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# Population and Sampling

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Population and Sampling
Quantitative Analysis

Content Population Sample Sample Size Sampling Technique
Data Collection Methods

Population Finite population Infinite population
What we are interested in as a whole All students of KMUTNB Students of faculty of IT Depend on in the study Finite population Countable, possible to count Infinite population Uncountable, impossible to count

Sample A part of population selected for study as it is not possible to study the whole population due to cost and time If study the whole population, then it is census Sample should have all the properties of the population be of proper size and scope correspond to the research properly selected (more of this later) – bad sample leads to error between the statistic obtained from sample and parameter of population e.g.

Sampling Sampling error Sampling Unit
Random error – error from sampling process Sampling bias – error from sample being bias to certain thing Sampling Unit The element in the sample e.g. each student in the sample from all the students in the university

Sampling Steps Define population Determine sample size
Population should correspond to the study Proper scope Determine sample size Select sampling method Select sample

Sample Size Larger sample size usually yields less error
Define sampling error Usually at 1% or 5% (0.01 or 0.05) In sensitive study, such as those in medical field, error should be set as low as possible e.g. 1% Confidence interval That the sample is not different from population Confidence level 95% means that 95 out of 100 samples will behave similarly to the population

Determine Sample Size Calculate sample size from population size, sampling error and confidence interval Criterion-based Calculation Taro Yamane Cochran Krejcie and Morgan “Cohen's d” – current accepted method Tables also available for Taro Yamane and Krejcie and Morgan

Criterion-based Population size of 100: take 15-30% as sample
Not reliable

Calculating Sample Size
Unknown population size To estimate population proportion To estimate population mean (to achieve certain margin of error) Known population size

Unknown Population Size
Estimate proportion - W.G. Cochran (1953) n = sample size p = proportion (if not known, use 0.5) z = represents confidence; the value is from z-score table If confidence at 95%, z = 1.96 If confidence at 99%, z = 2.58 d = acceptable error

Example Defining proportion of 0.1, with confidence at 99% and acceptable error of 5%

Unknown Population Size
Estimate mean - W.G. Cochran n = sample size σ = standard deviation of population z = represents confidence; the value is from z-score table If confidence at 95%, z = 1.96 If confidence at 99%, z = 2.58 e = acceptable random error (if σ is not known, e can defined as a percentage of σ e.g. 10% of σ (e = 0.10σ)

Example A study of students’ score in mathematics with confidence at 95%, acceptable error of +- 5 marks. Previous study revealed the average of 70 marks, with standard deviation (SD) of 15 marks

Known Population Size Taro Yamane Krejcie and Morgan
To estimate population proportion To estimate population mean (to achieve certain margin of error)

Taro Yamane Was popular but outdated n = sample size
N = population size e = acceptable sampling error

Example Population of 2000 allowing 5% error

Krejcie and Morgan n = sample size N = population size
e = acceptable sampling error χ2 = chi-square of degree of freedom 1 and confidence 95% = 3.841 p = proportion of population (if unknown, 0.5)

Example Population of 2000, allowing 5% error at confidence 95% and population proportion of 0.5

To Estimate Proportion
n = sample size N = population size e = acceptable sampling error z = represents confidence; the value is from z-score table If confidence at 95%, z = 1.96 If confidence at 99%, z = 2.58 p = proportion of population (if unknown, 0.5)

Example Population of 2000, allowing 5% error at confidence 95% and population proportion of 0.5

To Estimate Mean n = sample size N = population size
σ = standard deviation of population e = acceptable random error (if σ is not known, e can defined as a percentage of σ e.g. 10% of σ (e = 0.10σ) z = represents confidence; the value is from z-score table If confidence at 95%, z = 1.96 If confidence at 99%, z = 2.58

Example A study of 400 students’ scores in mathematics with confidence at 95%, acceptable error of +- 5 marks. Previous study revealed the average of 70 marks, with standard deviation (SD) of 15 marks

Using Table: Taro Yamane
Assume population proportion of 0.5 and confidence 95% Error (e) Pop. Size

