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Grade 9:  The Learning Equation Math

41.06 Sampling and Collecting Data

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Data Analysis

Refresher pp 104-5

 

 

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Prerequisite Skills:

 

Key Terms                 

sample, population , bias, proportional, cluster, extrapolate, cluster sampling, self selective sampling, systematic sampling, simple random sampling, stratified random sampling, convenience sampling

 

Interactive Component Under Construction

 

 

Learning Outcomes:

The student will:

Biases Affecting Information Processing

Sampling  

population - eligible people for a data collection investigation

sample - part of a population selected so as to give information about the population as a whole

biased sample - sample is not representative of the population from which it is taken because the method used to collect the data contains unwanted influence(s).

unbiased sample - sample is representative of the population from which it is taken

 Biased Samples

Unbiased Samples

convenience sampling - an easily accessible group of people is chosen, and everyone in that group is surveyed.

For example, the Pizzatime owners might survey all of the people who go to a nearby grocery store  from 5PM to 6PM on September 6th.

Advantages

  • easy to organize
  • quick

Disadvantages

  • there is no guarantee that
    the behaviors of these people represent behaviors of other groups.
systematic sampling - every nth member of the population is sampled.  The list being sampled may be ordered (alphabetical, seniority, street number, etc).

Question : Is it equivalent to simple random sampling? Strictly speaking the answer is No!, unless the list itself is in random order, which it never is (alphabetical, seniority, street number, etc).

Advantages

  • easier to draw, without mistakes (cards in file)
  • more precise than simple random sampling as more evenly spread over population

Disadvantages

  • if list has periodic arrangement then sample collected may not be an accurate representation of the entire population
self-selective sampling - a population provides information by volunteering their opinions.

Advantages

  • easy to organize

Disadvantages

  • there is no guarantee that
    the behaviors of these people represent behaviors of other groups.
simple random sampling - the sample is chosen randomly from the population.   Here each sample of size n from the population of size N has an equal chance of selection. In practice "each unit in the population is numbered 1 to N and n units are randomly drawn from the N''.

Advantages
  • simple to apply
  • analysis of data is reasonably easy and has a sound mathematical basis

Disadvantages

  • if population heterogeneous estimates have large variance
cluster sampling - a particular segment of the population is sampled using existing lists (Constituencies, Wards, Households, ...).

Advantages

  • reduced field costs
  • applicable where no complete list of units is available (special lists only need be formed for clusters).

Disadvantages

  • clusters may not be representative of whole population but may be too alike
  • analysis more complicated than for simple random sampling.
stratified random sampling - the population is divided into groups (strata) and the data is collected from the strata by simple random sampling.

Advantages
  • If data of known precision is wanted for certain subdivisions of the population, then each  subdivision or strata can be
    treated as a population.
  • Administrative convenience may dictate its use, so that each field office can supervise one strata.
  • Sampling problems may differ markedly within a population (e.g. people in prisons and people outside).
  • Stratification will almost certainly produce a gain in precision in the estimates of the whole population, because a heterogeneous population is split into fairly homogeneous strata.

Disadvantages

  • problems if strata not clearly defined.
  • analysis is (or can be) quite complicated.

 

Review:

Enrichment:

 

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