Ch 5 Sampling and Sampling Methods

population

the entire group of study

parameter

any measure for a population

ex. population mean, population median

sample

subset (small group) of a population

statistic

any measure you find for a sample

ex. sample mean

ex. trying to find avg. GPA of UGA students. what’s the population, sample, & subject?

population: all UGA students

sample: UGA students in class

subject: Mark

ex. households in US. what’s the population, sample, subject, statistic, & parameter?

population: all households in U.S.

sample: households in Athens

subject: each

statistic: avg. household income in Athens

parameter: avg. household income in U.S.

sampling frame

where they’re taking the samples (ideally the population)

ex. Athens public library wants to know how many hrs/month the residents of Athens spend reading. they randomly select 1000 people during checkout. what’s the sampling frame?

the ppl who check out something @ the library

what are the 4 scientific methods to take a sample?

simple random sampling

stratified random sampling

cluster sampling

systematic sampling

simple random sampling

randomly pick subjects from the population

what is the benefit of simple random sampling?

each subject in the pop. has an equal chance to be a part of the study

stratified random sampling

divide the pop. into several subpopulations, then take the samples from every sub-pop. according to the sub-pop. size

what is the benefit of stratified random sampling?

it’s very accurate

what are strata based on?

groups, ex. by state

cluster sampling

dividing pop. into clusters

randomly pick clusters, then take all the subjects in one cluster for the sample

clusters cannot overlap

diff. btwn clusters & strata?

clusters are diverse, strata are not

what is a cluster like?

a mini vers. of the population

what is a benefit of cluster sampling?

cheap, easy, convenient

what is a con of cluster sampling?

not an accurate rep. of population

systematic sampling

members of pop. chosen at regular, predetermined intervals

ex. each 4th subject

do clusters need to be the same size?

no

what are the types of bias?

undercoverage

response bias

non-response bias

voluntary response bias

undercoverage

some of the groups in the population are completely missing from the sample

response bias

subjects are giving incorrect answers to the questions (despite you picking a good sample)

non-response bias

subjects are not responding to your question (despite you picking a good sample)

how do you fix non-response bias?

giving incentives, following up

voluntary response bias

the samples are self-selected (subjects chose to participate, not selected by researcher)

ex. internet surveys

can any bias be reduced by increasing the sample size?

no

estimand

the quantity in the population we’re trying to measure

ex. pop. mean

estimate

the quantity/numerical value in the sample we’re trying to measure

ex. sample mean

estimator

the mathematical expression/equation of the estimate

ex. equation for sample mean

does the estimator relate to the estimand or estimate?

estimate

true

population

ex. true avg. lifespan of all electric vehicles (estimand)

amt of bias

expected value of estimator - estimand

equation for finding amt. of bias

E(estimator) - estimand

ex. E(x̄) - μ (true mean)

if estimator is unbiased, what does the bias =?

0

if bias =0, E(estimator) = __

estimand

mean square error (of an estimator)(MSE)

var(estimator) + bias² (estimator)

if est. is unbiased, bias² =0, so MSE = __

var(estimator)

μ is used to describe…

the mean of the population

sampling distribution

distribution of the sample results

central limit theorem (CLT)

if you sample for a large sample size (>30), & plug sample means in histogram, the shape of the dist. will be a normal dist.

what is considered a large sample size?

>30

even if each sample is skewed, when put into histogram using CLT…

it will have a normal dist. shape

(CLT) the mean value of the histogram will be equal to…

the estimand