Collecting Samples

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Collecting Samples

• Chapter 2.3 In Search of Good Data
• Mathematics of Data Management (Nelson)
• MDM 4U
• Author Gary Greer (ideas from K. Myers)

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Why Sampling?

• sampling is done because a census is too
  expensive or time consuming
• the difficulty is being confident that the sample
  represents the population accurately
• convenience sampling occurs when you simply take
  data from the most convenient place (for example
  collecting data by walking around the hallways at
  school)
• convenience sampling is not representative

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Random Sampling

• representative sampling almost always uses random
  samples
• random numbers are described as numbers that
  occur without pattern
• random events are events that are considered to
  occur by chance
• random numbers can be generated using a
  calculator, computer or random number table
• random choice is used as a method of selecting
  members of a population without introducing bias

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Simple Random Sampling

• this sample requires that all selections be
  equally likely and that all combinations of
  selections be equally likely
• the sample is likely to be representative of the
  population
• but if it isnt, this is due to chance
• example put entire populations names in a hat
  and draw them

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Systematic Random Sampling

• you decide to sample a fixed percent of the
  population using some random starting point is
  chosen and you select every nth individual
• n in this case is determined by calculating the
  sampling interval (population size divided by
  sample size)
• example you decide to sample 10 of 1000 people.
  Generate a random number between 1 and 10, start
  at this number and sample each 10th person

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Stratified Random Sampling

• the population is divided into groups called
  strata (which could be homerooms or grades)
• a simple random sample is taken of each of these
  with the size of the sample determined by the
  size of the strata
• example sample grade 12s by homerooms, with
  samples randomly drawn from each homeroom (the
  number drawn is determined by the size of the
  homeroom)

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Cluster Random Sampling

• the population is ordered in terms of groups
  (like homerooms or schools)
• groups are randomly chosen for sampling and then
  all members of the chosen groups are surveyed
• example student attitudes could be measured by
  randomly choosing schools from across Ontario,
  and then all students in these schools are
  surveyed

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Multistage Random Sampling

• groups are randomly chosen from a population and
  then individuals in these groups are then
  randomly chosen to be surveyed
• example to understand student attitudes a school
  might randomly choose homerooms, and then
  randomly choose students from within these
  homerooms

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Destructive Sampling

• sometimes the act of sampling will restrict the
  ability of a surveyor to return the element to
  the population
• example cars used in crash tests cannot be used
  again for the same purpose
• example individuals may acquire learning during
  sampling that would introduce bias if they were
  used again (like taking a test twice)

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Example do students at NDSS want a shorter lunch?

• Simple Random Sampling
• have a computer generate 350 names and interview
  each
• Systematic Random Sampling
• sampling interval 1400/350 4
• generate a random number from 1-4
• start with that number on the list and interview
  each 4th person after that

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Example do students at NDSS want a shorter lunch?

• Stratified Random Sampling
• group students by grade and have a computer
  generate a random group of names from each grade
  to interview
• the number of students interviewed from each
  grade is not equal, rather it is proportional to
  the size of the group
• if there were 320 grade 10s we would need to
  interview 80 of these

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Example do students at NDSS want a shorter lunch?

• Cluster Random Sampling
• randomly choose enough homerooms to sample 350
  students
• say there are 20 per homeroom, we would need 18
  home rooms (18 x 20 360)
• interview each student in each of these rooms

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Example do students at NDSS want a shorter lunch?

• Multi Stage Random Sampling
• group students by homeroom
• randomly choose 35 homerooms
• randomly choose 10 students from each room
• interview each of these students

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Sample Size

• the size of the sample will have an effect on the
  reliability of the results
• the larger the better
• factors
• variability in the population (the more
  variation, the larger the sample required to
  capture that variation)
• degree of precision required for the survey
• the sampling method chosen

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Techniques for Experimental Studies

• Experimental studies are different from studies
  where a population is sampled as it exists
• in experimental studies some treatment is applied
  to some part of the population
• however, the effect of the treatment can only be
  known in comparison to some part of the
  population that has not received the treatment

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Vocabulary

• treatment group
• the part of the experimental group that receives
  the treatment
• control group
• the part of the experimental group that does not
  receive the treatment

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Vocabulary

• placebo
• a treatment that has no value given to the
  control group to reduce bias in the experiment
• no one knows whether they are receiving the
  treatment or not (why?)
• double-blind test
• in this case, neither the subjects or the
  researchers doing the testing know who has
  received the treatment (why?)

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Exercises

• try page 99 1,5,6,10,11
• for 6b, see example 1 on page 95

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Creating Questions

• Chapter 2.4 In Search of Good Data
• Mathematics of Data Management (Nelson)
• MDM 4U
• Author Gary Greer (with ideas from K. Myers)

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Surveys

• these are commonly used in data collection
• can be conducted by interview, mail-in,
  telephone, internet
• they are a series of carefully designed questions
• bad questions create bad data
• good questions may create good data

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Question Styles

• Open Questions
• respondents answer in own words
• gives a wide variety of answers
• may be difficult to interpret
• does offer the possibility of gaining data you
  did not know existed
• sometimes used in preliminary collection of
  information, to gain a sense of what is going on
  and possibly define the categories of data you
  will end up studying

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Question Styles

• Closed Questions
• questions that require the respondent to select
  from pre-defined categories of responses
• options may be easily analyzed
• options present may bias the result
• options may not represent the population and
  researcher may miss what is going on
• sometimes used after an initial open ended survey
  as the researcher has already identified data
  categories

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Types of Survey Questions

• Information
• ex circle the correct response
• Sex F M
• Checklist
• ex check all of the following that apply
• Teacher Smart ? Wise ? Good Looking ?

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Types of Survey Questions

• Ranking Questions
• ex rank the following in order of importance
• ? Health Care ? Security ? Tax Relief
• Rating Questions
• ex How would you rate your teacher?
• ? Great ? Fabulous ? Incredible ? Outstanding

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Questions should be

• simple, relevant, specific, readable
• written without jargon, abbreviations, etc.
• should not lead the respondents
• sensitive to the respondents
• not be open to interpretation
• as brief as possible

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Exercises

• try page 105 1, 2 abc, 4, 5, 8, 9, 12
• try some review questions from Chapter 1
• page 71 2-9

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References

• Wikipedia (2004). Online Encyclopedia. Retrieved
  September 1, 2004 from http//en.wikipedia.org/wik
  i/Main_Page