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Chapter 3

Sampling andSampling Techniques

Chapter 3. Sampling and Sampling Techniques

Complete Enumeration versus Sampling

In complete enumeration or a census, we measure the variable/s of interest from all the elements of the population.

In sampling, we measure the variable/s of interest from the elements belonging in one subset of the population.

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Advantages of Sampling over Complete Enumeration (page 74)

more economical faster to accomplish wide scope of study is more viable measurement errors are more likely to

be smaller sometimes complete enumeration is not

feasible


Target Population vs Sampled Population (page 75)

Definition 3.1.

The target population is the population we want to study.

The sampled population is the population from where the sample is actually selected.

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Remarks: (page 75)

Inferences based on sample data will apply to the sampled population.

Ideally, the target and the sampled populations should be the same.


Example (page 75)

Target population: Collection of all residents in Metro Manila

Suppose the sample of residents was selected from the list of names in the telephone directory.

Sampled population: Collection of people listed in the telephone directory

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Elementary Unit vs. Sampling Unit (page 75)

Definition 3.2.

The elementary unit or element is a member of the population whose measurement on the variable of interest is what we wish to examine.

The sampling unit is the unit of the population that we select in our sample.

Note: Before selecting the sample, the population must first be divided into non-overlapping sampling units. Sometimes the sampling unit is the element itself. Sometimes the sampling unit is a group of more than one element.


Example

A researcher wishes to estimate the total number of children below 12 years old in Barangay X. In order to do this, he selects a sample of households in Barangay X by selecting a sample of blocks in the barangay then collects data on the number of children below 12 years old from each household in the selected blocks.

What is the parameter of interest in this study? What are the elementary units in this study? What are the sampling units in this study?

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Example 3.3: (page 76)

We now present a survey conducted by the National Statistics Office (NSO) in cooperation with the Department of Trade and Industry (DTI) to provide an actual illustration where the elementary unit and the sampling unit are different from each other. Title of the Study: Monthly Integrated Survey of Selected Industries This survey provides planners and policy-makers in both government and private sectors with indicators on the performance of growth-oriented industries in the agro-based, metallic mining and manufacturing sectors. Target population: set of all establishments in the manufacturing, mining, and agriculture industries Elementary unit: an establishment (which is an economic unit that engages under a single ownership or control in one or

predominantly one kind of economic activity at a fixed single physical location) in the manufacturing, mining, and agricultural industries

Sampling unit : an enterprise (which is an economic unit with one or more establishments under a single ownership or control) in the manufacturing, mining, and agricultural industries

For this survey, NSO partitioned the population of establishments into enterprises. An enterprise can consist of one or more establishments. San Miguel Corporation is an example of an enterprise. This enterprise consists of many establishments, namely, San Miguel Beer Division, Ginebra San Miguel, Inc., Coca-Cola Beverage Group, San Miguel Pure Foods Company, Inc., and San Miguel Packaging Products. NSO then selected a sample of enterprises but collected data from the establishments in the selected enterprises. Thus, the enterprises are the sampling units but the establishments are the elementary units.


Sampling Frame (page 76)

Definition 3.3.

The sampling frame or frame is a list or map showing all the sampling units in the population.

Note: The researcher will select sample from the sampling frame. The sampling frame will define the sampled population.

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Example 3.4a (page 77)

Suppose a researcher is interested in getting the opinion of eligible voters on the media campaign of candidates running for top positions in the government.

Target population : set of all eligible voters

Sampling frame: Commission on Elections (COMELEC) list of registered voters

Sampled population: set of registered voters in the list of COMELEC


Exercise

Give suggestions on where we can get a sampling frame for the following situations:

Target population: set of dentists in the PhilippinesSampling unit: dentist

Target population: set of elementary schools in M ManilaSampling unit: school (Assignment: Get a list of hospitals in Metro Manila including the city/municipality.)

Target population: set of UP B.S. Stat majors enrolled in the 2nd

sem, AY 2010-2011Sampling unit: UP B.S. Stat major

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Sampling error vs Non-sampling error(page 77)

Definition 3.4

Sampling error is the error attributed to the variation present among the computed values of the statistic from the different possible samples consisting of n elements.

