Lecture 2-Sampling

Question 1

Why a sample instead of a census?

Answer 1

Impossibility of conducting a census due to
time, cost, lack of access to the entire
population etc.

Question 2

Sample Objectives

Answer 2

To be as representative as possible of the
underlying population
* Why is this important?
* Because we are going to generalise from the
sample to the population; we are going to use the information from the sample and assume
that it is true of the entire population

Question 3

Sampling Approaches

Answer 3

Random sampling
– Simple random sampling
– Stratified random sampling
– Cluster sampling
* Non-Random sampling
– Quota sampling

Question 4

Census

Answer 4

a survey that includes every element
of the target population

Question 5

Sample survey

Answer 5

a survey that collects
information from a portion of the population

Question 6

Sampling Frame

Answer 6

includes all the members of the population who are eligible to be part of the sample
Examples
– The population census data
– Telephone directory
– Students registration database at the UWI

Question 7

Sampling with Replacement or without

Answer 7

A sample may be selected with replacement or without replacement.
* In sampling with replacement, each time we select an element
from the population, we put it back in the population before we select the next element of the sample
* Therefore, the population contains the same number of items each time a selection is made, and we can also select the same
item more than once
* Sampling without replacement occurs when the selected
element is not replaced in the population
* Therefore, each time we make a selection, the size of the population is reduced by one element. We cannot select the same item more than once.
* Most times, sample taken in statistics are without replacement.

Question 8

Random vs Non-Random Samples

Answer 8

• A sample may be random or nonrandom.
• A random sample is a sample that has been drawn so that each element of the population has a measureable chance of being selected for the sample.
• If a sample does not assign a chance of being included, to a specific set of elements within the
  population, it is nonrandom.
• It is important to note that the randomness is in the procedure and any corruption of that
  procedure is likely to “corrupt” the randomness, thereby introducing selection bias.

Question 9

Representative Sample

Answer 9

A sample that represents the characteristics of the population as closely as possible

Question 10

Sample Frames and Random Sampling

Answer 10

No matter what random sampling design is selected, the actual implementation of the exercise and the explicit choice of the individual members of the sample cannot be carried out without a sampling frame.
* Sampling frames may themselves be responsible for many of the inaccuracies of the resultant sample.
* For instance, if the frame is incomplete (which
immediately excludes some members of the population from the sample), if the frame is inaccurate, or if the frame is out of date.
Notwithstanding these limitations, a sampling frame is an immediate requirement for the selection of a sample, and no actual frame will possess all of the characteristics of an ideal sampling frame. What an investigator must consider at this point, therefore, is all the frames that are available and their limitations, and in this context select the frame that will enable the most complete, accurate and convenient sample of the population under study.

Question 11

Explanation of Random Sampling and Sampling Frames

Answer 11

Suppose, for example, that I want to determine the average age of the statistics class of 300 students by using a random sample of 10 students drawn from the class.
The random nature of the selection procedure does not necessarily ensure a truly representative sample since, for instance, it is quite within the realm of possibility to draw the ten youngest members of the class. Using the average age of these 10 as the average
age of the entire class is therefore erroneous.

Question 12

Simple Random Sample

Answer 12

is a sample that has
been drawn so that each element of the
population has an equal chance of being
selected for the sample.

Question 13

Advantages of Simple Random Sample

Answer 13

Simple random samples enjoy the principal
advantage that they eliminate selection bias.
* Furthermore, the elimination of selection bias
in Simple Random Sample has to do with the mode of selection and has nothing to do with the
representativeness of the resultant
sample.

Question 14

Disadvantages of Simple Random Sampling

Answer 14

Simple random samples can be very costly, for instance when the population being sampled is
distributed across a wide (geographical) area.
* Taking a simple random sample does not automatically ensure that the results obtained are reliable and there is the possibility that a sample selected by a simple random method would be a bad or imprecise indicator of the population from which it was taken, so leading to inaccurate estimates.
* In particular, when a population is stratified, simple random sampling can result in a sample
that is comprised of elements from just one or two strata; in which case the sample will not be
representative of the population.

Question 15

Stratified Random Sampling- explanation

Answer 15

Suppose I was interested in the average age of a student in ECON 1005
– What is my population?
– Suppose I take this class as my sample, and find the average age
– Will be sample be representative of the population?
– What has gone wrong?
* The stratified random sampling design involves the division of the population into various
categories or strata (singular stratum) using what is known as a stratification factor.
* The stratification factor must be chosen so that the strata are mutually exclusive. i.e. Each
member of the population must be assigned to exactly one stratum.
* A simple random sample is then drawn from each stratum to ensure adequate representation of all strata in the sample.
* The collection of simple random samples constitutes the stratified random sample.

