Statistics and sampling

1. Basic ideas in sampling
Gayan Dharmarathne

2. Target Population
• An observation unit can be considered as the entity on which information
is received in the process of collecting data.
• Following the above, a target population can be defined as the entire
group of observation units that we desire to collect information in a given
study.
Examples: In a marketing study, the target population would be the
entire group of customers of a particular business. In a political opinion
poll, the target population would be all registered voters.

3. What is a survey?
• A survey can be considered as a method of collecting information
from some or all units of a population and compiling the information
into a useful form.
• A good survey requires careful planning, methodical application and
detailed analysis of the results.
• There are two different types of surveys that can be used to collect
information in practice. They are census and sample survey.

4. Examples for surveys
• TV networks: How many and what type of people watch their programs?
• Car manufacturers: Customer satisfaction
• Household budget survey
• Evaluation of the smoking ban
• Political opinion polls
• Library: How the service can be improved?

5. Types of surveys
Surveys can be conducted in many ways.
• Observational studies: An observational study is used to answer a research question
based purely on what the researchers observe with no interferences or manipulations
of the research subjects. This is often due to ethical or practical concerns that prevent
the researcher from conducting a traditional experiment. The observational studies
are known to apply in hard sciences, medical and social sciences in general.
• Mail questionnaire
• Telephone interview
• Face‐to‐face interview
• Internet questionnaire

6. Census and sampling survey
• A census is a collection of the required information from all the observation
units in the target population of interest.
• It is not always possible to collect information from every observation unit in
the population due to several practical reasons. Some examples are time,
cost, labor and so on.
• Hence, sample surveys are frequently conducted in practice where the
information are collected from a subset of observation units from a given
population of interest. The size of the sample depending on the purpose of
the study.

7. Sampling survey
• Sampling surveys are cheaper: Require much fewer units to contact.
• Sampling surveys results can be obtained more quickly: Same reason as
above.
• Sampling surveys can be more accurate: Fewer units to contact, less
problems with interviewer effects and non‐response bias.
Note: Less data of high quality is better than more data of poor quality.

8. Sampled population
• Sampled population can be considered as a collection of observation units
from which the sample was taken. This applies when there are practically
difficulties to directly study all the observation units in the population. It is
certainly desirable for the target and sampled populations to match each
other.
• Now the sampling unit may be different to the observation units.
Sampling unit can be considered as the unit that was actually sampled.

9. Sampled population
Example 01: Consider a marketing study on the brand awareness; the
familiarity of consumers with a particular product or service, in a particular
area. Here, the target population consists of all the individual consumers of
the corresponding product or service in a particular area.
• Observation units: Individuals in households
• Sampling units: Households

10. Sampled population
Example 02: Consider a demographic and health survey where the main
target population is the ever married women aged 15-49 years. However, to
capture this population a general sample of household is selected. The
required no of sample units of the target group can be achieved by
increasing the sample of household units.
• Observation units: Ever married women aged 15-49 years
• Sampling units: Households

11. Sampling frame
• A sampling frame can be considered as a list, map or specification of
sampled units according to the study.
Examples:
• HH Telephone survey → directory of phone numbers
• HH in‐person interviews → street addresses
• Survey of farms → map of farms

12. Parameters and statistic
• A parameter is a value usually unknown (which therefore needs to be
estimated) relevant to a certain population characteristic. For example,
population mean 𝜇 which indicates the average of a certain quantity of
a population. Note that parameters are unknown constants.
• A statistic is a quantity that is calculated from a sample of data. Statistic is
a random variable as the calculated value of the statistic varies from
sample to sample. For example, sample mean 𝑋 is a statistic that can be
used to estimate the unknown population mean 𝜇 of a certain quantity.

13. Requirements of a good sample
• A good sample should be representative of the population in the sense
that characteristics of interest in the population can be estimated from
the sample with a known degree of accuracy.

14. Requirements of a good sample
• A good sample should be free from selection bias. Let us discuss some
examples of selection bias encountered in practice.

15. Examples of selection bias
1. Convenience samples
Surveys of convenience often produce biased results as they generally
target easy to select or most likely to respond persons and vise versa.
Example: In business studies, convenience samples are generally used to
obtain initial data on the opinions of perspective customers in relation to a
new design of a product from individuals who are conveniently available or
willing to participate in the study.
Hence, the selected sample may not represent the entire population of
customers in general.

16. Examples of selection bias
2. Judgement samples
In judgement sampling, the choice of sample units depends on the
judgement of the investigator. Here, the investigator select those sample
units which he feels are representative of the population under study.
Example: In a business study, suppose the objective is to estimate the
average amount spent by a shopper at MC. The investigator has sampled
some shoppers who seem to have spent an average amount.
Hence, there is a possibility that the selected sample of shoppers may not
represent the entire population of shoppers.

17. Examples of selection bias
3. Undercoverage
This occurs when a part of the target population is not included in the
sampling frame.
Example: Consider a telephone survey of households in a particular study.
• Some households do not have telephones; for example, low‐income
households are less likely to have telephones.
• Some households may have only the cell phones.
Hence, the selected sample of households may not represent the entire
population of households of the study.