Non-Sampling error is the error from other sources apart from sampling fluctuation. (ex: measurement errors)


Example 3.5 (page 78)Suppose we conducted a census on a small population consisting of N=15 students. From each student, we measured the variable of interest, X=weekly allowance.

400 400 450 475 500

500 500 525 550 575

600 700 750 750 800

Let the parameter of interest be the total weekly allowance of all students in the population.

Total = 400 + 400 + 450 + 475 + 500 +

500 + 500 + 525 + 550 + 575 +

600 + 700 + 750 + 750 + 800 = 8,475 pesos

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Example 3.5 cont’d

This time, let us take a sample of n=5 students using systematic sampling.

Sample Sample Data

1 400 475 500 575 750

2 400 500 525 600 750

3 450 500 550 700 800

estimated total = Nn x (sample total) = 15

5 x (sample total) = 3 x (sample total)

Sample Computation Estimated Total

1 3 x (400 + 475 + 500 +575 + 750) 8,100

2 3 x (400 + 500 +525 + 600 + 750) 8,325

3 3 x (450 + 500 + 550 + 700 + 800) 9,000

Note: Population Total = 8,475 pesos. However, all the estimates are not too far from the true value. Furthermore, the average of the 3 estimates is (8,100 + 8,325 + 9,000)/3 = 8,475 pesos, that is, it is equal to the population total.


Notes: (page 79)

It is possible to manage the possible sampling error introduced in the results through a good sampling design:

Choose an appropriate sample selection procedure. Sample size must be large enough. Select the right statistic to estimate the parameter of interest.

Census results do not have sampling errors. It is not possible to determine the difference between the estimate and

the true value of the parameter from sample data since the value of the parameter is unknown. What is possible though is to estimate (using sample data) how varied the estimates are from sample to sample and how far they are (on the average) from the parameter itself. This will then give us an idea on the size of the sampling error that could possibly have been introduced in the results. If the estimated variation is small then we say that our estimate is reliable. If in addition, the estimates are, on the average, close to the parameter then we say that our estimate is accurate and so we expect the sampling error to be small.

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Figure 3.1. Components of Total Error (page 80)

Response Error

Instrument Error

Processing Error

Interviewer Bias

Surrogate Information Error

Response Bias

Nonresponse Bias

Non-sampling Error Sampling Error

Total Error

Measurement Error Error in the Implementation of the Sampling Design

Selection Error

Frame Error Population Specification Error

Indicate the type of error encountered in the following situations: Example 3.6 (page 81)

sampling frame is outdated complicated sample selection procedure is done in

the field by confused enumerators who incorrectly select the respondents included in the sample

lazy enumerators do not follow the specified sample selection procedure

target population is the target consumers of a particular brand but researchers incorrectly defines the qualifications of the target consumers

Exercise 4 (page 83)

a) use of telephone directories as frame for a household expenditure survey

b) refusal of the respondent to answer c) replacing a respondent with a next-door neighbor d) the respondent cannot recall accurately e) the respondent inflates his monthly income f) the respondent does not understand the term “youth”


Two Methods of Sampling (page 83)

Definition 3.5.

Probability Sampling: method of selecting a sample wherein each element of the population has a known, nonzero chance of being included in the sample.

Non-probability sampling: method of selecting a sample wherein some elements of the population do not have a known chance of inclusion in the sample or the chance is zero.

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Remarks on Probability Sampling: (pages 83-84)

In probability sampling, the chances of inclusion need not be the same for all elements.

The use of a randomization mechanism in the selection of the sampling units included in the sample makes it possible for us to determine the chances of inclusion.

Knowing the chances of inclusion will allow us to determine if our estimates are reliable and accurate.Question: Will the use of probability sampling assure us of selecting a “representative sample”?