Question 16

Stratified Random Sample-definition

Answer 16

Stratified Random Sampling is divided into st rara based on shared characteristics for example age and gender, a random sample is then drawn from each stratum
*

Question 17

Advantages of Stratified Random Sampling

Answer 17

The stratified random sampling design makes use of knowledge of the population to increase the precision of the results obtained from the
sample.
* The chance of any individual being drawn is still measurable and all
possible samples of equal size still have the same chance of selection. So, although the choice of
the stratification factor is almost entirely dependent on human judgment, the procedure still maintains an element of randomness to it, especially since the mode of selection within each stratum is clearly random.
* This method can significantly reduce the cost of sampling, therefore,
because it can achieve accurate results from smaller samples.
* One advantage of stratification is that, besides facilitating the acquisition of
information about the entire population, we can also make inferences within each stratum or compare strata.

Question 18

Limitations from Stratified Random Sampling

Answer 18

One important consequence of stratifying the
population is that, now, each element of the population no longer has an equal chance of
being drawn.

Question 19

Best results from stratified random sampling

Answer 19

Stratified random sampling produces its best
results when the variation within each stratum/group is small compared to the variation
between strata/groups.
* When the within-group variation is small, it will
provide results nearly identical to those of Simple
random sampling.
* Go back to the examples of age of an ECON 1005
student, and height of an ECON 1005 student, and the choice of the stratification factors.
Describe the within-group and between-group
variations.
32

Question 20

Stratified vs Simple Random Sampling

Answer 20

Return to the Examples above; in the extreme case, simple random sampling could have resulted in an all-male or all female selection / an all FT or EU selection, causing, in either case, a misleading
result.
* Since the point of stratifying the population is to select some members from each stratum, then a sample consisting entirely of members from one stratum (which is theoretically possible when stratification is not employed) could not and should not be chosen.

Question 21

Cluster or Multistage Sampling

Answer 21

The cluster sampling design involves the
division of the population into groups called
clusters
*A simple random sampling process is then
applied to select a sample of clusters.
* All members of the selected cluster(s)
constitute the cluster sample.

Question 22

Cluster Sampling Example

Answer 22

Suppose we wish to establish student attitude to the University’s reform of its Policy on Consultations. It may be convenient to divide the University student population into faculties which will then constitute the clusters. We use simple random sampling to select a sample of 2 faculties. Each student in the 2 selected faculties forms part of the cluster sample and therefore must be surveyed.

Question 23

Cluster Sampling definition explained more

Answer 23

• Cluster sampling may seem to resemble stratified random sampling in that both sample designs involve a grouping of the members of the population. The similarity stops there!
• When we stratify, every stratum is sampled, whereas when we cluster, we select among the
  clusters, with the resultant cluster(s) constituting the sample.
• In addition, when we stratify, we use a simple random sample of each stratum, whereas when we cluster, we select each member of each of the selected clusters.

Question 24

Advantages of Cluster Sampling

Answer 24

• Cluster sampling is particularly useful when it is difficult or costly to develop a sampling
  frame.
• It is also useful when the population elements are widely dispersed geographically.
• The selection process remains a random one, since we select among the clusters in much the same way that we select among individual population members in random sampling.

Question 25

Limitations of Cluster Sampling

Answer 25

Under both the simple random and stratified
random sampling designs, one member at a
time (of the population or stratum) is selected. The selection of any one member is independent of the selection of another.
* Cluster sampling does not share this
characteristic.

Question 26

Cluster Sampling best results

Answer 26

• There are many ways of selecting the clusters themselves, but one general rule always
  applies - for maximum precision to be attained, clusters should be formed so that the variation
  within each cluster is large relative to the variation between clusters.
• In other words, the clusters are collectively homogenous but within each one, they are as
  heterogeneous as can be.
• The reason for this should be obvious - it is in this way that we will obtain a sample that is
  truly representative of the population as a whole.

Question 27

Non-random sampling techniques

Answer 27

Quota sampling
* Convenience sampling
* Judgement sampling

Question 28

Quota Sampling

Answer 28

involves the identification of a quota(s) that the selected sample is required to fulfill.
* This quota is based on the diversity of the population, and so represents an attempt to ensure that the population is truly represented by the resultant sample.
* Once the quota has been established, the actual selection of the members of the sample is left up to the discretion of the enumerators/interviewers (the people who conduct the survey).

Question 29

Quota Sampling Example

Answer 29

We may wish to draw a sample of 500 investors in Credit Unions in your country but 200 must be men; 175 must be women; and 125 must be persons under the age of twenty-five.
* We can appoint 3 enumerators/interviewers; one is assigned the task of sampling 200 male
investors in Credit Unions, another is assigned the task of sampling 175 female investors in Credit Unions, and the third is assigned the task of sampling 125 investors in the age group ‘under 25’ in
Credit Unions. Each interviewer selects his/her quota of investors utilising a first come first
served approach.

