Populations and SamplesPopulations and Samples

Dr. Fred Mugambi MwirigiDr. Fred Mugambi Mwirigi

JKUATJKUAT

IntroductionIntroduction

A sample is a subset of a larger population of A sample is a subset of a larger population of objects individuals, households, businesses, objects individuals, households, businesses, organizations and so forthorganizations and so forth

Sampling enables researchers to make Sampling enables researchers to make estimates of some unknown characteristics of estimates of some unknown characteristics of the population in questionthe population in question

A finite group is called population whereas a A finite group is called population whereas a non-finite (infinite) group is called universenon-finite (infinite) group is called universe

A census is a investigation of all the individual A census is a investigation of all the individual elements of a population elements of a population

Population Vs SamplePopulation Vs Sample

PopulationPopulation

SampleSample

Reasons for SamplingReasons for Sampling Budget and time Constraints (in case of large populations)Budget and time Constraints (in case of large populations)

High degree of accuracy and reliability (if sample is High degree of accuracy and reliability (if sample is representative of population) representative of population)

Sampling may sometimes produce more accurate results Sampling may sometimes produce more accurate results than taking a census as in the latter, there are more risks than taking a census as in the latter, there are more risks for making interviewer and other errors due to the high for making interviewer and other errors due to the high volume of persons contacted and the number of census volume of persons contacted and the number of census takers, some of whom may not be well-trained takers, some of whom may not be well-trained

The Sampling ProcessThe Sampling Process

Define the Targetpopulation

Define the Targetpopulation

Select a Sampling Frame

Select a Sampling Frame

Determine if a probability or non-probability sampling

method will be chosen

Determine if a probability or non-probability sampling

method will be chosen

Plan procedure for selecting sampling units

Plan procedure for selecting sampling units

Determine sample sizeDetermine sample size

Select actual sampling unitsSelect actual sampling units

Conduct fieldworkConduct fieldwork11

22

33

44

55

66

77

Defining the Target PopulationDefining the Target Population The target population is that complete group The target population is that complete group

whose relevant characteristics are to be whose relevant characteristics are to be determined through the samplingdetermined through the sampling

A target population may be, for example, all A target population may be, for example, all faculty members in the School for Human faculty members in the School for Human Resource Development at JKUA, all housewives Resource Development at JKUA, all housewives in Mombasa or even all past students of a in Mombasa or even all past students of a university university

The Sampling FrameThe Sampling Frame The sampling frame is a list of all those population The sampling frame is a list of all those population

elements that will be used in the sampleelements that will be used in the sample

Examples of sampling frames are a student database Examples of sampling frames are a student database (for the student population), the list of companies on the (for the student population), the list of companies on the stock exchange or the yellow pages (for businesses)stock exchange or the yellow pages (for businesses)

Often, the list does not include the entire population. The Often, the list does not include the entire population. The discrepancy is often a source of error associated with the discrepancy is often a source of error associated with the selection of the sample (sampling frame error)selection of the sample (sampling frame error)

Sampling UnitsSampling Units The sampling unit is a single element – or The sampling unit is a single element – or

group of elements – subject to selection in group of elements – subject to selection in a sample. Examples:a sample. Examples: Every student at JKUAT whose first name Every student at JKUAT whose first name

begins with the letter “F”begins with the letter “F” All child passengers under 18 years of age All child passengers under 18 years of age

who are traveling in a bus from destination X who are traveling in a bus from destination X to destination Y to destination Y

Sampling ErrorsSampling ErrorsRandom Sampling ErrorRandom Sampling Error This is defined as the “This is defined as the “difference between the sample difference between the sample

result and the result of a census conducted using result and the result of a census conducted using identical procedures”identical procedures” and is the result of chance and is the result of chance variation in the selection of sampling unitsvariation in the selection of sampling units

If samples are selected properly (for e.g. through the If samples are selected properly (for e.g. through the technique of randomization), the sample is usually technique of randomization), the sample is usually deemed to be a good approximation of the population deemed to be a good approximation of the population and thus capable of delivering an accurate resultand thus capable of delivering an accurate result

