Simple Random Sampling - Survey Sampling Techniques - Lecture Slides, Slides of Survey Sampling Techniques

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Selecting

a

simple

random

sampling

(SRS)

Simple

random

sampling

(SRS)

Most

basic

probability

sample

design

Used

in

combination

with

other

designs

Use

SRS

to

select

a

sample

and

estimate

the

parameters

of

the

population

distribution

How

to

select

a

sample

Estimators

for

population

parameters

of

y

under

SRS

Probability

sampling

notation

n

sample

size

Note lower case

n is always less than

N

for a sample

n

N

is a census

Probability

sampling

notation

A

index

set

(labels)

for

SUs

in

the

sample

Textbook calls this

S

but we will use

S

as the symbol for the standard deviation of the population distribution

To select a sample, we are selecting n indices (labels) from U -

A

is a subset of

U

Labels in

A

are generally not sequential because we are selecting a subset of

U

But we will often express A as if labels were sequential

SRS

Definition

The

converse

is

not

true

Other designs have the property that each

SU

has an equal probability of being included in the sample

This

is

called

an

“equal

probability”

design

SRS

is only one example of an equal probability sample design

Some stratified and cluster sampling designs also have an equal inclusion probability for all Sus - Example

Selecting

a

SRS

Two

types

of

selection

procedures

SRSWR

(SRS

with

replacement)

Return

SU

after each step in the selection process

There is a chance that a

SU

may be drawn twice or more

SRSWOR

(SRS

without

replacement)

Do not return

SU

after it has been selected

All units in the sample are unique (can’t draw a unit more than once)

SRSWOR

in

practice

Create a sampling frame

List of sampling units in the universe or population with a unique index or label for each SU - For SRSWOR, think of this as a list of population units (element = SU) with labels from 1 to N - Determine a selection procedure that performs

SRSWOR

Procedure must generate to n unique SUs such that each SRSWOR sample is equally likely - Can think of this as selecting a set of n unique random numbers (integers) between 1 and N -

A

SU

is included in the sample if its label that corresponds to one of the n random numbers selected

SRSWOR

in

practice

Examples

of

ways

to

generate

random

numbers

that

assign

equal

inclusion

probability

for

each

sample

Lottery:

mix

up

numbered

balls

and

randomly

select

each

ball

(without

returning

it

to

bin)

Computer:

PROC

SURVEYSELECT

METHOD=SRS

uses

a

random

number

generator

Data

collection

After

sample

is

selected,

data

are

collected

Sample

A

Course

data

courses

Textbook

data

textbooks

Cell

data

have

cell)

Data

collection

Sample

A

{28, 18, 16, 11} - Course data

classes

Textbook data

textbooks

Cell data

have cell)

Sample

A

{22, 9, 25, 10} - Class data

classes

Textbook data

textbooks

Cell data

have cell)

Class

example

Estimate

the

mean

number

of

courses

per

student

for

our

population

(sample

Is

the

sample

mean

equal

to

the

population

mean

courses

per

student)?

What

happens

if

we

take

another

sample?

The SUs, data, estimate may be different

Sample

or

 

n  i i y n y 1 1

Class

example

Sample

Data

y

Estimated

mean

(courses

per

student)

Sample

Data

y

Estimated

mean

(courses

per

student)

Class

example

Estimate

the

total

number

of

textbooks

purchased

by

our

population

(sample

Compare

estimated

total

with

the

true

population

total

textbooks)

  

n  i i y N n y N t 1 ˆ

Class

example

Sample

Data

y

Estimated

total

(textbooks)

Sample

Data

y

Estimated

total

(textbooks)