Question 30

Quota sampling advantages

Answer 30

One major advantage of the quota sampling
design is that it is relatively cheap to carry
out.
* It also does not require the existence of a
sampling frame and is useful in situations
where no such frames exist.

Question 31

Sampling error definition

Answer 31

differences between the sample and the population that exist only because of the observations that happened to be selected for the sample. This type of error is consequence of the chance factor involved in the elements of the sample that were selected from the population. As a statistical investigator/researcher, you have little control over this type of error.

Question 32

Quota sampling limitations

Answer 32

All the sampling designs discussed before this
one share, in some degree or another, a
random feature.
* However, this sample design is non random.

Question 33

Convenience Sampling

Answer 33

Sampling on a street corner or asking for volunteers. While it gives information, be wary of making generalizations!

Question 34

Types of Errors in Sampling

Answer 34

Sampling Error
*Non-Sampling Error

Question 35

Judgement Sampling

Answer 35

one where a sample is chosen by an expert, who deems that sample to be representative.

Question 36

Non-sampling error

Answer 36

is due to mistakes made by the researcher/ interviewers in the acquisition of the data or due to the improper selection of the sample. This type of error is within the control of the researcher/interviewer.

Question 37

Examples of non-sampling error

Answer 37

Poor design of the experiment
* Errors in the sampling frame used in the experiment
* Poorly phrased questions
* Poorly administered questions
* Incorrect recording of responses
* Non-response error
* Data Entry errors
* Data Coding Errors
* Selection bias

Question 38

Methods of data collection

Answer 38

Direct Observation
* Experiments
* Surveys
– Personal Interviews
– Telephone Interviews
– Self Administered Survey
– Mail Survey
– Internet Survey

Question 39

Cross section data

Answer 39

data collected on different elements at the same period of time

Question 40

Time series data

Answer 40

data collected on the same element for the same variable at different points in time or for different periods of time

Question 41

Government publications can be used as external sources of data

Answer 41

1. Statistical Abstract of the United States
2. Employment and Earnings
3. Handbook of Labor Statistics
4. Source Book of Criminal Justice Statistics
5. Economic Report of the President
6. County & City Data Book
7. State & Metropolitan Area Data Book
8. Digest of Education Statistics
9. Health United States
10. Agricultural Statistics

Question 42

summation notation

Answer 42

is used to denote the sum of values

Question 43

Continuous data

Answer 43

can assume any value within a specified range and can only represent approximations of true and exact measurements

Question 44

Name two organizations in the Caribbean that collect, summarize and publish DEMOGRAPHIC data. Identify two publications by each of these organizations.

Answer 44

1. Caribbean Community (CARICOM)
   Publications:

CARICOM Regional Census Report: Provides detailed data on population demographics across CARICOM member states from national censuses.
CARICOM Social and Demographic Statistics Report: Offers data and analysis on various social and demographic indicators across the region, including population, migration, and employment statistics.

2. Statistical Institute of Jamaica (STATIN)
   Publications:

Jamaica Population and Housing Census: A comprehensive report on Jamaica’s population, including age, sex, education, and housing conditions.
Jamaica Demographic and Health Survey (DHS): A survey that covers a wide range of demographic and health-related indicators such as fertility, family planning, and maternal and child health.

Question 45

Name two organizations in the Caribbean that collect, summarize and publish SOCIOECONOMIC data. Identify two publications by each of these organizations

Answer 45

1. Caribbean Development Bank (CDB)
   Publications:

Annual Economic Review: Provides an analysis of the economic performance of Caribbean countries, focusing on growth, inflation, fiscal and external balances.
Social and Economic Indicators Report: Offers socioeconomic data on key sectors such as education, health, poverty, and employment in Caribbean countries.

2. Central Bank of Trinidad and Tobago (CBTT)
   Publications:

Economic Bulletin: This quarterly publication provides detailed data and analysis on Trinidad and Tobago’s economic performance, including sectors such as trade, finance, and employment.
Annual Economic Survey: A yearly report that covers broad economic trends, including GDP growth, inflation, public finance, and external trade, along with social indicators like unemployment and poverty rates.

Question 46

A parameter

Answer 46

is a numerical value that summarizes a characteristic of the entire population.

Question 47

A statistic

Answer 47

is a numerical value that summarizes a characteristic of a sample drawn from the population.

Question 48

What is a sample?

Answer 48

a small portion of the population that is picked to be studied