Some Methods of Probability Sampling

Simple random sampling (SRS) pp 86 – 90 Stratified sampling pp 90 – 95 Systematic sampling pp 95 – 100 Cluster sampling pp 100 – 103 Multi-stage sampling pp 103 - 107

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Table of Random Numbers (Table A1, page 602)

The table of random numbers consists of digits from 0 to 9,arranged in a random manner in rows and columns. A computerprogram generated these numbers in such a way that all the digitsfrom 0 to 9 will always have equal chances of coming up.


Using the Table of Random Numbers to Select Numbers from 1 to N (page 85)

Step 1. Determine the number of digits in N. Denote this by m. Example: Suppose N=30 then m=2.

Step 2. Select a starting point. The starting point can be any row and any m consecutive columns.Example: Start at row 15, columns 10-11.

Step 3. Read the numbers in the selected column/s, starting with the selected row then move on by going down the rows. The numbers selected are the numbers from 1 to N that appear. Skip the number 00 and all numbers greater than N. If the n numbers have to be distinct then skip all numbers that you have already selected. If you reach the last row and have not yet generated n numbers, then proceed to the next m columns, starting with row 00. Stop once you obtain the nnumbers. Example: Choose n=10 distinct numbers.

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Using Data Analysis ToolPak of Excel

Installing Data Analysis Toolpak Excel 97-2003: (Appendix E: page 644) Excel 2007:

Step 1: Click Office Button Step 2: Click Excel Options bar Step 3: Choose Add-ins. Choose Excel Add-ins in Manage box then click Go. Step 4: Check Analysis ToolPak and Analysis ToolPak-VBA then Click OK.

To Select n Random Numbers from {1,2,…,N}: Step 1: In Column A, enter the integers from 1 to N from Row 1 to Row N. Step 2: In Column B, enter the formula =1/N from Row 1 to Row N. Step 3: Choose Data in Menu Bar. Click Data Analysis. Step 4: Select Random Number Generation. Click OK. Step 5: Fill-up dialogue box:

Number of vars = 1 Number of random numbers = n Distribution = Discrete Value and probability input range: cells containing values 1 to N and corresponding probs. Seed number: any positive integer less than 215



Simple Random Sampling (page 86)

Definition 3.6.

Simple Random Sampling (SRS) is a probability sampling method wherein all possible subsets consisting of n elements selected from the N elements of the population have the same chances of selection. Note: Consequently, all the elements of the population have the

same chances of inclusion in the sample.

Two Types of SRS:

Simple random sampling without replacement (SRSWOR): all the n elements must be distinct

Simple random sampling with replacement (SRSWR): the n elements need not be distinct

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Example 3.8. SRSWOR (page 86)

Population= {Janine, Josiel, Jan, Eryll, and Eariel}. Select a sample of size 2 using SRSWOR.

There are 10 possible subsets of size 2 containing distinct elements selected from the 5 elements in the population as follows:

{Janine, Josiel} {Janine, Jan} {Janine, Eryll}

{Janine, Eariel} {Josiel, Jan} {Josiel, Eryll}

{Josiel, Eariel} {Jan, Eryll} {Jan, Eariel}

{Eryll, Eariel)

By definition, all 10 samples have the same chances of selection. All 5 elements of the population have the same chances of inclusion. The common chance is 4/10=2/5 or 0.4. In general, it is n/N.


Example 3.8 cont’d. SRSWR (page 87)Population= {Janine, Josiel, Jan, Eryll, and Eariel}. Select a sample of size 2 using SRSWOR.

There are 25 possible ordered samples of size 2, where the coordinates need not be distinct.

(Janine, Janine) (Janine, Josiel) (Janine, Jan) (Janine, Eryll) (Janine, Eariel) (Josiel, Janine) (Josiel, Josiel) (Josiel, Jan) (Josiel, Eryll) (Josiel, Eariel) (Jan, Janine) (Jan, Josiel) (Jan, Jan) (Jan, Eryll) (Jan, Eariel) (Eryll, Janine) (Eryll, Josiel) (Eryll, Jan) (Eryll, Eryll) (Eryll, Eariel) (Eariel, Janine) (Eariel, Josiel) (Eariel, Jan) (Eariel, Eryll) (Eariel, Eariel)

By definition, all 25 ordered samples have the same chances of selection.

