Sampling

All examples based on: What is the average number of hours primary school students in SG study every week?

Population

• The group that we want to draw conclusions for
• e.g. Primary school students

Population parameter

• Something you want to find out about the population
• If the sample is not biased, the sample statistic can be used to estimate the population parameter
• e.g. average number of hours studied per week

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Sample

• Subset of the population selected in the study

Estimate

• Without information from every member of the population, we can only try to get a good estimate of the population parameter
• An Estimate is an inference about the population parameter

Sampling Frame

• The list from which the sample was obtained
• To be able to generalise findings from sample to population: sampling frame $\ge$ population (Generalisability)

Sampling Method

Probability Sampling

• All units in the sampling frame have a known, non-zero chance of being selected
• Probability of selecting each unit need not be the same
• Preferred, to reduce selection bias

Types of probability sampling:

• Applicable for any population
  • Simple random sampling
    • Draw names at random without replacement
    • Every sample of size n has an equal chance of being selected
    • +ve: Good representation of population
    • -ve: Time consuming
  • Systematic sampling
    • Include every $n^{\text{th}}$ unit in the population, with a random start point
    • +ve: Simpler than simple random
    • -ve: May under-represent population
• Applicable when population comes as groups
  • Stratified random sampling
    • Divide population into groups (strata) with similar characteristics (males & females), take a random sample from each subgroup (stratum), combine these to form final sample
    • +ve: Good representation of sample by stratum
    • -ve: Criteria required for classification of population into stratum
  • Cluster sampling
    • Divide population into natural subgroups (cities in a country), take a random sample of clusters, include whole cluster in final sample
    • +ve: Less time consuming and costly
    • -ve: Requires internally heterogeneous and externally homogeneous clusters

Non-Probability Sampling

• a human decides who to sample
• human brain is not a random

Sample Size

• the larger the better, to reduce random error

Bias

• Selection bias
  • When the sample does not equally represent the population due to biased selection of units into the sample
  • Caused by using non-probability sampling (human selection causes bias)
  • e.g. surveying only students from two classes in a primary school
• Non response bias
  • Participants’ non disclosure
  • Participants’ non participation
  • Applicable for all types of sampling
  • Ensure response rate is not too low to reduce
• Bias means that conclusion is not generalisable (Generalisability)

Generalisability

• Whether conclusions from the sample can be generalised to the population
• NOT generalisable when:
  • Sampling frame does not cover entire population
  • There is bias in the sample
• To be generalisable:
  • Have a good sampling frame greater or equal to the population
  • Use probability sampling to minimise selection bias
  • Minimise non-response rate
  • Have a large sample size to reduce variability and random error in sample

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Census

• An attempt to reach out to the entire population
• Disadvantages:
  • High cost
  • Takes a long time to complete
  • Can suffer from non response bias