Statistical Sampling

• Population


  The whole set of items that are of interest
• Raw data


  Information obtained from a population
• Census


  Measures or observes every member of a population
• Sample


  A selection of observations taken from a subset of population and used to find out more information about the population as a whole
• Advantages of Census


  • Results should be completely accurate
• Disadvantages of Census


  • Time consuming and expensive
  • Cannot be used when testing destroys process
  • Hard to process large quantity of data
• Advantages of Sample


  • Less time consuming and cheaper
  • Fewer people have to respond
  • Less data needs to be processed
• Disadvantages of Sample


  • Data may not be as accurate
  • Sample may not be large enough to give information about small subgroups of the population
• Sampling units


  Individual units of a population
• Sampling frame


  A list of named and numbered sampling units
• Random sampling


  Each member of the population has an equal chance of being selected
• Simple random sampling


  A simple random sample of size n is one where every sample of size n has an equal chance of being selected
• Simple random sampling


  • Using a calculator or random number generator to generate random numbers and select corresponding members
  • Lottery sampling by writing member names on cards and drawing 12 cards
• Advantages of simple random sampling


  • Free of bias
  • Easy and cheap for small samples and populations
  • Each sampling unit has a known and equal chance of selection
• Disadvantages of simple random sampling

  • Not suitable for large samples and populations
  • Sampling frame needed
• Quota sampling


  An interviewer or researcher selects a sample that reflects the characteristics of the whole population
• Advantages of quota sampling


  • Allows a small sample to still be representative of the population
  • No sampling frame required
  • Quick, easy and inexpensive
  • Easy comparison between different groups within a population
• Disadvantages of quota sampling


  • Non-random sampling can introduce bias
  • Population must be divided into groups, which can be costly or inaccurate
  • Increasing scope of study increases number of groups, which adds time and expenses
  • Non-responses not recorded
• Opportunity sampling or convenience sampling


  Sample is taken from people who are available at the time of study and who fits the criteria you are looking for
• Advantages of opportunity/convenience sampling


  • Easy and inexpensive
• Disadvantages of opportunity/convenience sampling


  • Unlikely to provide a representative result
  • Highly dependent on individual researcher
• Quantitative variables or quantitative data


  Variables or data associated with numerical observations
• Qualitative variables or qualitative data


  Variables associated with non-numerical observations
• Continuous variable


  A variable that can take any value in a given range
• Discrete variable


  A variable that can only take specific values
• Grouped frequency table


  The specific data values are not shown
• Class boundaries


  Show the maximum and minimum values in each group or class
• Midpoint


  The average of class boundaries
• Class width


  The difference between upper and lower class boundaries
• If you need to do calculations on large data sets in your exam, the relevant extract will be provided
• Systematic sampling


  The required elements are chosen at regular intervals from an ordered list
• Systematic sampling


  • A sample of size 20 is required from a population of 100. 100 ÷ 20 = 5 so every fifth person is chosen. The first person is chosen at random.
• Advantages of systematic sampling


  • Simple and quick to use
  • Suitable for large samples and large populations
• Disadvantages of systematic sampling

  • A sampling frame is needed
  • Bias introduced if sampling frame is not random
• Stratified sampling


  The population is divided into mutually exclusive strata and a random sample is taken from each
• Stratified sampling


  • A factory manager wants to find out about what his workers think about the factory canteen facilities. He decides to give a questionnaire to a sample of 80 workers. There are 75 workers between ages 18 and 32, 140 workers between ages 33 and 47, and 85 workers between ages 48 and 62. He can use stratified sampling to select the sample.
• Advantages of stratified sampling


  • Sample accurately reflects population structure
  • Proportional representation of group within population
• Disadvantages of stratified sampling


  • Population must be clearly classified into distinct strata
  • Same disadvantages as simple random sampling within each stratum