AP Statistics - Last Minute AP Review

guess who prioritized another AP class and forgot to study for stats lol gl to you all too!

variable

characteristics about each case

case

individual we collect data from

statistic

value calculated from a sample

parameter

value calculated from a population

variance

a measure of spread, standard deviation squared

when data is unimodal symmetric

use mean and standard deviation

when data is skewed

use median and iqr

outlier rule

data values below q1 - 1.5(iqr) and above q3 - 1.5(iqr) are outliers

cumulative frequency graph

y-axis is always 0 - 100%, slope is never negative

z-score

[x - (x-bar)] / s

shifting data

(adding or subtracting) affects measures of center only

rescaling data

(multiplying or dividing) affects measures of center and spread

describing distributions

the distribution of [context] is [shape], centered at a mean/median of [center] and spread out with a standard deviation/iqr of [spread]. [outliers]

explanatory

x, independent

values being changed in an experiment (factors)

response

y, dependent

values being measured in an experiment

describing associations

there is a [direction], [strength], [form] association between [variable 1] and [variable 2]

correlation constant (r)

affected by outliers, unaffected by shifting and rescaling

measures strength of the linear association

slope interpretation

for each additional [explanatory], the predicted [response] increases/decreases by [slope]

Intercept interpretation

the model predicts that a(n) [explanatory] of 0 [x-units] will be [y-intercept]

this is/is not significant…

R^2 interpretation

[R^2] of the variability in [response] is accounted for by differences in the linear model using [explanatory]

residual

y - (y-hat)

“actual minus predicted”

leverage

away from the other points horizontally that has great influence on the linear model and r

influential point

changes the slope significantly

bowl of soup

the size of the sample doesn't matter compared to the quality of the sample (bigger does not equal better)

census

sampling the whole population

sampling frame

the list you draw your sample from

simple random sample (srs)

every possible group of n from a population has an equal chance of being sampled

stratified sample

divide the population into groups of individuals, called strata, that are similar in some way and do an srs in each to form a full sample

cluster sample

divides the population into clusters and randomly select to sample all individuals within them

systematic sample

sample every nth person, randomly determining where to start

multistage sample

a combination of two or more sampling methods

voluntary response bias

people choose whether or not to respond, typically those with stronger opinions

response bias

leads people to respond a certain way

undercoverage

some groups of the population are left out of the sample

nonresponse bias

an individual chosen for the sample cannot be contacted or does not cooperate

convenience sample

type of bias where you choose individuals who are easiest to reach

retrospective observational study

past data

prospective observational study

looking at data as it happens

treatment

made up of a combination of factors, assigned randomly

statically significant

when the observed difference is so great that it couldn't have been due to chance/randomization

blocking

reduces variability so that differences we see can be attributed to the treatments imposed

control group

provides a baseline (“basis for comparison”)

placebo effect

subjects can respond to something that doesn't exist

blinding

single: subjects don't know

double: subjects and researchers don’t know

confounding variable

another variable other than the factors that affects the response variable

lurking variables

affect both the explanatory and response variables

matched pairs design

one subject gets both treatments or use naturally paired subjects

replication

there needs to be more than one subject in each treatment group, if not replicate the experiment again

designing an experiment: introduction

the factors/response variable/treatments are…

[treatment 1] is the control group, which provides a baseline for comparison so we can see if there is an actual difference in [response variable] for subjects who [explanatory]

designing an experiment: randomization

we will randomly assign the n subjects to the treatments

assign them a number, #1-n and use a random number generator

the first [# of subjects] unique numbers are group 1

the next [# of subjects] unique numbers are group 2/3/4..

the remaining [# of subjects] are the last group

repeat this process for the [other] block

designing an experiment: blocking

we block this experiment by [blocking variable] because we want to reduce variability so that we can attribute the differences we see to the treatments being imposed

designing an experiment: blinding

we will (double) blind this experiment

the subjects won’t know what treatment they get [context] {and/or} the researcher won’t know who got what treatment

we blind the subjects to nullify the placebo effect, because if the subjects knew what treatment they were getting, the result could be from knowing instead of [explanatory] {and/or} we blind the researchers to keep them honest

sample space

set of all possible outcomes (S = {1, 2, 3…})

mutually exclusive/disjoint

events don’t share any outcomes in common

addition rule

for mutually exclusive: P(AuB) = P(A) + P(B)in general: P(AuB) = P(A) + P(B) - P(AnB)

union (u)

either event A, B, or both occurring

intersection (n)

event A and B happening

multiplication rule

if there are multiple things happening, multiply their probabilities

Independent events

events A and B are independent if P(B) = [P(B|A)]

conditional probability

P(A|B) = P(AnB) / P(B)

at least one probability

P(not 0) = 1 - P(0)

law of averages

is a scam, do not believe in it or its lies

probabilities do not change the more times one event occurs, nor do they do so to balance things out :c

law of large numbers

as we repeat a random process over and over again, the true probability will emerge

random variable (X)

a number based on a random event

expected value of a random variable

E(X) = Σ(x * P(x))

sum of value of that outcome times the probability it will occur for every outcome

standard deviation of a random variable

SD(X) = sqrt {Σ[(x - (x-bar))^2 * P(X)]}

the square root of the sum of [the value of the outcome minus E(X)] squared times the probability of that event occurring, for every outcome

adding two random variables

E(X + Y) = E(X) + E(Y)

SD(X + Y) = sqrt [SD(X)^2 + SD(Y)^2]

subtracting two random variables

E(X - Y) = E(X) - E(Y)

SD(X - Y) = sqrt [SD(X)^2 + SD(Y)^2]

summing a series

E(X1, X2…Xn) = n * E(X)

SD (X1, X2…Xn) = sqrt [n * SD(X)^2]

Bernoulli trials

only two possible outcomes, probability of success (p) is the same for every trial, trials are independent of each other

geometric probability model

about getting to the first success

P(X=x) = (1-p)^(x-1) * p

probability that the first success is the nth trial

P(X=n) = (1-p)^(n-1) * p

geometric pdf (p, n)

probability that the first success within n trials

P(X=1) + P(X=2)…+ P(x=n)

geometric cdf (p, n)

binomial probability model

fixed number of trials

P(X=x) = (nx) * p^x * (1 - p)^(nx)

n = number of trials

probability of x successes within n amount of trials

P(X=x) = (nx) * p^x * (1 - p)^(nx)

binom cdf (n, p, x)

probability of fewer than x successes within n amount of trials

binom cdf (n, p, [x-1])

x is not included

probability of more than x successes within n amount of trials

1 - binom cdf (n, p, x)

x is not included

probability of at least x successes within n amount of trials

1 - binom cdf (n, p, [x-1])

x is included

probability of at most x successes within n amount of trials

binom cdf (n, p, x)

x is included

probability of between x1 and x2 successes in n amount of trials

binom cdf (n, p, x2) - binom cdf (n, p, (x1-1)