Sampling & PopulationSampling & Population

Normazhazlin AlzahariNormazhazlin Alzahari2009506635 2009506635 

Azlyn Sarafina A HamidAzlyn Sarafina A Hamid20091264212009126421

    Hanim OthmanHanim Othman 20093944532009394453

What is sample & population?

A sample is a finite part of a statistical population whose properties are studied to gain information about the whole (Webster, 1985). When dealing with people, it can be defined as a set of respondents (people) selected from a larger population for the purpose of a survey.

A population is a group of individuals, persons, objects, or items from which samples are taken for measurement for example a population of presidents or professors, books or students.

What is sampling?

Sampling is the act, process, or technique of selecting a suitable sample, or a representative part of a population for the purpose of determining parameters or characteristics of the whole population.

What is the purpose of sampling?

To draw conclusions about populations from samples, we must use inferential statistics which enables us to determine a population’s characteristics by directly observing only a portion (or sample) of the population. We obtain a sample rather than a complete enumeration (a census ) of the population for many reasons. Obviously, it is cheaper to observe a part rather than the whole, but we should prepare ourselves to cope with the dangers of using samples.

Defining the population

First task in selecting a sample:

to define the populations of interest(5 wives 1 Husband)

Some examples of populations:

- All high school principals in Selangor

- All students in Mrs Nadarajah’s form 4 class at STAR Klang

Defining the population

In educational research, the population of interest is usually a group of persons (students, teachers) who possess certain characteristics.

In some cases, the population may be defined as a group of classrooms, schools or even facilities.

Example: All Form 5 students in Kolej Islam Klg(The hypothesis might be that classrooms in which teachers / students display a greater number of achievements)

Target Versus Accessible Populations

Unfortunately, the actual populations a.k.a target populations are rarely available. The population to which a research is able to generalize is called accessible population.

Target Versus Accessible Populations

Research problem to be investigated: The effects of Sponge Bob Square standard 1 students in Selangor.

Target Population: All standard 1 students in Selangor.

Accessible population: Sekolah Kebangsaan Kg Jawa, Klang

Target Versus Accessible Populations

The more narrowly research define the population, the more they save on time, effort and money but, the more they limit their generalizability.

Failure to define in detail the population of interest, and the sample studied, is one of the common weaknesses of published research reports.

VERY important: to describe the characteristics of the actual sample studied in some detail.

Random Versus Nonrandom Sampling

There 2 main types of sampling. Random Sampling

A personnel from the Ministry’s office wishes to find out how many secondary school principals in Selangor is keen to have Mandarin taught in as one of their subject.

So she places all 100 names of secondary school, mix them thoroughly, and then draw out the names of 25 names of schools to interview.

Random Versus Nonrandom Sampling

Nonrandom sampling:

The Ministry wishes to sent its personnel to find out how many secondary school principals in Selangor is keen to have Mandarin taught in as one of their subject. There are 5 jr. personnel's in the department. They need to select only 3. Thus, 3 personnel’s were selected based on some criteria.

Example: Must be permanent staff

At least 5 years serving the Ministry etc

Random Sampling methods

4 types of random sampling methods Simple Random Sampling Stratified Random Sampling Cluster Random Sampling Two-stage Random Sampling

Random Sampling methods

Simple Random Sampling

Each and every member of the population has an equal and independent chance of being selected.

Best way to use when the sample is large – devised to obtain a sample representative of the population of interest.

The key to obtaining a random sample is to ensure that each number of population has an equal chance of being selected.

Random Sampling methods

This can be done by using the table of random numbers.

011723 223456 222167 032762 062231

912334 379156 233989 233989 934128

086401 016265 411148 251287 603255

059397 011348 080675 899030 198905

Random Sampling methods

Advantage: If large enough, it is likely to produce a representative

sample.Disadvantage: Not easy to do. Each member of the population must be identified.

A B C D Q R N M LT W E JK IS ZR YU

A DR M L W J I Z Y

SIMPLE RANDOM

Stratified Random Sampling

Stratified Random Sampling is a process where certain subgroups (strata) are selected for a sample in a same proportion as they exist in the population.

AB CD 25%

QR NM LT WE JK IS 50%

ZR YU 25%

A D 25%

R M L W J I 50%

Z Y 25%

STRATIFIED RANDOM

Cluster Random Sampling

A subject rather than individuals is known as cluster random sampling.

Is more effective with large numbers of clusters.

