2.3 Sampling Techniques(1)

7/22/2019 2.3 Sampling Techniques(1)

1/20

2.3 Sampling Techniques

MDM4U

Shaun Le Conte


2/20

Firstly, some terms to know!

Population all members of a group under study

Sampling Frame all members of a population whoactually have a chance of being included in the sample

e.g. you may want to take a random sample of Sarnia,

Ontario, Canada residents, but if you are calling peoplefrom the phone book, only those who have a listed

phone number and are home during the time that you

plan to call are part of the sampling frame


3/20

Populations

Population: all objects under study.

Usually, we do not have complete knowledge ofa population and therefore we seek to gathersamples in order to make inferences about thepopulation

E.g. true unemployment % among the populationis unknown, what you see in the media is anestimate


4/20

Sampling a Population

A large population may beimpractical and costly to studyso a sample is used instead

A sample is the part of thepopulation that is actuallyselected to be studied

http://mips.stanford.edu/public/classes/stats_data_analysis/lesson_1/pop_sam.mov

image from:
http://mips.stanford.edu/public/classes/stats_data_analysis/lesson_1/pop_sam.ovhttp://mips.stanford.edu/public/classes/stats_data_analysis/lesson_1/pop_sam.ov


5/20

What is random?

Can you tell the difference between

random and non-random?

Look at the next slide, filled with 1 and 0s

and decide whether the top or the bottom

row is random


6/20

Which section of 0s and 1s is the

randomly generated section?


7/20

Sampling Techniques

Simple random sample

Systematic sample

Stratified sample Cluster sample

Voluntary response sample

Convenience sample


8/20

A. Simple Random Sample

Key point:

Every member of the population has an

EQUAL chance of being selected.

Examples: picking names out of a box,

randomly generating numbers from a

calculator, using a random number table


9/20

B. Systematic Sample

Select members of the population at regular intervals

Interval, k = population size, N / sample size, n

Example: 25 students, sample size 5, select every 5thfrom the class list

Before proceeding, either the list must be randomized ora seed value must be generated, which is the startingpoint in between 1 and the sampling interval (inclusive)

Without the above step, the first 4 people in the list wouldhave no chance of being included in the survey

Refer to Example 2 on page 115.


10/20


11/20

C. Stratified Sample

Used when information is known about the proportions of different,mutually exclusive groups, or strata, within a population

Stratified sampling can help in reducing sampling error A sample is randomly collected from each strata.

The proportion of each strata in the sample should reflect theproportion of each strata in the population

Ensures that subgroups are represented in your sample

Examples:- comparing male students and female students

- comparing younger students and older students

Refer to example 3 on page 115 116.

e.g. age groups

The difference between the sample

statistic and the population parameter


12/20

page 117


13/20

Answer to #4


14/20

D. Cluster Sample

The entire population is divided into groups (known as a clusters)and a random sample of these clusters is selected.

Cluster sampling works best when clusters do not differ significantly

All members in the selected clusters are included in the sample.

Examples:

- studying job satisfaction at McDonalds by surveying all employeesat a few locations (cluster sample) rather surveying a few employeesat all locations (simple random sample)

- randomly selecting city blocks and surveying all households on theblock


15/20

Comparing stratified sampling and

cluster sampling Cluster sampling: a random sample is drawn from the

population of clusters. Only the selected clusters areanalyzed.

Main advantage: reduce costs by sampling a smallergeographical area.

Stratified sampling: a random sample is drawn from each ofthe strata. Analysis is performed on elements within strata.

Main advantage: take advantage of prior knowledge of apopulation to reduce sampling error


16/20

F. Voluntary Response Sample

The sample is made up of members in the

population who choose to participate in the

study. Examples: SMS surveys, radio shows in which

listeners call in, questions posted to message

boards

Are participants representative???


17/20

G. Convenience Sample

Sampling whoever is accessible.

Example: asking your next door neighbors oryour classmates.

Major problem: the sample may not representthe population (not representative). Estimates of

the population parameter are less valid than with

other types of sampling


18/20

Voluntary vs Convenience

Sampling Both are considered non-random sampling

There is an important distinction between the two types

In voluntary sampling, people will willingly seek to take part in the

sample

In convenience sampling, the surveyor seeks out others and asks

them to participate those asked depend on who is around at

that time and place, and most approachable (selection bias) Voluntary sampling is often considered the least representative

method of sampling since those who volunteer tend to hold

strong opinions for or against an issue


19/20

Some points to consider when doing

any sort of random sampling When you have determined who it is that has

been selected to be part of your sample, you

must of course find and contact that person! If the person declines to participate, they can't

be forced but the surveyor should ask if they

could talk at a later time (and pinpoint a time)

The more a surveyor fails to collect samplesfrom those on the to be surveyed list, the less

random it will become


20/20

Sample size?

Generally: as many as possible, provided that the

quality of sampling remains constant

Ultimately it will depend on the constraints: budget,

labor, time.

The larger your sample, the more likely your

statistic will be a good estimate of the population

parameter

Documents

2.3 Sampling Techniques(1)