Week 5

• Sampling


  The process of selecting a representative sample from populations
• Sample


  • A smaller (but hopefully representative) collection of units from a population used to determine truths about that population
• Sampling


  The process of selecting a representative sample from populations
• Sample


  • A smaller (but hopefully representative) collection of units from a population used to determine truths about that population
• Two Types of Samples

  • Probability Sample
  • Non-probability Sample
• Probability Sample


  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.
• Non-probability Sample


  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.
• 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?
• Sampling technique can be grouped into how selections of items are made

  • Probability sampling
  • Non-probability sampling
• 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.
• Simple Random Sampling


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

  2. Compute for the sampling interval

  3. Select a number, from 1 to k, using a randomization mechanism. The element in the population assigned to this number is the first element of the sample. The other elements of the sample are those assigned to the numbers and so on until you get a sample of size.
• 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
• 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.
• Obtaining a Stratified Random Sample

  There are two strata in this case. 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.
• 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.
• 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.
• 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
• 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.
• Multi-Stage Sampling


  Selection of the sample is done in two or more steps or stages, with sampling units varying in each stage. The population is first divided into a number of first-stage sampling units from which a sample is drawn. Smaller units, called the secondary sampling units, comprising the selected first-stage units then serve as the sampling units for the next stage. If needed additional stages may be added until the units of observation for the survey are clearly identified. The units comprising the samples selected from the previous stage constitute the frame for the stages.
• Obtaining a Multi-Stage Sampling

  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
• Multi-Stage Sampling


  • It is easier to generate adequate sampling frames. Transportation costs are greatly reduced since there is some form of clustering among the ultimate or final samples; i.e., they are in the sample lower-stage units.
  • Its complexity in theory may be difficult to apply in the field. Estimation procedures may be difficult for non-statisticians to follow.
• Used probability sampling if the main objective of the sample survey is making inferences about the characteristics of the population under study.
• Basic Sampling Technique of Non-Probability Sampling

  • Accidental Sampling
  • Quota Sampling
  • Convenience Sampling
  • Purposive Sampling
  • Judgement Sampling
• Cases wherein Non-Probability Sampling is Useful
• Sources of Errors in Sampling

  • Non-sampling Error
  • Sampling Error
• 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.
• Proportional allocation


  A sampling technique where the sample size for each stratum is proportional to the population size of that stratum
• Procedure in Constructing Frequency Table

  1. If the data is in the form of quantitative data:

  2. Highlight your data for the "INPUT RANGE".

  3. Highlight your data for the "BIN RANGE".

  4. Click the box of "LABELS IN FIRST ROW" then click "OK".

  5. The result will appear on the new worksheet of the excel file. Get the Percentage and total.
• Useless Information – Don't show decimals if they are not needed.
• Poor Alignment – Make sure alignment makes sense. Don't center numbers, always right justify – try to align decimal points. Consider the appropriate placement of row titles.
• Difficult to Read – Use commas used when the number exceeds a thousand.
• Graph


  • Displays data at a glance, facilitates comparison, and can reveal trends and relationships within the data such as changes over time, and correlation or relative share of a whole.
  • An important medium of communication as it creates a pictorial representation of the numerical figures.
  • Suited when we need to show the results of the study to nonprofessionals and or people who dislike numbers and too lengthy texts.
• Bar Graph


  • Constructed by labeling each category of data on either the horizontal or vertical axis and the frequency or relative frequency of the category on the other axis. Rectangles of equal width are drawn for each category. The height of each rectangle represents the category's frequency or relative frequency.
  • Used to organize discrete data.
• Simple Bar Graph


  • Used for the case of one variable only.
• Multiple Bar Graph/ Grouped Column Chart


  • An extension of a simple bar chart when there are quantities of several variables to be displayed. The bars representing the quantities for the different variables are piled next to one another for each attribute.
• Component Bar Graph/ Subdivided Column Chart

  • The components (quantities) of each variable are piled on top of one another. Saves space as compared to a multiple bar chart. One of the disadvantage is that it is not always easy to compare size of the components, or parts. Used to represent data in which the total magnitude is divided into different or components.
• Bar graphs may also be drawn with horizontal bars. Horizontal bars are preferable when category names are lengthy.