Error (e) Pop. Size

Using Table: Krejcie and Morgan
Assume population proportion of 0.5 and confidence 95% and error 5% Population Size Sample Size Population Size Sample Size Population Size Sample Size

Population Size Sample Size Population Size Sample Size Population Size Sample Size

Sampling Methods Probability Sampling Non-probability Sampling
Each unit in population has the same chance to be selected as sample Non-probability Sampling Each unit in population has different chance to be selected as sample – some unit might never be selected

Probability Sampling Simple Random Sampling Systematic Random Sampling
Stratified Random Sampling Cluster Sampling Multi-stage Sampling

Simple Random Sampling
Randomly select a unit from population until we have the according to the sample size The method must ensure that each unit has the same chance to be selected Population must be listed and then Random from number associated with each unit (for smaller population) Use table of random number (for larger population) which is now replaced by random number generation in computer

Pro & Con Easy to do but should only be used on the population that is homogeneous A complete list of population must be present Not suitable for very large population

Systematic Random Sampling
Systematic sampling arranges the target population according to non-bias ordering scheme and then selecting elements at regular intervals Systematic sampling involves a random start and then proceeds with the selection of every kth element from then onwards. k=(population size/sample size). It is important that the starting point is not automatically the first in the list, but is instead randomly chosen from within the first to the kth element in the list Example would be to select every 10th name from the telephone directory (an 'every 10th' sample, also referred to as 'sampling with a skip of 10').

Pro & Con Easy to do but The selection of sample after the first element is dependent on the first element

Stratified Random Sampling
Divide population into subgroups, or strata The members of the same strata should be homogeneous (all elements should be similar with respect to the variables being studied) The size of each stratum is decided by its proportion in the population Each stratum is then sampled as an independent sub-population using Simple or Systematic Random Sampling

Stratified Random Sampling

Example Population of 1000 students in 5 faculties: Engineering 200, Science 300, IT 150, Business 150, and Education 200 Grouped into 5 strata based on faculty Using Taro Yamane yields sample size of 286 Engineering = (286/1000) x 200 = 57 Science = (286/1000) x 300 = 86 IT = (286/1000) x 150= 43 Business = (286/1000) x 150 = 43 Education = (286/1000) x 200 = 57 Then use simple/systematic sampling to obtain the sample

Pro & Con Samples are selected from all kinds in the population, thus
Sample may best represent the population Each stratum must be different from other (unique enough) Do not divide into too many strata

Cluster Sampling It might not be possible to select sample from very large population. Select from existing grouping called cluster Clusters should be homogenous The size of each cluster should be relatively equal The number of clusters is decided by researcher depending on each study

Cluster Sampling

Pro & Con Save time and cost of study
Cannot ensure that the sample can properly represent the population Example A study on Asian countries: assuming every country is similar (homogeneous) then select only Thailand, Malaysia and Vietnam as sample

Multi-stage Sampling A mix of the first 4 methods
Usually start with Stratified Sampling or Cluster Sampling End with Simple or Systematic random sampling Used when strata or clusters are still too large or too complex to study

Non-probability Sampling
Accidental Sampling Quota Sampling Purposing Sampling Convenience Sampling Snowball Sampling

Accidental Sampling No rules, only set the sampling condition to match the research objective Worst method as it cannot guarantee that the sample can represent the population

Quota Sampling Similar to Stratified Random Sampling
Except that the member of each stratum is NOT selected using the probability sampling method

Purposive Sampling AKA Judgment Sampling
Researcher select sample based on the objective of the study Cannot guarantee that the samples will maintain the status as time changes Example Study the attitude of director of successful companies

Convenience Sampling Use the method convenient to researching to gather data Example Phone Letter The sample is like to NOT being able to represent the population Bias

Snowball Sampling Randomly select a unit (i.e. a person) from population Then that person suggests the next sample Repeat until meet the sample size “Throw a snowball”

Non-probability Sampling
Cannot appropriate represent the population unless the sample is carefully selected The sample is dependent on the sample selector (researcher) therefore cannot determine sampling error

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