Topic 4 Sampling and Statistical Theory

Population (universe)

Any complete group of interest.

Census

An investigation of all individual elements making up the population

Sample

A subset of some larger population that is measured or observed in some way to infer what the entire population is like

Statistic

To sample as parameter is to population

Pragmatic reasons (sample)

Sampling cuts costs, reduces labor requirements, and gathers vital information quickly

Accurate and reliable results (sample)

A sample on occasion is more accurate than a census
Increased volume of work in a census may lead to interviewer mistakes, tabulation errors, and other non sampling errors.

Destruction of test units (sample)

Occurs in the process of the research project
Provides the case against using a census.

Sampling frame

a list of elements from which the sample may be drawn

Stages in selection of sample

1. Define the target population

2. Select a sampling frame

3. Determine if a probability or non probability sampling will be used

4. Plan procedure for selecting sampling units

5. Determine sample size Select actual sampling
   units

6. Conduct fieldwork

Sampling frames

Demographics
• Age, Gender, Income
Psychographics
• Attitudes towards a firm/brand, political affiliation
Geographics
• City, State, County
Behavioral variables
• Purchase behavior, Social media usage, online search behavior

Sampling services

Market research firms
• Dyanta
• Nielsen
Online panels
• Prolific
• Amazon M-Turk

Random Sampling Error

Refers only to statistical fluctuations that occur because of chance variations in the elements selected for the sample

A function of sample size
• As sample size increases, random sampling error decreases
• Margin of error is determined by the sample size

Systematic Sampling Error

Result from non sampling factors, primarily the nature of a study’s design and the correctness of execution, not due to chance fluctuation, Sample biases account for a large portion of errors in marketing research

Systematic Sampling Error examples

68% people prefer EVs over gas vehicles. Conclusion: 68% of Americans preferred EVs over gas vehicles.
Domino’s sent a customer satisfaction survey to customers who selected opt in for notifications to measure overall customer satisfaction.

Less than representative samples

Random sampling errors and systematic errors combine to yield sample that is not representative of population

If individuals refuse to be interviewed or cannot be contacted it may cause the sample to not be representative

Administrative Error

Data processing error, sample selection error, interviewer error, interviewer cheating, measurement errors

Data processing error

Error made by administrator during data entry or coding or editing or tabulation or analysis stages

Sample selection error

Error made by administrator in selecting sampling units

Interviewer error

Unintentional error made by administrator while administering the interview/survey

Interviewer cheating

Deliberate manipulation by administrator while administering the interview/survey

Measurement errors

Error made by administration where he fails to communicate the scale of measurement.
Ex: you are measuring satisfaction on a 7-point scale, but the respondent thinks you are using a 5-point scale.

Response Bias

Deliberate falsification, Acquiescence bias, Extremity bias, unconcsious misrepresentation, social desirability bias 

Deliberate falsification

Intentionally changing information to deceive others with a goal to gain an advantage or avoid consequences

Acquiescence bias/agreement bias

When respondents tend to select a
positive response option(such as ‘Yes’ or ‘True’) regardless of actual opinion

Extremity bias

The survey respondents answer questions
with extreme views, even if they don’t actually feel that way.

Unconscious misrepresentation

Learned stereotypes/attitudes influence understanding and actions, leading to unconscious judgements

Social desirability bias

When respondents give answers to questions that they believe will make them look good to others, concealing their true opinions or experiences

Probability sampling

Every population element has a known, nonzero probability of selection.
Respondents have an equally likely chance of being included in the sample

Non probability sampling

Probability of any member of the population being chosen is unknown, the selection of sampling units is quite arbitrary, pragmatic and are used in market research

Non probability sampling examples

Assume there are 40 students in the class. I need to take a sample of 10 to determine their satisfaction with the course

Convenience sample example

Ask the 10 students who are near to me

Judgmental sample example

Ask the students who scored in the top quartile (top 25 percentile)

Quota sample example

Ask the 5 girls and 5 boys who come first to class

Snowball sample example

Ask a student and then ask him to refer another of his friends. Continue till we get 10 responses.

Probability sampling example

Assume there are 40 students in the class. I need to take a sample of 10 to determine their satisfaction with the course (probability)

Simple random sampling example

Assign each student a number from 1-40. Randomly select 10 numbers between 1-40.

Systematic sampling example

Assign each student a number from 1-40. After
selecting the first number randomly select numbers at equal intervals till we reach a sample size of 10.

Stratified sampling example

Consider different groups. For example, male and female students. Select 5 female and 5 male respondents

Cluster sampling example

Consider different groups. For example, male and female students. Select one group for example, female and ask 10 female students.

Proportional stratified sampling

The number of sampling units drawn from each stratum is in proportion to the relative population size of the stratum.

Disproportional stratified sampling

The sample size for each stratum is not allocated in proportion to the population size but is dictated by analytical considerations.

Multistage Area Sampling

A cluster sampling approach involving multiple steps with a combination of multiple probability techniques.
Research use multiple steps as per their requirement to achieve a representative sample.

Computing Sample Size

For ‘large’ populations, sample size needed
to draw inferences about the population
bears no necessary relationship to population size, and requires only:
• Precision
• Confidence
• Estimate of population variability

Precision (D)

How much are you willing to be wrong by? Ex: Results within certain range

Confidence Level (→Z)

How sure are you of this result? 

Most common values are 99%, 95%, and 90%

Population Variability (→S)

How much variability is there in the population?

The greater the variability in the population,
the larger the sample size needed to obtain a
given level of precision at a specified confidence level

The number of sample elements (sample
size) required to achieve a given
precision at a specified confidence is (formula)

N=Z² * S²/ D²

Z = Confidence interval

S = Variability

D = Precision

90% CI

1.6

95% CI

2

99% CI

2.6

Computing Sample Size for means

Z2 * S2 / D2 =
=(1.6)² * 250 /5² = 67.6

Computing Sample size for proportions

Z² * S² / D²

S² = (proportion #1) * (1 - proportion #1)

What if Variability and Confidence Change?

Variability: Assume now that 80% of consumers have a positive view
• S² now = .8 * .2 = .16
• Z still = 2 and D still = .05
• Sample size needed now is: 256

Suppose confidence requirements is 90%
• Z for 90% interval is ~ 1.60
• Needed sample size is now: 164

What if Precision Changes?

Now want a precision of .03
• Revert to assumed 50/50 split and 95% confidence, Results would now be reported as 50%, ± .03’
• Sample size = 1111

Type 1 error

Innocent defendant is convicted

Type 2 error

Guilty defendant is acquitted

Type 1 error hypothesis testing

We reject a true null hypothesis (think it’s false but actually true)

Type 2 error hypothesis testing

We fail to reject a false null hypothesis (think it’s true but actually false)