How does a sample in statistics represent a population given
certain parameters? How do I demonstrate sampling procedures and
use those to make conclusions about a population?
How do I understand statistics as a process for making
inferences about population parameters based on a random sample
from that population? How do I recognize the purposes of and
difference among statistical data gathering methods? Introduction
to StatisticsWhat is/are statistics? Statistics is a way of
reasoning, along with a collection of tools and methods, designed
to help us understand the world.
Statistics are particular calculations made from dataPopulation
data is used when you are gathering data from every individual of
interest. Ex: Asking the entire football team a questionSample data
is used when you are gathering data from some of the individuals of
interest.Ex: Asking only the offensive line a question and apply it
to the entire football teamPopulation Data or Sample
Data?Population Data or Sample Data?The US Government takes a
census of its citizens every 10 years to gather information.
PopulationSample[Default][MC Any][MC All]
Population Data or Sample Data?
You want to know what sports teens prefer so you send out a
survey to all the students in your high school.
PopulationSample[Default][MC Any][MC All]
Population Data or Sample Data?Population DataSample
Data[Default][MC Any][MC All]You want to know what sports teens
prefer so you send out a survey to all the students in your high
school.
You want data on the shoe size of all Parkland students, so you
interview every student at school.PopulationSample[Default][MC
Any][MC All]Population Data or Sample Data?
You want to know how long people in Winston-Salem visited the
beach last summer, so you polled 50 random people at the Dixie
Classic Fair.PopulationSample[Default][MC Any][MC All]Population
Data or Sample Data?
You want to know the average GPA of a Parkland student, so you
ask all of the students in all of your classes.
PopulationSample[Default][MC Any][MC All]Population Data or Sample
Data?
Parameter vs. StatisticA statistic is a descriptive measure
computed from a sample of data.
A parameter is a descriptive measure computed from an entire
population of data.
Inferential statistics enables you to make an educated guess
about a population parameter based on a statistic computed from a
sample randomly drawn from that population.Parameter or
statistic?You want to know the mean income of the people who
subscribe to People magazine, so you question 100 subscribers.
ParameterStatistic[Default][MC Any][MC All]
Parameter or statistic?You want to know the average height of
the students in this math class, so you have everyone in the class
write their height on a sheet of paper. ParameterStatistic
[Default][MC Any][MC All]
Activity:A committee on community relations in a college town
plans to survey local businesses about the importance of students
as customers. From telephone book listings, the committee chooses
150 businesses at random. Of these, 73 return the questionnaire
mailed by the committee. What is the population for this sample
survey? What is the sample? Ways to Gather Data Survey a
questionnaire used to collect interesting data on a certain topic
from a sample of people.
EX: You want to find out how many students in your class had a
summer job.
EX: The government wants to determine average household income
in the United States.
EX: You want to know if tattoos have an influence on a persons
GPA.
Ways to Gather Data Obervational Study we observe individuals
and measure variables of interest but do not attempt to influence
the responses. Observational Studies may show a correlation between
variables, but cannot always guarantee causation.EX: A study of
child care enrolled 1364 infants in 1991 and planned to follow them
through their sixth year in school. In 2003, the researchers
published an article finding that the more time children spent in
child care from birth to age four-and-a-half, the more adults
tended to rate them, both at age four-and-a-half and at
kindergarten, as less likely to get along with others, as more
assertive, as disobedient, and as aggressive. Ways to Gather
DataExperiment we deliberately impose some treatment on (that is,
do something to) individuals in order to observe their responses.
Experiments can carry more convincing evidence of a cause and
effect relationship.
EX: Take the Pepsi Challenge in the 80s Pepsi had a huge
marketing scheme that had people do a blind taste test to see which
soda they preferred Pepsi or Coke.
EX: Does Vitamin C reduce the causes of getting a common
cold?
Which method would you choose?
You want to know the average GPA of a football player at school
this year.
SurveyObservational StudyExperiment
[Default][MC Any][MC All]Which method was used?
The Gallop Poll questions a sample of about 1500 adult U.S.
residents to determine national opinion on a variety of issues.
SurveyObservational StudyExperiment[Default][MC Any][MC
All]Which method would you choose?
Does working with computers improve student performance in
school?
SurveyObservational StudyExperiment[Default][MC Any][MC All]
Which method is used?
A kindergartener is given the option to eat a marshmallow
immediately or if they can wait 5 minutes they can have 2
marshmallows. Years later, the response of the kindergartener was
used to determine if delaying gratification can have an effect on
SAT scores .
