econ 325 ch4-6

descriptive statistics

organize, summarize, and present the data you have

inferential statistics

use sample data to learn about a wider population or process

statistics describe

samples

parameter describe

populations

inference use statistics to

learn more about parameters

parameter

numerical characteristics of the population

why do we sample

speed, cost, feasibility

importance of estimate

accurate and precise

what does it mean noisy of estimate

variance of estimate

simple random sampling

every unit in the population has the same probability of selection and selection is random

why simple random sampling means

gives a clean starting point for sampling distributions, standard errors, LLN, CLT

stratified sampling method

sample within subgroups to ensure every group is represented

cluster sampling method

sample whole groups survey selected areas

systematic sampling method

random start every kth

IID - independent part

one observation does not carry info about another

IID - identically distributed

each observation comes from the same underlying distribution

IID importance

justify the standard error formulas and CLT for inference

to avoid bias what to do

increase sample size

simple random sampling

sampling method on how units are selected from the population

can sample be SRS but not IID

when sampling without replacement from small population

sample without replacement reduce

independence as choosing one observation can change the probabilities for alter selection

when SRS treated as IID

population size is large and sample is small relative to population

importance of IID

makes sample stats predictable and allow us to use SE, LLN, CLT and regression inference

when standard errors can become misleading

when observations are dependent or drawn from different processes

sampling distribution

probability distribution of a statistic across all possible samples of a fixed size from the same population

population distribution

individual values in the full population

sample distribution

observed values in one sample

sample means 3 conditions when sample size increases

keeps same center, less spread, shape changes (more bell shaped)

sample mean estimates

population mean mean

unbiased estimator may not be perfect

it can miss the true value in one sample and unbiased is the center of the sampling distribution

standard error of the mean meaning

if you repeatedly drew samples of the same size the SE tells you how much the sample mean would typically move from sample to sample

how to reduce SE and tighter spread with same center

larger samples

finite population correction used when

sample is not small relative to the finite population

z scores tells us

how many SE the sample mean is from the population mean

law of large numbers

reliability of the average

central limit theorem

shape of the sampling distribution

central limit theorem under right conditions

the standardized sample mean gets closer to standard normal distribution

when CLT works well

random sampling, weak dependence, finite variance

what is considered large enough n

n ~ 30

importance of CLT

help understand confidence intervals, hypothesis test, regression

sample portion (p hat)

average of bernoulli observation

chi square link under normality about

inference for variance not sample mean

when to use z score when

SD is known and population is normal

when to use t test

when SD is unknown and small sample size