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Mathematics 101: Elementary Statistics

Mathematics 101: Data Collection and Sampling Techniques

Olive R. Cawiding

Department of Mathematics and Computer Science College of Science, University of the Philippines

• Gov. Pack Road, Baguio City 2600 Philippines
• rcawiding@up.edu.ph

Mathematics 101: Elementary Statistics

Outline

1 Data Collection

Classification of Data Data Collection Methods

2 Sampling Techniques

Important Terms Sampling Procedures

Probability Sampling Non-probability Sampling

Mathematics 101: Elementary Statistics Data Collection Classification of Data

Sources of Data

We can classify data in two ways:

• 1. Primary vs. Secondary
• a. Primary - data measured by the researcher or agency that

published it

• b. Secondary - any republication of data by another agency

EXAMPLE.The Philippine Statistics Authority, Pulse Asia, and the Department of Health are primary sources of data. What are examples of secondary data?

Mathematics 101: Elementary Statistics Data Collection Classification of Data

Classification of Data

• 2. External vs. Internal
• a. Internal Data - information that refers to the operations and

functions of the organization collecting the data

• b. External Data - information that relates to some activity
• utside the organization collecting the data

Mathematics 101: Elementary Statistics Data Collection Data Collection Methods

Data Collection Methods: Survey Method

In the survey method, questions are asked to obtain information, either through self-administered questionnaire or personal interview. Self-administered questionnaire

• Obtained information is

limited to subjects’ written answers to prearranged questions Personal Interview

• Missing information and

vague responses are minimized with proper probing of interviewer

Mathematics 101: Elementary Statistics Data Collection Data Collection Methods

Data Collection Methods: Survey Method

Self-administered questionnaire

• It can be administered to a

larger number of people simultaneously Personal Interview

• It is administered to a person
• r a group one at a time

Mathematics 101: Elementary Statistics Data Collection Data Collection Methods

Data Collection Methods: Survey Method

Self-administered questionnaire

• Respondents may feel freer

to express views and are less pressured to answer immediately Personal Interview

• Respondents may feel more

cautious particularly in answering sensitive questions for fear of disapproval.

Mathematics 101: Elementary Statistics Data Collection Data Collection Methods

Data Collection Methods: Survey Method

Self-administered questionnaire

• It is more appropriate for
• btaining objective

information. Personal Interview

• It is more appropriate for
• btaining information about

complex emotionally-laden topics or probing sentiments underlying an expressed

• pinion.

Mathematics 101: Elementary Statistics Data Collection Data Collection Methods

Data Collection Methods: Observation Method

The observation method makes possible the recording of the behavior but only at the time of occurrence EXAMPLES.

• response to a certain stimulus
• traffic count
• behavior of animals in wildlife

Mathematics 101: Elementary Statistics Data Collection Data Collection Methods

Data Collection Methods: Experimental Method

The experimental method involves a scientific investigation conducted under controlled situations where treatments are applied and their effects measured on the response of interest to the experimenter.

Mathematics 101: Elementary Statistics Data Collection Data Collection Methods

Data Collection Methods: Experimental Method

Defintion. The independent variable or explanatory variable in an experimental study is the one being manipulated by the

• researcher. The resultant variable is called the dependent

variable or the outcome variable. Definition. A confounding variable is one that influences the dependent

• r outcome variable but was not separated from the

independent variable

Mathematics 101: Elementary Statistics Data Collection Data Collection Methods

Data Collection Methods: Use of Existing Studies

Another way of collecting data is through the use of existing studies (e.g. census, health statistics and weather bureau reports). (a) documentary sources (b) field sources

Mathematics 101: Elementary Statistics Data Collection Data Collection Methods

Data can also be collected through registration method. EXAMPLES.

• car registration
• student registration
• hospital admission

Mathematics 101: Elementary Statistics Sampling Techniques Important Terms

Some Imporant Terms

Definition. Census or complete enumeration is the process of gathering information from every unit in the population. Example. The Philippine Statistics Authority conducts four censuses on a regular basis:

• Census on Population and Housing
• Census of Philippine Business and Industry
• Census of Agriculture and Fisheries
• Census of Buildings

Mathematics 101: Elementary Statistics Sampling Techniques Important Terms

Some Important Terms

Definition. Survey sampling is the process of obtaining information from the units in the selected sample. Important Questions.

• What are the advantages of survey sampling?
• When is it more appropriate to collect data from a sample

than to conduct a census?

