Statistics

• Mean is a measure of central tendency that represents the average value of a dataset.
• Probability Sampling


  Also known as random sampling in general. Samples are obtained using some objective chance mechanism, thus involving randomization. They require the use of a complete listing of the elements of the universe called the sampling frame. The probabilities of selection are known. They are generally referred to as random samples. They allow drawing of valid generalizations about the universe/population.
• Types of Probability Sampling

  • Simple Random Sampling
  • Systematic Random Sampling
  • Stratified Random Sampling
  • Cluster Sampling
• Simple Random Sampling


  Also known as Fish Bowl Sampling. Most basic method of drawing a probability sample. Assigns equal probabilities of selection to each possible sample. Results to a simple random sample.
• Simple Random Sampling


  • It is very simple and easy to use
  • The sample chosen may be distributed over a wide geographic area
• When to use Simple Random Sampling

  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.
• Systematic Random Sampling


  It is obtained by selecting every kth individual from the population. The first individual selected corresponds to a random number between 1 to k.
• Steps for Systematic Random Sampling

  1. Decide on the number of samples to obtain

  2. Use the formula k = N/n to know your interval of choice

  3. The responses that will fall on the kth count will be part of the samples
• Systematic Random Sampling


  • Drawing of the sample is easy. It is easy to administer in the field, and the sample is spread evenly over the population
  • May give poor precision when unsuspected periodicity is present in the population
• When to use Systematic Random Sampling


  This is advisable to us if the ordering of the population is essentially random and when stratification with numerous data is used.
• Stratified Random Sampling


  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.
• Example of Stratified Random Sampling

  • 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?
• Stratified Random Sampling


  • Stratification of respondents is advantageous in terms of precision of the estimates of the characteristics of the population. Sampling designs may vary by stratum to adjust for the differences in the conditions across strata. It is easy to use as a random sampling design.
  • Values of the stratification variable may not be easily available for all units in the population especially if the characteristic of interest is homogeneous. It is possible that there are not representative in one or two strata. Also, transportation costs can be high if the population covers a wide geographic area.
• When to use Stratified Random Sampling


  If the population is such that the distribution of the characteristics of the respondents under consideration concentrated in small and spread segment of the population. Thus, this is preferred to use if precise estimates are desired for stratified parts of the population and if sampling problems differ in the various strata of the population.
• 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.
• Example of Cluster Sampling


  • A researcher wants to survey academic performance of high school students in MIMAROPA. 1. He/She can divide the entire population into different 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 through simple or systematic random sampling.
• Cluster Sampling


  • 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.
  • In actual field applications, adjacent households tend to have more similar characteristics than households distantly apart.
• When to use Cluster Sampling


  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.
• 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.
• Types of Non-Probability Sampling

  • Accidental Sampling
  • Quota Sampling
  • Convenience Sampling
  • Purposive Sampling
  • Judgement Sampling
• Accidental Sampling


  There is no system of selection but only those whom the researcher or interviewer meets by chance.
• Quota Sampling


  There is specified number of persons of certain types is included in the sample. The researcher is aware of categories within the population and draws samples from each category. The size of each categorical sample is proportional to the proportion of the population that belongs in that category.
• 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.
• When to use Non-Probability Sampling


  Only few are willing to be interviewed, Extreme difficulties in locating or identifying subjects, Probability sampling is more expensive to implement, Cannot enumerate the population elements.
• Sources of Sampling Errors

  • Non-sampling Error
  • Sampling Error
• Non-Sampling Error


  Errors that result from the survey process. Any errors that cannot be attributed to the sample-to-sample variability.
• Sources of Non-Sampling Error

  • Non-responses
  • Interviewer Error
  • Misrepresented Answers
  • Data entry errors
  • Questionnaire Design
  • Wording of Questions
  • Selection Bias
• 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.
• Three Ways to Present Data

  • Textual Presentation
  • Tabular Presentation
  • Graphical Presentation
• Textual Presentation of Data


  All the data is presented in the form of text, phrases, or paragraphs. It involves enumerating characteristics, emphasizing significant figures and identifying important features of data. Text is the principal method for explaining findings, outlining trends, and providing contextual information.
• Textual Presentation of Data

  • The data would be more interpreted directly, Can help in emphasizing some important points in data, Small sets of data can be easily presented.
• Tabular Presentation


  It is a systematic and logical arrangement of data in the form of Rows and Columns with respect to the characteristics of data. A table is best suited for representing individual information and represents both quantitative and qualitative information.
• Main Parts of an Ideal Table

  • Title
  • Boxhead
  • Stubs
  • Footnotes
• Title


  The title must tell as simply as possible what is in the table. It should answer the questions: Who? What are the data? Where are the data from? When?
• Boxhead


  The boxhead contains the captions or column headings. The heading of each column should contain as few words as possible, yet explain exactly what the data in the columns represent.
• Stubs


  The row captions are known as the stub. Items in the stub should be grouped to facilitate interpretation of the data.
• Footnotes


  Footnotes are given at the foot of the table for explanation of any fact or information included in the table which needs some explanation.
• Considerations in Construction of Data Tables

  • Comparison
  • Alternative location of stubs
  • Headings
  • Footnote
  • Size of columns
  • Use of abbreviations
  • Units