Mathematics 101: Data Collection and Sampling Techniques Olive R. - PowerPoint PPT Presentation

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 orcawiding@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 outside 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 Personal Interview questionnaire • Missing information and • Obtained information is vague responses are minimized limited to subjects’ written with proper probing of answers to prearranged interviewer questions

Mathematics 101: Elementary Statistics Data Collection Data Collection Methods Data Collection Methods: Survey Method Self-administered simultaneously questionnaire Personal Interview • It can be administered to a • It is administered to a person larger number of people or a group one at a time

Mathematics 101: Elementary Statistics Data Collection Data Collection Methods Data Collection Methods: Survey Method Self-administered Personal Interview questionnaire • Respondents may feel more • Respondents may feel freer cautious particularly in to express views and are less answering sensitive questions pressured to answer for fear of disapproval. immediately

Mathematics 101: Elementary Statistics Data Collection Data Collection Methods Data Collection Methods: Survey Method Self-administered Personal Interview questionnaire • It is more appropriate for • It is more appropriate for obtaining information about obtaining objective complex emotionally-laden information. topics or probing sentiments underlying an expressed opinion.

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 or 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 out 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 k th 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 + 2 k , r + 3 k , . . . , 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.