All 5 elements have the same chances of inclusion. This common probability is 9/25=1 – 42/52. In general, it is 1 – (N-1)n/Nn.

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Sample Selection Procedure using SRS (page 88)

Step 1: Look for a sampling frame listing down all the elements in the population. Assign a unique serial number, from 1 to N, to each one of the elements in the list.

Step 2. Generate n numbers from 1 to N using any randomization mechanism such as the table of random numbers. These n numbers must be distinct if we are using simple random sampling without replacement. In simple random sampling with replacement, these n numbers need not be distinct.

Step 3. The sample will consist of the elements with the same serial number as the numbers generated in Step 2.


Stratified Sampling (page 90)

Definition 3.7.

Stratified sampling is a probability sampling method where we divide the population into nonoverlapping subpopulations or strata, and then select one sample from each stratum. The sample consists of all the samples in the different strata.

Note: If the sample selection procedure is SRSWOR for all of the strata, then we specifically refer to this method as stratified random sampling.

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Sample Selection Procedure using Stratified Random Sampling (page 90)

Step 1. Identify the variable whose categories will serve as the strata in the study. This will be the stratification variable.

Step 2. Look for a sampling frame that lists down all of the elements in the population and contains data on the value of the stratification variable for each element.

Step 3. Use the data on the stratification variable to place each element of the population into its appropriate stratum.

Step 4. Select a sample from each stratum using SRSWOR.

Step 5. The sample will consist of all the samples selected in the different strata.

Choosing the stratification variable (page 91-94)

In stratified random sampling, we get estimates that are more reliable if the stratification variable partitions the population into strata wherein the elements within the same stratum are homogeneous with respect to the characteristic of interest, but the strata themselves vary considerably among each other.

choice of strata may facilitate the administration and supervision of data collection (ex: geographic subdivision)

strata may be the subpopulations of interest

information on stratification variable must be available for each element of the population


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Example 3.12 (pages 92-93)


Variable of interest: farm production

Parameter of interest: total farm production

Stratification variable: size of farm with categories - small, medium, and large

How does this compare with SRS?

Exercise #3 (page 110)

Identify an appropriate stratification variable for the following variables under study:

Height of schoolchildren in an elementary school Annual earnings of UP graduates since 1990


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Allocation of Sample (page 94)

Involves determining the sample size for each stratum

Affects the chance of including an element in the sample

Proportional allocation : the only allocation method wherein each element is given the same chance of selection. However, the sampling error will not always be expected to be small when we use this method.


Proportional Allocation (pages 94-95)


Under proportional allocation, the size of the sample in each stratum is proportional to the population size of the stratum Example 3.14. Suppose we want to get the opinion of business administration college students regarding premarital sex. A good stratification variable is sex because the views of the males may be very different from the views of the females. The population consists of N =500 business administration students and the sample size is n=50. Out of the 500, there are 300 female and 200 male students. The list of business administration students, together with their respective sex, is available at the records section of the college, or at the Office of the Registrar. Stratum Population Proportion of Sample No. Sex Size Students Size 1 Male N1=200 200/500= 0.4 n1=50 x 0.4 =20 2 Female N2 = 300 300/500 =0.6 n2=50 x 0.6 =30 TOTAL N = 500 n = 50

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Definition of Systematic Sampling (page 95)

Definition 3.8.

Systematic sampling is a probability sampling method wherein the selection of the first element is at random and the selection of the other elements in the sample is systematic by subsequently taking every k th element from the random start, where k is the sampling interval.


Sample Selection Procedure using Systematic Sampling where n is a divisor of N - Method A (page 95)

Step 1: Decide on a method of assigning a unique serial number, from 1 to N, to each one of the elements in the population.

Step 2: Choose n so that it is a divisor of N. Compute the sampling interval, k=N/n.