Mathematics 101: Elementary Statistics Sampling Techniques Important Terms

Some Important Terms

Definition. The target population is the population from which information is desired. Definition. The sampled population is the collection of elements from which the sample is actually taken. Definition. The population frame is a listing of all the individual units in the population.

Mathematics 101: Elementary Statistics Sampling Techniques Sampling Procedures

Sampling

Definition. A sampling procedure that gives every element of the population a (known) nonzero chance of being selected in the sample is called probability sampling. Otherwise, the sampling procedure is called non-probability sampling.

Mathematics 101: Elementary Statistics Sampling Techniques Sampling Procedures

Probability Sampling: Simple Random Sampling

Simple random sampling is a method of selecting n units

• ut of the N units in the population in such a way that every

distinct sample of size n has an equal chance of being drawn.

• 1. Simple random sampling with replacement
• 2. Simple random sampling without replacement

Mathematics 101: Elementary Statistics Sampling Techniques Sampling Procedures

Probability Sampling: Simple Random Sampling

SAMPLE SELECTION PROCEDURE Step 1. Make a list of the sampling units and number them from 1 to N. Step 2. Select n numbers from 1 to N using some random process. Step 3. The sample consists of the units corresponding to the selected random numbers.

Mathematics 101: Elementary Statistics Sampling Techniques Sampling Procedures

Probability Sampling: (1-in-k) Systematic Sampling

Systematic samples are obtained by numbering each element in the population and then selecting every kth subject. Here, k is called the sampling interval and the reciprocal 1/k is the sampling fraction.

Mathematics 101: Elementary Statistics Sampling Techniques Sampling Procedures

Probability Sampling: (1-in-k) Systematic Sampling

SAMPLE SELECTION PROCEDURE Step 1. Number the units of the population consecutively from 1 to N. Step 2. Let k be the nearest integer to N/n. Step 3. Select the random start r, where 1 ≤ r ≤ k. The unit corresponding to r is the first unit of the sample. Step 4. The other units of the sample correspond to r + k, r + 2k, r + 3k, . . ., r + (n − 1)k

Mathematics 101: Elementary Statistics Sampling Techniques Sampling Procedures

Probability Sampling: Stratified Sampling

Stratified sampling is a sampling method where the population N is divided into groups (called strata) according to a characteristic important to the study. Samples are then taken from each stratum.

Mathematics 101: Elementary Statistics Sampling Techniques Sampling Procedures

Probability Sampling: Stratified Sampling

SAMPLE SELECTION PROCEDURE Step 1. Divide the population into strata. Ideally, each stratum must consist of more or less homogeneous units. Step 2. After the population has been stratified, a random sample is selected from each stratum.

Mathematics 101: Elementary Statistics Sampling Techniques Sampling Procedures

Probability Sampling: Stratified Sampling

Advantages and disadvantages?

Mathematics 101: Elementary Statistics Sampling Techniques Sampling Procedures

Probability Sampling: Cluster Sampling

Cluster sampling is a method of sampling where a sample of distinct groups, or clusters, of elements is selected and then a census of every element in the selected clusters is taken.

Mathematics 101: Elementary Statistics Sampling Techniques Sampling Procedures

Probability Sampling: Stratified Sampling

SAMPLE SELECTION PROCEDURE Step 1. Number the clusters from 1 to N. Step 2. Select n numbers from 1 to N at random. The clusters corresponding to the selected numbers form the sample of the clusters. Step 3. Observe all elements in the sample of clusters.

Mathematics 101: Elementary Statistics Sampling Techniques Sampling Procedures

Probability Sampling: Multistage Sampling

In multistage sampling, the population is divided into a hierarchy of sampling units corresponding to the different sampling stages.

Mathematics 101: Elementary Statistics Sampling Techniques Sampling Procedures

Probability Sampling: Multistage Sampling

SAMPLE SELECTION PROCEDURE Step 1. The population is divided into primary stage units (PSU) then a sample of PSUs is drawn. Step 2. Each selected PSU is subdivided into second-stage units (SSU) then a sample of SSUs is drawn. Step 3. The process of subsampling can be carried to a third stage, fourth stage and so on, by sampling the subunits instead of enumerating them completely at each stage.

Mathematics 101: Elementary Statistics Sampling Techniques Sampling Procedures

Non-probability Sampling

• 1. Purposive Sampling - sets out to make a sample agree

with the profile of the population based on some pre-selected characteristic.

• 2. Quota Sampling - selects a specified number (quota) of

sampling units possessing certain characteristics.

• 3. Convenience Sampling - selects sampling units that come

to hand or are convenient to get information from.

• 4. Judgment Sampling - selects sample in accordance with

their knowledge and professional judgment.