Behave how you know perfectly well you are expected to.
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Transcript of Behave how you know perfectly well you are expected to.
Behave how you know perfectly well you are expected to.
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Collecting Samples
Chapter 2.3 – In Search of Good DataMathematics of Data Management (Nelson)MDM 4U
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
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
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 isn’t, this is due to chance example: put entire population’s names in a
hat and draw them
Systematic Random Sampling you decide to sample a fixed percent of the
population using some random starting point 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 800 people. Generate a random number between 1 and 10, start at this number and sample each 10th person (n = 800 / 80 = 10)
Stratified Random Sampling
the population is divided into groups called strata (which could be MSIPs 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 CPHS students by MSIP, with samples randomly drawn from each MSIP (the number drawn is determined by the size of the MSIP)
Cluster Random Sampling
the population is ordered in terms of groups (like MSIPs 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
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 MSIPs, and then randomly choose students from within these MSIPs
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)
Example: do students at CPHS want a longer lunch? Simple Random Sampling
have a computer generate 200 names and interview each
Systematic Random Sampling sampling interval = 800 / 200 = 4 generate a random number from 1-4 start with that number on the list and interview
each 4th person after that
Example: do students at CPHS want a longer 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 200 grade 10’s we would need to interview 50 of these
20050
800 200
xx
Example: do students at CPHS want a shorter lunch? Cluster Random Sampling
randomly choose enough MSIPs to sample 200 students
say there are 25 per MSIP, we would need 8 MSIPs (8 x 25 = 200)
interview each student in each of these rooms
Example: do students at CPHS want a shorter lunch? Multi Stage Random Sampling
group students by MSIP randomly choose 20 MSIPs randomly choose 10 students from each MSIP interview each of these students
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
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
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
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?)
Exercises
try page 99 #1,5,6,10,11 for 6b, see example 1 on page 95
Creating Questions
Chapter 2.4 – In Search of Good DataMathematics of Data Management (Nelson)MDM 4U
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 lead to bad data good questions may create good data
Question Styles
Open Questions respondents answer in own words gives a wide variety of answers may be difficult to interpret 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
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
Types of Survey Questions
Information ex: circle the correct response Gender M F
Checklist ex: Subjects currently being taken (check all that
apply):□ Math
□ Computer Science
□ Music
Types of Survey Questions
Ranking Questions ex: rank the following in order of importance (1 =
most important, 3 = least important) __ Health Care __ Security __ Tax Relief
Rating Questions ex: How would you rate your teacher?
□ Great □ Fabulous □ Incredible □ Outstanding
Questions should…
Be simple, relevant, specific, readable Be written without jargon/slang,
abbreviations, acronyms, etc. Not lead the respondents Allow for all possible responses on closed Qs Be sensitive to the respondents Not be open to interpretation Be as brief as possible
Exercises
try page 105 #1, 2 abc, 4, 5, 8, 9, 12
References
Wikipedia (2004). Online Encyclopedia. Retrieved September 1, 2004 from http://en.wikipedia.org/wiki/Main_Page