Step 3: Select a number from 1 to k using a randomization mechanism. Denote the selected number by r. The element assigned to this number is the first element of the sample.

Step 4: The other elements of the sample are those assigned to the numbers, r+k, r + 2k, r + 3k,... and so on until you get a sample of size n.

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Sample Selection Procedure using Systematic Sampling wheren is not a divisor of N – Method B (page 96)

Step 1 : Treat the list as a circular list.

Step 2: Compute for k as the greatest integer of N/n.

Step 3: Select a number from 1 to N using a randomization mechanism. Denote the selected number by r. The element assigned to this number is the first element in the sample.

Step 4 : The other elements are those assigned to the numbers r + k, r + 2k, r + 3k . . ., and so on until you get a sample of size n.

Example 3.16 (page 97)

Let us consider the same problem described in example 3.15. However, this time let us select a sample of n = 8 seniors from our population of N = 50.


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Cluster Sampling (page 100)

Definition 3.9.

Cluster sampling is a probability sampling method wherein we divide the population into nonoverlapping groups or clusters consisting of one or more elements, and then select a sample of clusters. The sample will consist of all the elements in the selected clusters.

Notes: The sampling units in cluster sampling are the clusters and not the

elements. If the clusters are selected using SRSWOR, then this is called

simple one-stage cluster sampling.


Sample Selection Procedure using Simple One-Stage Cluster Sampling (page 100)

Step 1: Divide the population into nonoverlapping clusters.

Step 2: Number the clusters in the population from 1 to N.

Step 3: Select n distinct numbers from 1 to N using a randomization mechanism. The selected clusters are the clusters associated with the selected numbers.

Step 4: The sample will consist of all the elements in the selected clusters.

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ExampleClusters: sections consisting of 10 studentsElements: students

20191817

15141312

1098

543

7

2

16

11

6

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The National Statistics Office conducts the Census of Agriculture and Fisheries (CAF) to collect data from all agricultural and fishing operators, and all households engaged in agricultural and fishing activities.

However, due to budgetary constraints, NSO was only able to collect sample data for the 1991 CAF. NSO used cluster sampling, where the barangays served as the clusters. For each city/municipality, NSO prepared a list of barangays arranged in descending order, according to the total farm area in the whole barangay. From this list, NSO selected a sample of barangays using systematic sampling. All agricultural and fishing operators and all households engaged in agricultural and fishing activities in the selected barangays were included in the study. In the end, NSO included a total of 5,997,427 operators and households for this study.

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Examples of Clusters (page 102)

city blocks serve as clusters of residents hospitals serve as clusters of patients schools serve as clusters of teachers class sections serve as clusters of students elements other than people are often sampled in clusters.

A car forms a cluster of four tires for studies of tire wear and safety.

A circuit board manufactured for a computer forms a cluster of semiconductors for testing.

A mango tree forms a cluster of mangoes for investigating insect infestation.

A plot in a forest contains a cluster of trees for estimating timber volume or proportions of diseased trees.

Stratified Sampling vs Cluster Sampling (page 102)

Stratified Sampling A sample is selected from

each stratum. Consequently, all strata will be represented in the sample.

Estimates will be more reliable if the elements in a stratum are homogeneous with respect to the characteristic under study.

Cluster Sampling Only a sample of clusters will

be selected in the sample then all elements in the selected clusters will be included in the sample.

Estimates will be more reliable if the elements in a cluster are heterogeneous with respect to the characteristic under study.

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Definition of Multi-Stage Sampling (page 103)

Definition 3.10

Multistage sampling is a probability sampling method where there is a hierarchical configuration of sampling units and we select a sample of these units in stages.

Notes:

In the first stage of sampling, the sampling units are called primary stage units (PSUs). In the second stage of sampling, the sampling units are called second stage units (SSUs). In the third stage of sampling, the sampling units are called third stage units (TSUs). And so on.

The sample selection procedure may vary in each stage. If the elements in the sample can already be identified on the second stage and the sample selection procedure is SRSWOR in each stage then this is referred to as simple 2-stage sampling. If the elements in the sample can already be indentified on the third stage and SRSWOR is used in each stage then this is referred to as simple 3-stage sampling.


