MR2300: MARKETING RESEARCH PAUL TILLEY Unit 9: Sampling Designs, Sampling Procedures & Sample Size.
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