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AP Statistics Unit 3 Cheat Sheet by

AP Statistics Unit 3 Study Guide

Simula­tions Terms

simulation
the imitation of chance behavior, based on a model that accurately reflects the experiment under consid­eration
stopping rule
"­con­tinue selecting until ..."

How to Write Simulation Descri­ption

1. Select __ digit numbers to represent __.
2. Let __ - __ represent ___ and let __ - __ represent ___.
3. Select __ or Continue selecting ___ until ___.
4. Record ___.
5. Trial One : ___ ; Trial Two : ___ ; Trial Three : ___

Simulation Example

Alex needs a blood transf­usion. She needs to find someone with B+ blood or she will die. 9% of all people have B+ blood. How many people on average would you need to check the blood type of until you find someone who can save Alex's life?
1. Select 2-digit numbers to represent people
2. Let 00-08 represent people with B+ blood and 09-99 represent people without B+ blood
3. Continue selecting people until you find someone with B+ blood
4. Record how many people you select before you find someone with B+ blood
5. Trial One:6 ; Trial Two:16 ; Trial Three:15

Sampling Design Example

a college professor wants to survey a sample of students taking her large lecture course. There are about 150 students in the course, and 10 of those students are graduate students. She wants to take a systematic random sample of approx­imately 30 students. Which strategy will accomplish her intended design?
randomly select one of the first 5 students to arrive to class, and every 5th student thereafter to take the survey.

Biases

bias
a systematic error in measuring the estimate that would repeatedly cause the data to be wrong
voluntary response bias
people select themselves to partic­ipate in the study
nonres­ponse bias
indivi­duals who are randomly chosen for the sample cant be contacted or refuse to cooperate
conven­ience sampling
asking people who are easy to ask; convenient but not random
under coverage bias
some groups are left out of the selection process
response bias
the behavior of the respondent or interv­iewers causes you to get incorrect answers
wording bias
when wording of the question influences the answers that are given

Bias Examples

voluntary bias
online polls, facebook questi­onn­aires
nonres­ponse bias
mailed polls, new apps on phone
conven­ience bias
friendly looking people, all people at the park
under coverage bias
only your neighb­orhood, phone books
response bias
cosplayer asking if people think cosplay is weird
wording
using strong vocabulary
 

Sampling Design Terms

population
the entire group of indivi­duals we want inform­ation about
census
a complete count of the popula­tion; when you gather general inform­ation about the entire population
sample
a part of the population we actually examine in order to gather inform­ation
sampling design
the method used to choose the sample from the population
sampling frame
a list of every individual in the population
simple random sample
every individual has an equal chance of being chosen
stratified random sample
population is divided into strata and then simple random sample is used on each stratum
systematic random sample
randomly select a number between one and n and survey every nth person after that
cluster random sample
randomly pick a location and sample all from that location
multistage sample
a combin­ation of different sampling techniques

How to Describe Sampling Design

simple random sample
put the names/­numbers of all ___ on slips of paper and place in a hat. Mix and randomly draw ___ slips of paper without replac­ement. Survey the corres­ponding people.
systematic random sample
number all ___ and place ___ numbers in a hat. Mix and randomly select one number and survey the corres­ponding person. Survey every nth person on the list after that.
cluster random design
number all clusters and put the numbers into a hat Mix and randomly select a number from the hat. Survey everyone in that cluster.
stratified random sample
sort everyone into strata then number ___ in all the stratum. place the numbers in a hat and draw __ numbers. survey the corres­ponding people in that specific stratum. repeat the process for all strata

Experi­mental Design Types

completely randomized design
experi­mental units are assigned completely at random to treatments
randomized block design
experi­mental units are blocked in homoge­neous groups and then randomly assigned to treatments
matched pairs design
a special type of block design; match up experi­mental unit according to similar charac­ter­istics and randomly assign one to treatment A and the other get treatment B automa­tically

Experi­mental Design Terms

observ­ational study
observe outcomes without imposing any treatment
experiment
actively impose a randomly assigned treatment in order to observe the response
experi­mental unit
the single individual to which the different treatments are randomly assigned
factor / explan­atory variable
what we test or what we change
level
a specific value or type for the factor
response variable
what you measure or record at the end of the experiment
treatment
a specific experi­mental condition applied to the units
control group
a group that is used to compare the factor against; can be placebo
placebo
a "­dum­my" treatment that can have no physical effect; not required in every experiment
blinding
method used so that units or evaluators do not know which treatment units are getting
double blinding
neither the units nor the evaluators know which treatment a subject recieved
confou­nding variable
a third variable that potent­ially affects both the factor and the response variable

Three Principles of Experi­mental Design

control the effects of extraneous variables on the response
random­ization used to assign subjects to treatments
replic­ation of the experiment on many subjects to quantify the natural variation in the experiment

Completely Randomized Design

Randomized Block Design

Experiment Example

A consumer group wants to test cake pans to see which works the best. It will test aluminum, glass, and plastic pans in both gas and electric ovens
experi­mental unit: cake batter
factors: material of pan & type of oven
levels: aluminum, glass, or plastic & gas or electric
response variable: evenness of cake
amount of treatm­ents: six
 

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  • Published: 28th February, 2024

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