MR2300: MARKETING RESEARCH

PAUL TILLEY

Unit 9: Sampling Designs, Sampling Procedures & Sample Size.

IN THIS VIDEO WE WILL:

1. Define a sample; a population; a population element and a census

2. Explain why researchers use samples.

3. Design an appropriate sample.

4. Use appropriate statistical tools to extract a useful sample from a population.

5. Identify the key concepts in a sampling plan

6. Control for errors that can occur in sampling

7. Illustrate the distinctive features of probability and non-probability samples

8. Calculate and interpret the Mean, Median, Mode and Standard Deviation of data.

9. Develop frequency distributions for data

10. Calculate sample size and the sample size of a proportion.

POPULATION

Any complete group

Usually people

Cda Population= 35,540,400

NL Population= 526,977

Target Population

Target Population: Canada? NL?

CENSUS Investigation of all individual elements that make up a

population

difficult, slow and very expensive to measure

SAMPLE A sample is a subset of a larger target population

The Sampling process involves drawing conclusions about an entire population by taking a measurement from only a portion of all the population elements

Taking samples of populations is easier, faster and cheaper than taking a census of the population. Sample size relative to the population size will determine how accurately the sample results will mirror the population results. The difference is known as Error.

Samples may have to be used if testing results in destruction of the test unit

Define the target population

Select a sampling frame

Conduct fieldwork

Determine if a probability or nonprobability sampling method will be chosen

Plan procedure for selecting sampling units

Determine sample size

Select actual sampling units

Stages in the Selectionof a Sample

SAMPLING FRAME A list of elements from which the sample may be drawn

Working population

Mailing lists - data base marketers

Sampling frame error

SAMPLING UNITS

Group selected for the sample

Primary Sampling Units (PSU)

Secondary Sampling Units

Tertiary Sampling Units

RANDOM SAMPLING ERROR

The difference between the sample results and the result of a census conducted using identical procedures

Statistical fluctuation due to chance variations

SYSTEMATIC ERRORS

Nonsampling errors

Unrepresentative sample results

Not due to chance

Due to study design or imperfections in execution

ERRORS ASSOCIATED WITH SAMPLING Sampling frame error

Random sampling error

Nonresponse error

TWO MAJOR CATEGORIES OF SAMPLING Nonprobability sampling

Probability of selecting any particular member is unknown

Convenience Sample

Judgment Sample

Quota Sample

Snowball Sample Probability sampling

Known, nonzero probability for every element Simple Random Sample

Stratified Sample

Cluster Sample

Multistage Area Sample

NONPROBABILITY SAMPLING Convenience Sampling - (also called haphazard or accidental sampling) refers to

the sampling procedure of obtaining the people who are most conveniently available.

Judgment - is a nonprobability technique in which an experienced individual selects the sample upon his or her judgment about some appropriate characteristic required of the sample members

Quota - In quota sampling, the interviewer has a quota to achieve. to ensure that the various subgroups in a population are represented on pertinent sample characteristics to the exact extent that the investigators desire.

Snowball - refers to a variety of procedures in which initial respondents are selected by probability methods, but additional respondents are then obtained from information provided by the initial respondents. This technique is used to locate members of rare populations by referrals.

PROBABILITY SAMPLING

Simple random sample

Systematic sample

Stratified sample

Cluster sample

Multistage area sample

SIMPLE RANDOM SAMPLING

A sampling procedure that ensures that each element in the population will have an equal chance of being included in the sample

A simple random sample of 10 students is to be selected from a class of 50 students. Using a list of all 50 students, each student is given a number (1 to 50), and these numbers are written on small pieces of paper. All the 50 papers are put in a box, after which the box is shaken vigorously to ensure randomisation. Then, 10 papers are taken out of the box, and the numbers are recorded. The students belonging to these numbers will constitute the simple random sample.

SYSTEMATIC SAMPLING

A simple process

Every nth name from the list will be drawn

Systematic sampling works well when the individuals are already lined up in order. In the past, students have often used this method when asked to survey a random sample of CNA students. Since we don't have access to the complete list, just stand at a corner and pick every 3rd person walking by.

STRATIFIED SAMPLING Probability sample

Subsamples are drawn within different strata

Each stratum is more or less equal on some characteristic

Do not confuse with quota sample

One easy example using a stratified technique would be a sampling of people at CNA. To make sure that a sufficient number of students, faculty, and staff are selected, we would stratify all individuals by their status - students, faculty, or staff. (These are the strata.) Then, a proportional number of individuals would be selected from each group.

CLUSTER SAMPLING The purpose of cluster sampling is to sample economically while retaining the

characteristics of a probability sample.

The primary sampling unit is no longer the individual element in the population

The primary sampling unit is a larger cluster of elements located in proximity to one another

Suppose your company makes light bulbs, and you'd like to test the effectiveness of the packaging. You don't have a complete list, so simple random sampling doesn't apply, and the bulbs are already in boxes, so you can't order them to use systematic. And all the bulbs are essentially the same, so there aren't any characteristics with which to stratify them.To use cluster sampling, a quality control inspector might select a certain number of entire boxes of bulbs and test each bulb within those boxes. In this case, the boxes are the clusters.

WHAT IS THE APPROPRIATE SAMPLE DESIGN? Degree of accuracy

Resources

Time

Advanced knowledge of the population

National versus local

Need for statistical analysis

AFTER THE SAMPLE DESIGN IS SELECTED Determine sample size

Select actual sample units

Conduct fieldwork

SAMPLE STATISTICS

Variables in a sample

Measures computed from data

English letters for notation

Frequency (number ofpeople making deposits

Amount in each range)

less than $3,000 499$3,000 - $4,999 530$5,000 - $9,999 562$10,000 - $14,999 718$15,000 or more 811

3,120

FREQUENCY DISTRIBUTION OF DEPOSITS

Amount Percentless than $3,000 16$3,000 - $4,999 17$5,000 - $9,999 18$10,000 - $14,999 23$15,000 or more 26

100

PERCENTAGE DISTRIBUTION OF AMOUNTS OF DEPOSITS

MEASURES OF CENTRAL TENDENCY

Mean - arithmetic average µ, Population; , sample

Median - midpoint of the distribution

Mode - the value that occurs most oftenX

Number ofSalesperson Sales calls

Mike 4Patty 3Billie 2Bob 5John 3Frank 3Chuck 1Samantha 5

26

NUMBER OF SALES CALLS PER DAY BY SALESPERSONS

MEASURES OF DISPERSION OR SPREAD

Range - the distance between the smallest and the largest value in the set.

Variance - measures how far a set of numbers is spread out.

Standard deviation - square root of the variance

THE NORMAL DISTRIBUTION

Normal curve

Bell shaped

Almost all of its values are within plus or minus 3 standard deviations

I.Q. is an example

2.14%

13.59% 34.13% 34.13% 13.59%

2.14%

NORMAL DISTRIBUTION

INGREDIENTS IN DETERMINING SAMPLE SIZE

Estimated standard deviation of population

Magnitude of acceptable sample error

Confidence level

2

E Z S

n=

Where: n = Number of items in samples

Z = Standard Deviation Confidence interval

S = Standard Deviation Estimate for Population

E = Acceptable error

SAMPLE SIZE CALCULATION FOR QUESTIONS INVOLVING MEANS

2

2

Epqz

n=

Where: n = Number of items in samples

Z2 = The square of the confidence interval in standard error units.

p = Estimated proportion of success

q = (1-p) or estimated the proportion of failures

E2 = The square of the maximum allowance for error between the true proportion and sample proportion or zsp squared.

SAMPLE SIZE CALCULATION FOR A PROPORTION