AB CDQR NM LT WE JK IS ZR YU

QR LT YU

CLUSTER RANDOM

Two-stage Random Sampling

Often useful to combine cluster random sampling with individual random sampling.

AB CDQR NM LT WE JK IS ZR YU

CD

WEZR

Random sampleof clusters

Random sampleof individuals

C, E, R

TWO-STAGE RANDOM

Nonrandom Sampling

The purpose of this method is to make an explicit The purpose of this method is to make an explicit choice based on our own judgement about exactly choice based on our own judgement about exactly whom to include in the sample.whom to include in the sample.

When random sampling is not possible, then we When random sampling is not possible, then we may choose the following :-may choose the following :- Systematic SamplingSystematic Sampling Convenience SamplingConvenience Sampling Purposive SamplingPurposive Sampling

Systematic Sampling

Every Every nnth individual in the population list is th individual in the population list is selected for inclusion in the sample; when selected for inclusion in the sample; when nn is the is the use number.use number.

The number may be chosen by the researcher The number may be chosen by the researcher to avoid from any bias in the sample.to avoid from any bias in the sample.

eg. in a population of 3,000 staff of a company, eg. in a population of 3,000 staff of a company, the researcher would chose the the researcher would chose the 33rdrd name in the name in the list of a sample of 300 staff.list of a sample of 300 staff.

Systematic Sampling

Sampling Interval

The distance in the list between each of the The distance in the list between each of the individuals selected for the sample.individuals selected for the sample.

The interval can be determined using the following The interval can be determined using the following formula:-formula:-

Population size___Population size___ Desired sample sizeDesired sample size

Sampling IntervalSampling Interval

eg. the ABC Bank wants to know how its staff eg. the ABC Bank wants to know how its staff perceive their new tools used for dissemination of perceive their new tools used for dissemination of information amongst the staff.information amongst the staff.

Total number of staff : 9,000Total number of staff : 9,000Sample sizeSample size : 1,000 : 1,000

Sampling IntervalSampling Interval Population size___ Population size___ Desired sample size Desired sample size

9,0009,000 1,0001,000

= 9= 9

Sampling RatioSampling Ratio

The proportion of individuals in the population that is The proportion of individuals in the population that is selected for the sample.selected for the sample.

The ratio can be determined using the following The ratio can be determined using the following formula:-formula:-

Sample Size____Sample Size____ Population SizePopulation Size

Sampling Ratio

Total number of staff : 9,000Total number of staff : 9,000Sample sizeSample size : 1,000 : 1,000

Sampling IntervalSampling Interval Sample Size____ Sample Size____ Population size Population size

1,0001,000 9,0009,000

= 0.11= 0.11

Convenience Sampling

A group of individuals who are available at any point of A group of individuals who are available at any point of time and are ready for the study for the research.time and are ready for the study for the research.

eg. a nurse of an aesthetic clinic interviews the eg. a nurse of an aesthetic clinic interviews the patients in the clinic on their opinion about the patients in the clinic on their opinion about the effectiveness of the radiofrequency machine in the effectiveness of the radiofrequency machine in the clinic.clinic.

However, they hardly could be considered in However, they hardly could be considered in representing any population.representing any population.

Convenience Sampling

Purposive Sampling

Selection of samples are based on the researchers’ Selection of samples are based on the researchers’ judgment that the samples could contribute to the judgment that the samples could contribute to the research in providing the information for the data research in providing the information for the data better as they are the involved party in the research better as they are the involved party in the research matter itself.matter itself.

The power of purposive sampling lies in selecting The power of purposive sampling lies in selecting information rich-cases for in-depth analysis related to information rich-cases for in-depth analysis related to the central issues being studiedthe central issues being studied

Purposive Sampling

cc eg. researcher eg. researcher interviewedinterviewed

the old man to find the old man to find out howout how

he feels staying in old he feels staying in old folksfolks

home managed and home managed and administered by the administered by the government.government.

SAMPLE SIZESAMPLE SIZE

1.1. The sample should be as large as the researcher The sample should be as large as the researcher can obtain with a reasonable expenditure of time can obtain with a reasonable expenditure of time and energy.and energy.

2.2. It means that, the researcher should try to obtain It means that, the researcher should try to obtain as large as a sample they reasonably can.as large as a sample they reasonably can.

