprecise

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cluster sampling example

Students from Waterloo Region, randomly selects 20 schools from 120 schools, then contacts every student from each of the 20 chosen schools

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stratified random sampling

Population divided into subgroups (strata) and random samples taken from each strata

Pros: can be very precise, and unbiased

Cons: sometimes can be difficult to implement

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stratified random sampling example

divide demographics by age, gender etc., then random sample each 'strata'

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Judgemental/convenience sample

Someone is easily chose, not by random number generator

Pros: None

Cons: biased

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convenience sample example

To represent all the students attending a school, the principal surveys the students in one math class.

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voluntary response bias

bias introduced to a sample when individuals can choose on their own whether to participate in the sample (tends to be people with strong opinions)

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Selection bias

A polling error in which the sample is not representative of the population being studied, so that some opinions are over- or underrepresented

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undercoverage bias

occurs when some members of the population are inadequately represented in the sample

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non-response bias

Bias introduced into survey results because individuals refuse to participate.

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Response bias

anything in a survey design that influences responses.

Ex: the people who are asking, the environment

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Wording bias

a type of response bias where the question is posed to achieve a desired result

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Measurement bias

a form of inaccurate measurement in which the data consistently overestimate or underestimate the true value of an event. On the person doing the measurement.

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observational study

Observes individuals and measures variables of interest but does not attempt to influence the responses. There's no treatment imposed.

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observational study example

Compare the grades on the next unit math test of 25 students who use calculators and 25 students who do not use calculators. The students decide which group they're in.

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retrospective study

A study using information on events that have taken place in the past

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retrospective study example

investigating the link between childhood exposure to lead paint and current rates of cognitive impairment in adults by reviewing medical records of individuals born in a specific time period to identify past lead exposure levels and then comparing those levels to their current cognitive function test results

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prospective study

an observational study in which subjects are followed to observe future outcomes

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prospective study example

female nurses who smoke and those who do not smoke) and compares them for a particular outcome (such as lung cancer)

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Explanatory variable(factor/independent)

helps explain/predict response

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response variable (dependent variable)

measures an outcome of a study

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confounding variable

a factor other than the factor being studied that might influence a study's results (influences explanatory and response variables)

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Experiment

A research method in which an investigator manipulates one or more factors to observe the effect on some behavior or mental process (treatment imposed, shows casuation)

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Treatment

What is done (or NOT done) to the experimental units,

- levels x levels

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Experimental units

who/what the treatment is imposed on (if humans we call them subjects)

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factors

the explanatory variables in an experiment. (EX: type of drink, caffeine, etc)

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Levels

different values of the factor

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Control group

In an experiment, the group that is not exposed to the treatment or gets a placebo; serves as a comparison for evaluating the effect of the treatment.

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Placebo

any treatment given as a control, appears real but has no benefit

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placebo effect

experimental results caused by expectations alone; when a fake treatment works

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blinding

when subjects (single-blind) and/or experimenters (double-blind) who interact with subjects are unaware of what treatment was assigned

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Everyone _____ blinded.

cannot be. Someone has to know

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Key Principles of a well-designed experiment

1. Comparison: 2 or more treatments

2. Random Assignment

3. Control: Keep all other variables besides the treatments constant; minimize confounding

4. Replication: Using enough experimental units to distinguish differences

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Control is _____.

Not required for an experiment

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Block

a group of experimental units that have a similar characteristic

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How to describe an experiment

1. State subjects/experimental units if not yet listed

2. Justify blocks/pairs similar if needed - choose one

3. Randomly assign to treatments (elaborate if asked) stating how many go to each

4. Repeat if needed for other blocks

5. State what you are comparing in(response variable) context.

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Randomized block

units are blocked into groups and then randomly assigned to treatments within each block

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Matched pair

A block design of size 2 (pairs), there are two possible formats:

1. Subjects are paired first and then randomly assigned to the two treatments

2. Each subject receives two treatments in a random order.

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Different Samples...

yield different results due to natural variation

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Larger sample sizes...

reduce the variability of estimates

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Margin of error

creates an interval of plausible values

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plausible

(adj.) appearing true, reasonable, or fair

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Statistically significant

refers to a result that is statistically unlikely to have occurred by chance

-if proportion of dots < 5%, then statistically significant

-if proportion of dots > 5%, then not statistically significant

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Random sampling allows us to...

make generalizations about the population from which we sampled

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Random assignment

Allows us to say a treatment causes changes in the response variable

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Randomly selected and random assignment

Inferences about pop: yes

Inferences about cause and effect: yes

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NOT randomly selected & IS randomly assigned

Inferences about pop: no

Inferences about cause and effect: yes

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Randomly selected and NOT randomly assigned

Inferences about pop: yes

Inferences about cause and effect: no

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NOT randomly selected and NOT randomly assigned

Inferences about pop: no

Inferences about cause and effect: no