Systematic (Non-Sampling) ErrorsSystematic (Non-Sampling) Errors

These errors result from factors such as an These errors result from factors such as an improper improper research designresearch design that causes response error or from that causes response error or from errors committed in the execution of the research, errors errors committed in the execution of the research, errors in recording responses and non-responses from in recording responses and non-responses from individuals who were not contacted or who refused to individuals who were not contacted or who refused to participateparticipate

Both Random sampling errors and systematic (non-Both Random sampling errors and systematic (non-sampling) errors reduce the representativeness of a sampling) errors reduce the representativeness of a sample and consequently the value of the information sample and consequently the value of the information which is derived by business researchers from it which is derived by business researchers from it

Probability and Probability and Non-Probability SamplingNon-Probability Sampling

Probability Sampling – Every element in the Probability Sampling – Every element in the population under study has a non-zero population under study has a non-zero probability of selection to a sample, and every probability of selection to a sample, and every member of the population has an equal member of the population has an equal probability of being selectedprobability of being selected

Non-Probability Sampling – An arbitrary means Non-Probability Sampling – An arbitrary means of selecting sampling units based on subjective of selecting sampling units based on subjective considerations, such as personal judgment or considerations, such as personal judgment or convenience. convenience.

Non-Probability SamplingNon-Probability Sampling

1.1. Convenience SamplingConvenience Sampling

2.2. Judgment (purposive) SamplingJudgment (purposive) Sampling

3.3. Quota SamplingQuota Sampling

4.4. Snowball SamplingSnowball Sampling

Convenience SamplingConvenience Sampling This is a sampling technique which selects those This is a sampling technique which selects those

sampling units most conveniently available at a certain sampling units most conveniently available at a certain point in, or over a period, of time point in, or over a period, of time

Major advantages of convenience sampling is that is quick, Major advantages of convenience sampling is that is quick, convenient and economical; a major disadvantage is that the convenient and economical; a major disadvantage is that the sample may not be representativesample may not be representative

Convenience sampling is best used for the purpose of Convenience sampling is best used for the purpose of exploratory research and supplemented subsequently with exploratory research and supplemented subsequently with probability samplingprobability sampling

Judgment (purposive) SamplingJudgment (purposive) Sampling A sampling technique in which the business A sampling technique in which the business

researcher selects the sample based on researcher selects the sample based on judgment about some appropriate characteristic judgment about some appropriate characteristic of the sample membersof the sample members

Quota Sampling Quota Sampling A sampling technique in which the business researcher A sampling technique in which the business researcher

ensures that certain characteristics of a population are ensures that certain characteristics of a population are represented in the sample to an extent which he or she represented in the sample to an extent which he or she desiresdesires

Example: A business researcher wants to determine through Example: A business researcher wants to determine through interview, the demand for Product X in a district which is very interview, the demand for Product X in a district which is very diverse in terms of its ethnic composition. If the sample size is to diverse in terms of its ethnic composition. If the sample size is to consist of 100 units, the number of individuals from each ethnic consist of 100 units, the number of individuals from each ethnic group interviewed should correspond to the group’s percentage group interviewed should correspond to the group’s percentage composition of the total population of that district composition of the total population of that district

Contd.Contd. Quota Sampling has several advantages and disadvantages:Quota Sampling has several advantages and disadvantages:

Advantages include the speed of data collection, less cost, Advantages include the speed of data collection, less cost,

the element of convenience, and representativeness (if the the element of convenience, and representativeness (if the

subgroups in the sample are selected properly) subgroups in the sample are selected properly)

Disadvantages include the element of subjectivity Disadvantages include the element of subjectivity

(convenience sampling rather than probability-based which (convenience sampling rather than probability-based which

leads to improper selection of sampling units) leads to improper selection of sampling units)

Snowball SamplingSnowball Sampling A sampling technique in which individuals or organizations are A sampling technique in which individuals or organizations are

selected first by probability methods, and then additional selected first by probability methods, and then additional respondents are identified based on information provided by the first respondents are identified based on information provided by the first group of respondentsgroup of respondents

