Lecture 1-3 Biophysics PDF

What is STATISTICS? De Polytechnic University of the Philippines F.L. MINGO, MSAM College of Science Department of Mathematics and Statistics  nition? The information referred to the de fi ...

What is STATISTICS? De Polytechnic University of the Philippines F.L. MINGO, MSAM College of Science Department of Mathematics and Statistics  nition? The information referred to the de fi  cation of Variables Variables can be classi fi fi  Reason for Sampling Important that the individuals included in a sample represent a cross section of individuals in the population. If sample is not representative it is biased -- you cannot generalize to the population from your statistical data. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics Basic Terms Need to Know Observation unit - An object on which a measurement is taken. This is the basic unit of observation, sometimes called an element. In studying human populations, observation units are often individuals. Target population - The complete collection of observations we want to study. Sampled population - The collection of all possible observation units that might have been chosen in a sample; the population from which the sample was taken. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics Basic Terms Need to Know Sample - A subset of a population. Sampling unit - A unit that can be selected for a sample. We may want to study individuals, but do not have a list of all individuals in the target population. Instead, households serve as the sampling units, and the observation units are the individuals living in the households. Sampling frame - A list, map, or other speci Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics fi Basic Terms Need to Know Sampling technique/Sampling Strategies - It is a plan you set to be sure that the sample you use in your research study represents the population from which you drew your sample. Bias Sampling - This involves problems in your sampling, which reveals that your sample is not representative of your population. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Bias Selection 1. Deliberately or purposively selecting a “representative” sample. 2. Not specifying the target population. 3. Failing to include all of the target population in the sampling frame, called undercoverage. 4. Including population units in the sampling frame that are not in the target population, called overcoverage. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Bias Selection 5. Having multiplicity of listings in the sampling frame. 6. Substituting a convenient member of a population for a designated member who is not readily available. 7. Failing to obtain responses from all of the chosen sample. (Nonresponse) 8. Allowing the sample to consist entirely of volunteers. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Advantage of Sampling Over Complete Enumeration Less Labor Reduced Cost Greater Speed Greater Scope Greater Ef Convenience Ethical Considerations Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics fi  Two Types of Sampling 1. Probability 2. Non - Probability Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Probability Sampling Samples are obtained using some objective chance mechanism, thus involving randomization. They require the use of a complete listing of the elements of the sampling frame. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Probability Sampling The probabilities of selection are known. They are generally referred to as random samples. They allow drawing of valid generalizations about the universe/ population. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Non-Probability Sampling Samples are obtained haphazardly, selected purposively or are taken as volunteers. The probabilities of selection are unknown. They should not be used for statistical inference. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Sampling Procedure 1. Identify the population. 2. Determine if population is accessible. 3. Select a sampling method. 4. Choose a sample that is representative of the population. 5. Ask the question, can I generalize to the general population from the accessible population? Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Basic Sampling Technique of Probability Sampling Sampling technique can be grouped into how selections of items are made such as probability sampling and non-probability sampling. Simple Random Sampling Systematic Random Sampling Strati Cluster Sampling Multi-stage Sampling Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics fi  Simple Random Sampling Most basic method of drawing a probability sample. Assigns equal probabilities of selection to each possible sample. Results to a simple random sample Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Simple Random Sampling Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics Advantage: It is very simple and easy to use. Disadvantage: Dif When to Use: This is preferable to use if the population is not widely spread geographically. Also, this is more appropriate to use if the population is more or less homogenous with respect to the characteristics of the population. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics fi Systematic Random Sampling It is obtained by selecting every kth individual from the population. The Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics fi Systematic Random Sampling Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics Obtaining a Systematic Random Sample 1. Decide on a method of assigning a unique serial number, from 1 to N, to each one of the elements in the population. N PopulationSize 2. Compute for the sampling interval k= = n SampleSize 3. Select a number, from 1 to k, using a randomization mechanism. The element in the population assigned to this number is the Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics fi Advantage: Drawing of the sample is easy. It is easy to administer in the Disadvantage: May give poor precision when unsuspected periodicity is present in the population. When to Use: This is advisable to us if the ordering of the population is essentially random and when strati Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics fi fi  Example: We want to select a sample of 50 students from 500 students under this method kth item and picked up from the sampling frame. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Solution: 500 k= = 10 50 We start to get a sample starting form i and for every kth unit subsequently. Suppose the random number i is 6, then we select 16, 26, 36, 46,... Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics Strati It is obtained by separating the population into non-overlapping groups called strata and then obtaining a simple random sample from each stratum. The individuals within each stratum should be homogeneous (or similar) in some way. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics fi Strati Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics fi Advantage: The selection of units using a strati Disadvantage: Values of the strati Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics fi fi When to Use: We need to have information in the sampling frame that can be used to form the strata. For each group, we need to know how many and which members of the population belong to that group. When such information is available, it is easy to use strati Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics fi  Example: A sample of 50 students is to be drawn from a population consisting of 500 students belonging to two institutions A and B. The number of students in the institution A is 200 and the institution B is 300. How will you draw the sample using proportional allocation? Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Solution: There are two strata in this case. Given: N1 = 200 N2 = 300 N = 500 n = 50 If n1 and n2 are the sample size, (N) ( 500 ) n 50 n1 = N1 = 200 = 20 (N) ( 500 ) n 50 n2 = N2 = 300 = 30 The sample sizes are 20 from A and 30 from B. Then the units from each institution are to be selected by simple random sampling. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Cluster Sampling You take the sample from naturally occurring groups in your population. The clusters are constructed such that the sampling units are heterogeneous within the cluster and homogeneous among the clusters. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Cluster Sampling Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics Obtaining a Cluster Sample 1. Divide the population into non-overlapping clusters. 2. Number the clusters in the population from 1 to N. 3. Select n distinct numbers from 1 to N using a randomization mechanism. The selected clusters are the clusters associated with the selected numbers. 4. The sample will consist of all the elements in the selected clusters. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics Advantage: There is no need to come out with a list of units in the population; all what is needed is simply a list of the clusters. It is also less costly since the elements are physically closer together. Disadvantage: In actual When to Use: If the population can be grouped into clusters where individual population elements are known to be different with respect to the characteristics under study, this preferable to use. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics fi  Example: A researcher wants to survey academic performance of high school students in MIMAROPA. 1. He/She can divide the entire population into different clusters (Mindoro, Marinduque, Romblon, and Palawan). There are 4 clusters. 2. Then the researcher selects a number of clusters depending on his research through simple or systematic random sampling. 3. Then, from the selected clusters the researcher can either include all the high school students as subject or he can select a number of subjects from each cluster. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Multi - Stage Sampling Selection of the sample is done in two or more steps or stages, with sampling units varying in each stage. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Multi - Stage Sampling Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics Obtaining a Multi-Stage Sample 1. Organize the sampling process into stages where the unit of analysis is systematically grouped. 2. Select a sampling technique for each stage. 3. Systematically apply the sampling technique to each stage until the unit of analysis has been selected. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Advantage: Transportation costs are greatly reduced since there is some form of clustering among the ultimate or Disadvantage: Due to the fact that multi-stage sampling cuts out portions of the population from the study, the study’s When to Use: If the population covers a wide area. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics fi fi  Example: https://research-methodology.net/sampling-in-primary-data-collection/multi-stage-sampling/ Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Basic Sampling Technique of Non-Probability Sampling Accidental Sampling - There is no system of selection but only those whom the researcher or interviewer meets by chance. Quota Sampling - There is speci Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics fi  Convenience Sampling - It is a process of picking out people in the most convenient and fastest way to get reactions immediately. This method can be done by telephone interview to get the immediate reactions of a certain group of sample for a certain issue. Purposive Sampling - It is based on certain criteria laid down by the researcher. People who satisfy the criteria are interviewed. It is used to determine the target population of those who will be taken for the study. Judgement Sampling - selects sample in accordance with an expert’s judgment. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Cases wherein Non-Probability Sampling is Useful ✦ Only few are willing to be interviewed ✦ Extreme dif ✦ Probability sampling is more expensive to implement ✦ Cannot enumerate the population elements. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics fi Sources of Errors in Sampling 1. Non-sampling Error 2. Sampling Error Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Non - Sampling Error ✦ Errors that result from the survey process. ✦ Any errors that cannot be attributed to the sample-to-sample variability. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics Sources of Non-Sampling Error 1. Non-responses 2. Interviewer Error 3. Misrepresented Answers 4. Data entry errors 5. Questionnaire Design 6. Wording of Questions 7. Selection Bias Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  Sampling Error ✦ Error that results from taking one sample instead of examining the whole population. ✦ Error that results from using sampling to estimate information regarding a population. Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics  References: http://www.economicsdiscussion.net/statistics/sampling/ advantages-of-sampling-over-complete-enumeration-in- statistics/11980 http://www.natco1.org/research/ https://data36.com/statistical-bias-types-explained/ Statistics. Informed Decision using Data by Michael Sullivan, III,. Fifth Edition Sampling: Design and Analysis by Sharon L. Lhr. Second Edition Polytechnic University of the Philippines College of Science Department of Mathematics and Statistics fi