3.3. Here is the suggestion:Here is the suggestion:

Type of studiesType of studies No. of samplesNo. of samples

DescriptiveDescriptive 100100

CorrelationCorrelation 5050

ExperimentalExperimental 3030

Causal-comparativeCausal-comparative 3030

Replicated studiesReplicated studies 15 per gp15 per gp

EXTERNAL VALIDITYEXTERNAL VALIDITY

POPULATION GENERALIZABILITY ECOLOGICAL GENERALIZABILITY

WHAT IS EXTERNAL VALIDITY?WHAT IS EXTERNAL VALIDITY?

This is the term used in research, refers to the This is the term used in research, refers to the extent that the results of the study can be extent that the results of the study can be generalized from a sample to a population.generalized from a sample to a population.

Most researchers wish to generalize their Most researchers wish to generalize their findings to appropriate populations.findings to appropriate populations.

When is generalizing warranted?When is generalizing warranted? When can researchers say with confidence that When can researchers say with confidence that

what they have learned about sample is also what they have learned about sample is also true of the population?true of the population?

Both Both the nature of the samplethe nature of the sample and and the the environmental conditions-environmental conditions- the setting-within the setting-within which a study takes place must be which a study takes place must be

considered in thinking about generalizability.considered in thinking about generalizability.

POPULATION GENERALIZABILITYPOPULATION GENERALIZABILITY

1.1. The term population generalizability refers to The term population generalizability refers to the extent to which the result of the study ca the extent to which the result of the study ca be generalized to the intended population.be generalized to the intended population.

2.2. Ex: a study that randomly selects students but Ex: a study that randomly selects students but not teachers is only entitled to generalized the not teachers is only entitled to generalized the outcomes to the population of the students.outcomes to the population of the students.

3.3. In research, it is very important to obtain a In research, it is very important to obtain a representative sample.representative sample.

4.4. Representativeness referring only to the Representativeness referring only to the essential, or relevant, characteristics of a essential, or relevant, characteristics of a population. (what is relevant?)population. (what is relevant?)

Example:Example: To study the effects of reading method on To study the effects of reading method on

students achievement.students achievement. Characteristics such as height, eye color, Characteristics such as height, eye color,

jumping ability would be irrelevant.jumping ability would be irrelevant. Characteristics such as age, gender or visual Characteristics such as age, gender or visual

acuity (might logically) have an effects and acuity (might logically) have an effects and hence should be appropriately represented in hence should be appropriately represented in the sample.the sample.

When random sampling is not When random sampling is not feasible?feasible?

1.1. There is another possibility when a random There is another possibility when a random sample is impossible to obtain.sample is impossible to obtain.

2.2. It is called replication.It is called replication.

3.3. The researcher/ other researchers repeat the The researcher/ other researchers repeat the study using different group of subjects in study using different group of subjects in different situation.different situation.

4.4. If the study is repeated several times, a If the study is repeated several times, a researcher may have additional confidence researcher may have additional confidence about generalizing the findings.about generalizing the findings.

Reasons for why random samples have not Reasons for why random samples have not been used?been used?

11st: st:

The educational researchersThe educational researchers may be unaware of the hazards may be unaware of the hazards involved in generalizing when one does not have involved in generalizing when one does not have a random sample.a random sample.

22ndnd

In many studies, it is simply notIn many studies, it is simply not feasible for a researcher to feasible for a researcher to invest the time, money or other resources invest the time, money or other resources necessary to obtain a random sample.necessary to obtain a random sample.

ECOLOGICAL GENERALIZABILITYECOLOGICAL GENERALIZABILITY

1.1. Refers to the extent to which the results of a study can be Refers to the extent to which the results of a study can be generalized to conditions or setting other than those that generalized to conditions or setting other than those that prevailed in a particular study.prevailed in a particular study.

2.2. The researchers must make clear the nature of the environmental The researchers must make clear the nature of the environmental conditions-the setting-under which study takes place (must be the conditions-the setting-under which study takes place (must be the same).same).

3.3. Research results from urban school environments may not be Research results from urban school environments may not be apply to suburban or rural schools environments.apply to suburban or rural schools environments.

4.4. What holds true for one subject, or with certain materials, or What holds true for one subject, or with certain materials, or under certain conditions, or at certain times may not be under certain conditions, or at certain times may not be generalized to other subjects, material, condition, or times.generalized to other subjects, material, condition, or times.

5.5. Therefore, researchers must be cautious about generalizing the Therefore, researchers must be cautious about generalizing the results from anyone study.results from anyone study.

Thank you