ap stats sigma review

1-10: unit one, 11/12: unit two, 13-21: unit three, 22-29: unit four, 30-33: unit five, 34-42: unit six, 43-45: unit seven, 46-48: unit eight, 49-51: unit nine

categorical variable

classifies by a category/group (countries, colors, zip codes)

quantitative variable

classifies by a numerical, measurable value (height, number of something, etc.) can be discrete (only so many valuables) or continuous (many values)

frequency table vs relative frequency table

frequency table has the individual values, relative frequency table has the proportion

how to describe a distribution of a quantitative variable

center: median/mean
unusual features: outliers
shape: symmetrical, skewed, uniform
spread: range, iqr, sd

statistic vs parameter

statistic = sample

parameter = population

how to find outliers

q1 - 1.5(IQR) = leftmost outliers
q3 + 1.5(IQR) = rightmost outliers

or over 2 sd from the mean

resistant/robust statistics

median and iqr (not affected by outliers)

nonresistant/nonrobust statistics

mean, sd, range (affected by outliers)

five number summary plot

boxplot (min, q1, mean, q3, max)

empirical rule

68-95-99.7 = 68% of the data is 1 sd away, 95% is 2 sd, and 99.7 is 3 sd

how to describe a scatterplot

direction: positive/negative
unusual features: outliers
form: linear/nonlinear association
strength: weak or strong based on the line of best fit

extrapolation

BAD!!! DONT TAKE AN X FROM OUTSIDE THE GIVEN RANGE

experiment

participants are assigned treatments. CAN DETERMINE CORRELATION!

observational study

no treatments assigned. CANNOT DETERMINE CAUSATION!!!

simple random sample

everyone has an equal chance of being chosen

stratified random sample

divided into groups and then individuals are selected randomly in each group

cluster sample

divided into groups and the entire group is randomly selected

systematic random sample

first sample is random, then systematically chosen afterwards (every 5th person)

biases

voluntary response bias, undercoverage bias, nonresponse bias, and question wording bias

blinding

single blind: subjects dont know what treatment they’re getting
double blind: subjects and researchers don’t know what treatment they’re getting

experimental designs

completely randomized, randomized block design (sorted into groups then assigned treatments), and matched-pairs

conditional probability

a will occur, given b
p(a|b)= p(anb)/p(b)

multiplication rule for joint probabilities

p(anb)= p(a) x p(b|a)

how to tell if a and b are independent

p(a|b)= p(a) / p(b|a)= p(b)

addition rule / union

probability that either a or b will occur
p(aub)= p(a)+p(b)-p(anb)

mutually exclusive

p(anb)= 0
p(aub)= p(a)+p(b)

bernoulli trial

only two possible outcomes (success/fail) and probability of success is the same every time the experiment is conducted

binomial distribution

probability of a specific amount of successes in a specific amount of trials

geometric distribution

probability of first success on a specific trial number

standard normal distribution

bell curve shape (tails touching the line!!!), mu = 0 and sd = 1. named N(mu,sd)

central limit theorum

original population is normally distributed or SAMPLE SIZE IS >=30!!! also independent

assumptions and conditions for proportions

randomization, sample size (>10% of pop.), independence

assumptions and conditions for means

randomization, independence, sample size (>10% of pop. and n>=30)

confidence interval rules

sample size increases, width of confidence interval decreases
width of confidence interval increases, confidence level increases

conditions for confidence interval for one proportion

independence and normality (>=10)

conditions for confidence interval for two proportions

independence and normality for each proportion (>=10)

hypothesis test

procedure for testing a claim about a population based on a sample

null - h(o) = 0
alternative - h(a) >,<,=/= 0

p is more than alpha - fail to reject the null hypothesis
p is less than alpha - reject the null hypothesis

type 1 error

null hypothesis is rejected, but is actually true / false positive / probability of this error is alpha

type 2 error

null hypothesis is not rejected when it actually false / false negative

power of the test

null hypothesis will be rejected if it actually is false / beta

alpha and beta rules

inverse relationship - b increases, a decreases, etc.

b decreases, sample size increases/standard error decreases

z score

z = phat-p/sqrt(pq/n)

df

degrees of freedom = n-1

df increases, tail height decreases (looks more like normal model)

hypothesis test for mean

h(o) - mu = 0
h(a) - mu <,>,=/= 0

t score

t = (mean - mu)/(sd/sqrt(n))

t = (mean1 - mean2)/(SE)

chi square goodness of fit

whether a population fits a certain distribution

h(o) = there is no difference
h(a) = there is a difference

chi square homogeneity

test if two or more populations follow the same categorical distribution

h(o) = there is no difference in proportions
h(a) = there is a difference in proportions

chi square independence

like homogeneity, but for two variables for a single population

h(o)= there is no association
h(a)= there is an association

least squares regression line

yhat = a+bx

df = n-2

assumptions and conditions for lsrl

linearity, residuals, randomization, nearly normal

hypothesis test for slope

h(o) - b = 0
h(a) - b >,<,=/= 0