18. Examples of selection bias
4. Overcoverage
This occurs when the sampling frame includes units that are not in the
target population. The reasons for this would be if the units are not
screened out of the sample or if the data collectors don’t check the sample
eligibility of units
Example: Consider a phone survey on radio listening habits of persons over
18 and suppose that some interviewers might include persons under 18.
Here, children and teenagers may well listen to different radio stations than
adults and therefore the results of the survey can be biased.

19. Examples of selection bias
5. Multiplicity of listings in sampling frame
This occurs when some units in the sampling frame have a higher chance of being
selected into the sample.
Example: Consider a phone survey on household income and random digit dialing is
used to obtain a sample of house holds.
• Households with more than one phone can have a higher chance of being selected.
• This multiplicity can be compensated in the estimation and the result can be biased if
ignored.
• Households with more telephones to be larger or wealthier, if there is no adjustment,
the estimated average income may be too large.

20. Examples of selection bias
6. Substituting
This occurs when a designated unit who is not readily available or
accessible is substituted by a convenient unit.
Examples:
• No one is at home in the designated household and trying the next
household.
• In a wildlife survey, substituting an area next to a road for a less accessible
area.

21. Examples of selection bias
Substituting continued….
• In each case, the sampled units most likely to differ on a number of
characteristics from the designated units.
• The substituted household may include members who do not work
outside of the house than the originally selected household.
• The area by the road may have fewer frogs than the area that is harder to
reach.

22. Examples of selection bias
7. Nonresponse
Nonresponse generally distorts the results of many surveys.
• Often, nonrespondents differ critically from the respondents, but the
extent of that difference is unknown unless you can later obtain
information about the nonrespondents.
• Some surveys have dismal response rates, as low as 10%. It is difficult to
see how results can be generalized to the population when 90% of the
targeted sample cannot be reached or refuses to participate.

23. Examples of selection bias
8. Voluntary response
This occurs when the samples are allowed to consist entirely of volunteers.
Generally, the results from such surveys cannot be trusted as the volunteer
respondents can often be quite opinionated (certain about their beliefs and
often expresses their ideas strongly) or emotional. Thus, there is a
possibility to obtain misleading conclusions that my not represent the
general view of the population under study.

24. Types of errors in surveys
Two types of errors in surveys.
1. Sampling error
This is the error caused by studying only a part of the population instead of
the entire population.
Example: Assume that the population mean of a certain variable is 6500
units. A random sample of 1000 units has been taken and the sample
mean of the corresponding variable is 5750 units. Then, the sampling error
is 6500 – 5750 equals to 750 units.

25. Types of errors in surveys
• Sampling error continued….
Note: Sampling errors can be reduced by utilizing the most appropriate
sampling technique and by increasing the sample size appropriately. It is
required consider cost, expected accuracy when deciding the sample size.

26. Types of errors in surveys
2. Non-sampling error
This is the error caused when collecting data, recording data, preparation of
data and so on. This error must be controlled by careful inspection in
collecting, recording, and preparation of data.
Note: Understand that non-sampling errors can be occurred in both census
and sampling surveys.

27. Practical difficulties in obtaining accurate
responses
1. People sometimes do not provide the true information.
Examples: Income, drug use, certain diseases.
2. People do not always understand the questions.
Example: Consider a question like “Did you enjoy a certain food product?”. This
question may be not clear. Here, the respondents might not be sure about what
were they supposed to enjoy?. The ambiguity of this question can be reduced by
asking questions on a wide range of aspects of the product such as
➢ What did you think about the color of the product?
➢ What did you think about the flavor of the product?
➢ What did you think about the smell of the product?

28. Practical difficulties in obtaining accurate
responses
3. People sometimes forget the answers.
Example: Experiences as a crime victim in the last six months.
4. People sometimes give different answers to different interviewers.
Example: Answers to sex related questions can be different depending on
the gender of the interviewer.
5. Some responses are perceived socially desirable than others
Examples: Over report behaviors such as exercising and donating to
charities, underreport behaviors such as smoking or drinking.

29. Practical difficulties in obtaining accurate
responses
6. Impact of the interviewer on the accuracy of the responses.
Examples:
• An interviewer may affect the accuracy of the responses by misreading
questions, recording responses inaccurately, annoying the respondent and
so on.
• A poorly trained interviewer with strong feelings about a certain question
may encourage the respondents to provide one answer rather than the
others. For example, attitudes on abortion.

30. Practical difficulties in obtaining accurate
responses
7. Certain words mean different things to different people.
Example: A simple question such as “Do you own a car?”
Here, the respondents might think whether it refers to just the individual or
to the household and the word “own” counts if leased and so on.
8. Order of questions can have impact on the responses.
Example: Consider the following two questions. Reversing the order may
have an impact on the answer of the first question.
• How happy are you with life in general?
• How often do you normally go out on a date? About __ times a month