MDM 4U1 – Analysis of Class Database Survey: Types of Data, Sampling and Assessing Bias
1) Consider the survey we have at hand. It was designed to harvest a plethora of measurements to better understand the metrics of High School Students in Ontario in general.
a) Consider the technique used to sample the members of our class. Again, if the population we
were intending to study was all Ontario high school students … then what type of sampling technique did use? Justify your Answer. (2)
b) Let’s say you now want to use this survey (as is) to sample High School students in Ontario.
You perform a Multi-stage sample and wind up choosing Loyola as a site for sampling.
You contact the school administration and receive the following information to help you
determine any and all of the amount of each “type” of student you intend to select:
M:F Ratio = 44:56 Average age: 15.7 yrs
Median Age: 15.5 yrs
# Grade 9’s 271
# Grade 10’s 328 You can estimate any other demographic you
# Grade 11’s 220 like and use this in your sampling technique
# Grade 12’s 138
PIP students 18
Note: You will have access to any and all information and equipment necessary to do this sampling
(provided it can be found at the school). Funding for supplies and a staff of two volunteers will be
provided for you.
i. Devise a sampling strategy that combines both systematic and stratified sampling
techniques. Explain this strategy in detail. (2)
ii. Devise a sampling strategy that is both random and systematic. Explain your strategy in
detail (2)
iii. A colleague of yours tells you that they would not use any of the above strategies.
Instead they suggest the following:
1. Stratify the population as follows:
Grade Total # of classes Classes Sampled
9 11 5
10 14 5
11 8 5
12 6 5
PIP 2 1
2. Randomly choose the required number of classes by drawing their teacher’s
names ‘out of a hat’.
3. Sample the entire class.
4. Have the teachers sort the survey’s alphabetically.
5. Choose every other survey and those remaining surveys become your sample.
Explain two problems that exist with this strategy and then describe how you could use
their framework to effectively perform a random, stratified, and systematic sample. (4)
2) Before we implement our study we must consider the quality of our survey.
a) We have gathered many different types of data and as such may need to treat each differently.
ON YOUR SURVEY indicate which of the data is Categorical (C), Discrete (D) or Continuous (I).
Place these labels to the left of the question number at the beginning of each statement in
the survey. (3)
b) There is some question as to whether or not the response(s) to question #37 constitutes a
discrete or a continuous variable. Choose which one is appropriate and defend your position
VIGOROUSLY!!! (3)
c) Many of these questions can solicit incorrectly measurements when the survey is administered
to uninformed students. Outline the flaws in question #1, #4, #34. Without throwing the
question out of the survey, repair each question to ensure it generates an effective
measurement. (4)
3) There are many sources of error that would act to introduce bias in our information gathering
process. We should look to our survey to ensure we eliminate these ahead of time and ensure we
measure the true patterns that exist in our population.
a) Indicate at least three instances where measurement bias will occur in the gathering of the data
fro this survey. Address leading and loaded questions in the selection of these instances (you
should have one example of each). Explain your reasoning for these choices and either fix them
or suggest how one would go about doing so. (8)
b) Use question 16 – 18 to explain the concept of response bias. (2) THEN, outline two other
questions that would elicit this type of bias and correct for this bias by providing adequate
editing, conditions, and/or controls to ensure the responses to said questions have a decreased
propensity for response bias. (4)
c) Outline strategies that you could reasonably and legally implement to remove the likelihood of
non-response bias (and explain how they would be effective in lessening this problem!). A
minimum of two ideas (with explanations!) is suggested. (4)
Note – You can be creative and you can use any control that an administrator or teacher has at
their disposal. However, you must consider the rights and responsibilities these people have to
students, parents, to the school board, and to their professional/ethical governing institutions!