Sample Selection Procedure using Simple 3-Stage Sampling (page 104)

Step 1. List down the primary stage units in the population and number them from 1 to N.

Step 2. Select a sample of primary stage units using simple random sampling.

Step 3. For each of the selected primary stage units, list down the second-stage units and number them from 1 to the total number of second- stage units.

Step 4. Select a sample of second-stage units from each one of the selected primary stage units using simple random sampling.

Step 5. For each of the selected second-stage, list down the third-stage units and number them from 1 to the total number of third-stage units. The third-stage units are already the elementary units in the study.

Step 6. Select a sample of third-stage units from each one of the selected second-stage sampling units using simple random sampling.

Step 7. The sample consists of all the third-stage units selected in step 6.

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Suppose we wish to study the expenditure patterns of households in the National Capital Region (NCR). We can select a sample of households for this study using simple three-stage sampling where the PSUs are the cities/municipalities, the SSUs are the barangays, and the third-stage units TSUs are the households.


Example (cont’d)List down all the 17 cities/municipalities in NCR and number them from 1 to 17.

01 Manila 07 Caloocan City 13 Pateros02 Quezon City 08 Malabon 14 Las Piñas03 City of Mandaluyong 09 Navotas 15 Muntinlupa04 San Juan 10 Valenzuela 16 Parañaque05 Marikina 11 Makati 17 Pasay City06 Pasig 12 Taguig

Suppose we decide to include 3 PSUs in the sample. We need to generate 3 distinct numbers from 1 to 17 using a randomization mechanism. If the numbers selected are 11, 13 and 05 then the cities/municipalities included in the sample are Makati, Pateros and Marikina.

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Example (cont’d) List down all the 33 barangays in Makati and number them from 1 to 33. List down all the

10 barangays in Pateros and number them from 1 to 10. List down all the 14 barangays in Marikina and number them from 1 to 14.

Suppose we decide to include in our sample 4 barangays from each selected city/municipality.

For Makati, we need to generate 4 distinct numbers from 1 to 33 using a randomization mechanism. If the numbers selected are 08, 25, 33 and 15 then what are the SSUs in the sample from Makati?

For Pateros, we need to generate 4 distinct numbers from 1 to 10 using a randomization mechanism. If the numbers selected are 03, 05, 09 and 06 then what are the SSUs in the sample from Pateros?

For Marikina, we need to generate 4 distinct numbers from 1 to 14 using a randomization mechanism. If the numbers selected are 01, 10, 13 and 06 then what are the SSUs in the sample fro Marikina?

List of Barangays in Makati

Makati: 01 Bangkal 12 La Paz 23 San Antonio02 Bel-Air 13 Magallanes 24 San Isidro03 Cembo 14 Olympia 25 San Lorenzo04 Comembo 15 Palanan 26 Santa Cruz05 Carmona 16 Pembo 27 Singkamas06 Dasmariñas 17 Pinagkaisahan 28 South Cembo07 East Rembo 18 Pio del Pilar 29 Tejeros08 Forbes Park 19 Pitogo 30 Urdaneta09 Guadalupe Nuevo 20 Poblacion 31 Valenzuela10 Guadalupe Viejo 21 Post Proper North 32 West Rembo11 Kasilawan 22 Post Proper South 33 Rizal

Nos. selected: 08, 25, 33, 15Chapter 3. Sampling and Sampling Techniques

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List of Barangays in Pateros

Pateros: 01 Aguho 05 San Pedro 09 Sto. Rosario Silangan02 Magtanggol 06 San Roque 10 Tabacalera03 Martires Del 96 07 Sta. Ana04 Poblacion 08 Sto. Rosario Kanluran

Numbers selected: 03, 05, 09, 06


List of Barangays in Marikina

Marikina: 01 Barangka 06 Nangka 11 Tañong02 Calumpang 07 Parang 12 Concepcion Dos03 Concepcion Uno 08 San Roque 13 Marikina Heights04 Jesus dela Peña 09 Santa Elena 14 Industrial Valley05 Malanday 10 Santo Niño

Nos. selected: 01, 10, 13, 06


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Example (cont’d) For each one of the 12 selected barangays, list down

all the households and number them accordingly.

