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Sections 2.3 – 2.6 Recap Unit Test on Tuesday, October 2, 2012

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2.3 Sampling Techniques Scenario: A sample of young adults were surveyed regarding their diets. If the sample consists of young adults, then who is the population of this study?

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Scenario: A sociology professor talks to every 9 th elementary school student walking into the local library about their reading skills. If he interviewed 34 people, what is the population size?

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A sociology professor talks to every 9 th elementary school student walking into the local library about their reading skills. If he interviewed 34 people, what is the population size? interval = pop. size / sample size Re-arrange it to get pop. size = interval x sample size = 9 x 34 = 306 elem. school students

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Was that an example of systematic sampling or stratified sampling?

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Sample Types Sample Simple random sample Systematic sample Stratified sample

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Sample Types Cluster sample – Multi-stage sample Voluntary-response sample Convenience sample

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Sample Types Cluster sample - the total population is divided into groups (or clusters) and a simple random sample of the groups is selected. Multi-stage sample Voluntary-response sample Convenience sample

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Sample Types Cluster sample - the total population is divided into groups (or clusters) and a simple random sample of the groups is selected. *My drawing on the white board was not a definition, it was only describing the textbook’s fast-food chain example. Multi-stage sample - Voluntary-response sample Convenience sample

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Sample Types Cluster sample - the total population is divided into groups (or clusters) and a simple random sample of the groups is selected. *My drawing on the white board was not a definition, it was only describing the textbook’s fast-food chain example. Multi-stage sample – several levels of random sampling Voluntary-response sample – Convenience sample

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Sample Types Cluster sample - the total population is divided into groups (or clusters) and a simple random sample of the groups is selected. *My drawing on the white board was not a definition, it was only describing the textbook’s fast-food chain example. Multi-stage sample – several levels of ran. sampling Voluntary-response sample – researcher invites any member of population into survey Convenience sample

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Sample Types Cluster sample - the total population is divided into groups (or clusters) and a simple random sample of the groups is selected. *My drawing on the white board was not a definition, it was only describing the textbook’s fast-food chain example. Multi-stage sample – several levels of ran. sampling Voluntary-response sample – researcher invites any member of population into survey Convenience sample

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Sample Types Cluster sample - the total population is divided into groups (or clusters) and a simple random sample of the groups is selected. *My drawing on the white board was not a definition, it was only describing the textbook’s fast-food chain example. Multi-stage sample – several levels of ran. sampling Voluntary-response sample – researcher invites any member of population into survey Convenience sample - sample selected but it’s easily accessible

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Question A community centre chooses 15 of its members and asks them to have each member of their families complete a short questionnaire. A) What type of sample is the community centre using?

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Question A community centre chooses 15 of its members and asks them to have each member of their families complete a short questionnaire. A) What type of sample is the community centre using? Answer: Cluster Sample

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Question A community centre chooses 15 of its members and asks them to have each member of their families complete a short questionnaire. B) Are the 15 community-centre members a random sample of the community?

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Question A community centre chooses 15 of its members and asks them to have each member of their families complete a short questionnaire. B) Are the 15 community-centre members a random sample of the community? Answer: No, not every member has an equal chance of being selected

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Question A community centre chooses 15 of its members and asks them to have each member of their families complete a short questionnaire. C) To what extent are the family members randomly chosen?

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Question A community centre chooses 15 of its members and asks them to have each member of their families complete a short questionnaire. C) To what extent are the family members randomly chosen? Answer: to the same extent as the member of the community was selected

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2.4 Bias in Surveys Sampling Bias Non-response Bias Measurement Bias Response Bias

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2.4 Bias in Surveys Sampling Bias – sample doesn’t rep. population Non-response Bias – groups under-represented in survey b/c they chose not to participate Measurement Bias – data collection method misestimates population characteristics Response Bias – false/misleading answers given because of sensitive survey questions

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Intentional bias – Unintentional bias – Leading questions – Loaded questions -

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Intentional bias – used to manipulate stats in favour of a certain point of view Unintentional bias – can be introduced if sampling and data collection methods are not chosen carefully Leading questions – can give suggested answers which causes a bias Loaded questions – contains wording or information intended to influence respondents’ answers

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Any bias below? Can the proposed record level of healthcare expenditures be justified in view of the enormous deficits facing the Canadian people and the pressing social needs that are currently unmet?

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2.5 Measure of Central Tendency What does the above mean?

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2.5 Measure of Central Tendency What does the above mean? values around which a set of data tends to cluster

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What is the difference between and ?

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refers to mean of population refers to mean of sample

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What is the difference between and ?

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Hand back quizzes & … Exercise: Calculate mean quiz mark with proper weights Knowledge/Understanding 40% Application 30% Communication 10% Thinking 20%

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Grade 10 Exam Question on Determining the Centroid

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x mean = (1+3+5)/3 = 3 y mean = (2+4+0)/3 = 2 centroid = (3, 2)

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You can calculate x mean, y mean & z mean to get centroid of 3D objects

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Grade 10 breaks down when weights are applied. Consider bottom right vertex mass = 2.2 kg top vertex mass = 5.7 kg left vertex mass = 0.2 kg Determine the center of the mass

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x mean = [1(0.2)+3(5.7)+5(2.2)] / (0.2 + 5.7 + 2.2) = 3.5 y mean = [2(0.2)+4(5.7)+0(2.2)] / (0.2 + 5.7 + 2.2) = 2.9 Grade 10 breaks down when weights are applied. Consider bottom right vertex mass = 2.2 kg top vertex mass = 5.7 kg left vertex mass = 0.2 kg Determine the center of the mass

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2.6 Measures of Spread We’ll do this tomorrow

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Review Questions Q #1, 5, 6, 7, 9, 11, 14 Page 151-152

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MATH 2311-06 Section 6.1. Sampling: Terms: Population – each element (or person) from the set of observations that can be made Sample – a subset of the.

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