Example: Through a sample of 500 individuals, 20 scuba-diving Example: Through a sample of 500 individuals, 20 scuba-diving enthusiasts are identified which, in turn, identify a number of enthusiasts are identified which, in turn, identify a number of other scuba-diversother scuba-divers

The advantage of snowball sampling is that smaller sample The advantage of snowball sampling is that smaller sample sizes and costs are necessary; a major disadvantage is that the sizes and costs are necessary; a major disadvantage is that the second group of respondents suggested by the first group may second group of respondents suggested by the first group may be very similar and not representative of the population with that be very similar and not representative of the population with that characteristic characteristic

Probability SamplingProbability Sampling

1.1. Simple Random SamplingSimple Random Sampling

2.2. Systematic SamplingSystematic Sampling3.3. Stratified SamplingStratified Sampling

Simple Random SamplingSimple Random Sampling This is a technique which ensures that each This is a technique which ensures that each

element in the population has an equal chance element in the population has an equal chance of being selected for the sampleof being selected for the sample

Example: Choosing raffle tickets from a drum, Example: Choosing raffle tickets from a drum, computer-generated selections, random-digit computer-generated selections, random-digit telephone dialingtelephone dialing

The major advantage of simple random sampling is The major advantage of simple random sampling is its simplicityits simplicity

Systematic SamplingSystematic Sampling This is a technique which in which an initial starting point This is a technique which in which an initial starting point

is selected by a random process, after which every is selected by a random process, after which every nthnth number on the list is selected to constitute part of the number on the list is selected to constitute part of the samplesample

Example: From a list of 1500 name entries, a name on the list is Example: From a list of 1500 name entries, a name on the list is randomly selected and then (say) every 25randomly selected and then (say) every 25 thth name thereafter. name thereafter. The sampling interval in this case would equal 25.The sampling interval in this case would equal 25.

For systematic sampling to work best, the list should be random For systematic sampling to work best, the list should be random in nature and not have some underlying systematic pattern in nature and not have some underlying systematic pattern

Stratified SamplingStratified Sampling A technique which in which simple random sub samples are drawn A technique which in which simple random sub samples are drawn

from within different strata that share some common characteristic from within different strata that share some common characteristic

Example: The student body of JKUAT is divided into two groups Example: The student body of JKUAT is divided into two groups (management science, engineering) and from each group, (management science, engineering) and from each group, students are selected for a sample using simple random sampling students are selected for a sample using simple random sampling in each of the two groups, whereby the size of the sample for in each of the two groups, whereby the size of the sample for each group is determined by that group’s overall strength each group is determined by that group’s overall strength

Stratified Sampling has the advantage of giving more Stratified Sampling has the advantage of giving more representative samples and less random sampling error. representative samples and less random sampling error. However, it is more complex and information on the strata may be However, it is more complex and information on the strata may be difficult to obtaindifficult to obtain

OthersOthers

1.1. Cluster Sampling Cluster Sampling

2.2. Multistage Area Sampling Multistage Area Sampling

3.3. Internet SamplingInternet Sampling

Issues in Sample Design and SelectionIssues in Sample Design and Selection

Accuracy – Samples should be Accuracy – Samples should be representative of the target populationrepresentative of the target population

Resources – Time, money and individual Resources – Time, money and individual or institutional capacity are very important or institutional capacity are very important considerations due to the limitation on considerations due to the limitation on them. Often, these resources must be them. Often, these resources must be “traded” against accuracy“traded” against accuracy

Issues in Sample Design and SelectionIssues in Sample Design and Selection

Availability of Information – Often information on sample Availability of Information – Often information on sample participants in the form of lists, directories etc. is participants in the form of lists, directories etc. is unavailable which makes some sampling techniques unavailable which makes some sampling techniques (e.g. systematic sampling) impossible to undertake(e.g. systematic sampling) impossible to undertake

Geographical Considerations – The number and Geographical Considerations – The number and dispersion of population elements may determine the dispersion of population elements may determine the sampling technique used (e.g. cluster sampling)sampling technique used (e.g. cluster sampling)

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