Suppose we decide to include in our sample 20 households from each of 12 selected barangays. We need to select these samples using simple random sampling without replacement.

Our sample will consist of the 240 households selected in Step 6 from the 12 selected barangays in Step 4 from the 3 selected cities/municipalities in Step 2.


The Food and Nutrition Research Institute (FNRI) of the Department of Science and Technology (DOST) conducts the National Nutrition Survey (NNS) every 5 years. This survey aims to determine the prevalence of malnutrition and specific health problems in the country and to provide data on food consumption and nutrient intake.

For this study, FNRI used 2-stage sampling to select a sample of individuals from each province. The primary stage units are the barangays. The second-stage units are the individuals.

In each province, FNRI prepared a list of barangays arranged in ascending order, according to the total number of households in the barangay. They then selected a sample of barangays using systematic sampling. In each one of the selected barangays, they listed down all the individuals. They collected data on variables like sex, age, and classification of woman (pregnant or lactating mother). They formed strata based on these variables. From each stratum, they selected a sample of individuals using systematic sampling.


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The Department of Tourism (DOT) conducts the Visitor Sample Survey (VSS) every month. This survey aims to collect data on the demographic profile, travel characteristics, and preferences of foreign and overseas Filipinos who visited the country for tourism development planning and policy-making purposes.

DOT selects the sample of visitors using three-stage sampling. The primary stage units are the weeks of the month. The second-stage units are the weekly flights. The third-stage units are the visitors.

For this monthly survey, DOT selects the week of the month using simple random sampling. From the selected week, they select a sample of weekly flights. They perform this using stratified random sampling. DOT stratified all the regular weekly international flights leaving the different international airports in the Philippines according to country market. It then selects a sample of flights from each country market using simple random sampling. From the selected flights, DOT selects a sample of visitors using simple random sampling.



Assignment:Population: collection of all hospitals in Metro Manila

Select a sample of 8 schools using SRSWOR. Select a sample of 8 schools using systematic sampling. Select a sample of 8 schools using stratified random sampling with

proportional allocation, where location (north or south) is the stratification variable

North: located in Caloocan, Valenzuela, Navotas, Malabon, Quezon City, Marikina, San Juan, Manila, Mandaluyong, Pasig

South: all others

Show all pertinent steps in the selection of the 3 samples. Use the table of random numbers. Always indicate the initial row and column numbers.

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Exercise 1 (page 109)

Identify the sample selection procedure used in each of the following cases:a) A survey obtained a sample of laborers by first classifying the different areas as

either rural or urban. After which, a sample of laborers was taken from each area.

b) To select a sample of households in a province, a sample of provinces were selected, then a sample of municipalities were chosen from each of the selected provinces, then a sample of barangays were chosen from each of the selected municipality, and all households in the selected barangays were included.

c) A study selected a sample of municipalities from every province in the country and included all child laborers in the selected municipalities.

d) In the game of lotto, they select six balls from a container with 42 balls.e) A car manufacturer conducts quality checking on every 20th car in the production

line from the random start.



Common Types of Non-probability Sampling (pp 111-114)

Accidental/Convenience sampling: items or units that are most accessible are included in the sample. (Examples include a sample of volunteers, street corner interviews, and pull-out questionnaires in a magazine.)

Purposive sampling: sample is selected in accordance with an expert’s subjective judgment on what a “representative” sample should contain. Usually sampling units are clusters whose profile is similar to the profile of the population. (Example: identify barangays where the income distribution of households is the same as the population)

Quota sampling: It the nonprobability sampling version of stratified sampling where the researcher just sets a quota or number of sampling units in each grouping but uses convenience sampling in selecting the units in each group. (Example: sample includes any 50 Globe subscribers and any 50 Smart subscribers)

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