MR2300: Marketing Research Paul Tilley Unit 9: Sampling Designs, Sampling Procedures & Sample Size.

In THIS Video WE WILL: Define a sample; a population; a population element and a census Explain why researchers use samples. Design an appropriate sample. Use appropriate statistical tools to extract a useful sample from a population. Identify the key concepts in a sampling plan Control for errors that can occur in sampling Illustrate the distinctive features of probability and non-probability samples Calculate and interpret the Mean, Median, Mode and Standard Deviation of data. Develop frequency distributions for data Calculate sample size and the sample size of a proportion.

Population Target Population: Canada? NL? Target Population Any complete group Usually people Target Population: Canada? NL? Target Population Cda Population= 35,540,400 NL Population= 526,977

Investigation of all individual elements that make up a population difficult, slow and very expensive to measure Census

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

Stages in the Selection of a Sample Define the target population Select a sampling frame Determine if a probability or nonprobability sampling method will be chosen Plan procedure for selecting sampling units Determine sample size Select actual sampling units Conduct fieldwork

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 Distribution of Deposits Frequency (number of people 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

Percentage Distribution of Amounts of Deposits Amount Percent less 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

Measures of Central Tendency Mean - arithmetic average µ, Population; , sample Median - midpoint of the distribution Mode - the value that occurs most often

Number of Sales Calls Per Day by Salespersons Salesperson Sales calls Mike 4 Patty 3 Billie 2 Bob 5 John 3 Frank 3 Chuck 1 Samantha 5 26

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

Normal Distribution 13.59% 13.59% 34.13% 34.13% 2.14% 2.14% Conventional Product Adoption Life Cycle: Five types of customers who will end up adopting a product INNOVATORS (2.5%): People who are the first to adopt a product. They are trend-setting, risk-taking, and are not typical consumers. Example: See a movie first weekend it’s out or in a preview. EARLY ADOPTERS (13.5%): People who are among the first but not as risk-taking. They adopt ideas early but with consideration, and they enjoy roles as opinion leaders. They spread the word about the product. Example: See a movie the first week of its release. EARLY MAJORITY (34%): Deliberate customers; adopt earlier than most customers but are not leaders. Example: See a movie after a few weeks, after reading all the reviews and getting recommendations from early adopters. LATE MAJORITY (34%): Skeptical customers, will only adopt an idea if the majority of people have tried it. Example: See a movie after it has been nominated for an Oscar. LAGGARDS (16%): Tradition-bound, suspicious of change; will adopt an idea only after it has been around long enough. Example: See a movie after it has come out on video. 2.14% 2.14%

Ingredients in determining Sample Size Estimated standard deviation of population Magnitude of acceptable sample error Confidence level

Sample size calculation for questions involving means 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 a Proportion 2 E pq z 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.