SurveyObservational StudyExperiment[Default][MC Any][MC All]
Which method is used?
Medical records were used to determine if there is a correlation
between inducing labor and autism in children. SurveyObservational
StudyExperiment[Default][MC Any][MC All]SamplingWhen conducting a
survey, experiment, or observational study, it is almost impossible
to survey everyone in a population so people use various sampling
methods to gather information.One major concern about sampling
methods is whether it is a biased or unbiased method to gather
information. Sampling MethodsRandom sampling: when everyone in a
population has an equal chance of being chosen in the
experiment.Stratified sampling: when the population is first
divided into similar categories and the number of members in each
category is determined. Systematic sampling: when you determine a
method for which to choose members of the population (assign
numbers to the population and then choose every 5th person to
participate)Cluster sampling: when you randomly put the population
into clusters and then choose a cluster randomly and then randomly
choose people in that cluster to participate. Random sampling: when
everyone in a population has an equal chance of being chosen in the
experiment.Randomly selecting 10 from all 50 animalsStratified
sampling: when the population is first divided into similar
categories and the number of members in each category is
determined. Select 5 from 25 dogs, 3 from 15 cats and 2 from the
rabbitsSystematic sampling: when you determine a method for which
to choose members of the population (assign numbers to the
population and then choose every 5th person to participate) Give
every animal a random number and then choose every 5th
numberCluster sampling: when you randomly put the population into
clusters and then choose a cluster randomly and then randomly
choose people in that cluster to participate. Randomly put the
animals into 2 groups of 25, choose a group, and then choose 10
from that selected group.Example if selecting 10 animals from 25
dogs, 15 cats, and 10 rabbitsWhich sampling method is used in the
scenario below? RandomStratifiedSystematicCluster[Default][MC
Any][MC All]A Gallop poll surveyed 1,018 adults by telephone in
each region of the country, and 22% of them reported that they
smoked cigarettes within the past week.
Which sampling method is used in the scenario below?
RandomStratifiedSystematicCluster[Default][MC Any][MC All]A
principal goes to one classroom in each department and chooses two
students from each classes to participate in a school climate
survey.
Which sampling method is used in the scenario below?
RandomStratifiedSystematicCluster[Default][MC Any][MC All]WSFCS
sends out a survey to parents by generating a list of student
numbers from PowerSchool.
Biased QuestionsSome questions may use language that people can
associate with emotions:How much of your time do you waste on
facebook?Some questions may refer to a majority or supposed
authority:Would you agree with the NCAE that teachers should be
paid more for earning their masters degree?Phrased awkwardly: Do
you disagree with people who oppose the ban on smoking in public
places?Sampling BiasSampling Bias occurs when one or more sub
groups of a population are either over represented or under
represented when conducting a survey or experiment. Using the
appropriate sampling method for the question reduces bias. Discuss
with your partner some examples of bias that could occur when
choosing a sample from a population. Be prepared to share your
examples. Biased or Unbiased be prepared to defend your
response.Biased Unbiased[Default][MC Any][MC All]A person asks, Do
you prefer delicious pancakes or cold soggy cereal?Biased or
Unbiased be prepared to defend your response.Biased
Unbiased[Default][MC Any][MC All]Asking people shopping at a
farmers market if they think locally grown fruit and vegetables are
healthier than supermarket fruits and vegetables.Biased or Unbiased
be prepared to defend your response.Biased Unbiased[Default][MC
Any][MC All]A survey about whether or not teachers who earn their
masters degrees should be paid more is sent out to all teachers in
NC.Activity: Martha wants to construct a survey that shows which
sports students at her school like to play the most.
List the goal of the survey.What population sample should she
interview?How should she administer the survey?Create a data
collection sheet that she can use to record her results. What is
needed to determine causation for the populationRandom SelectionNo
Random SelectionRandom AssignmentCausalityPopulationCausalityOnly
to sample No Random AssignmentNo causalityPopulationNo causalityNo
results!Resources used: "Next: Introduction to Data and Measurement
Issues Surveys and Samples." CK-12 Foundation. N.p., n.d. Web. 21
Aug. 2013.Yates, Daniel S., David S. Moore, and Daren S. Starnes.
The Practice of Statistics: TI-83/84/89 Graphing Calculator
Enhanced. New York: W.H. Freeman, 2008. Print.Greg Fisher Mount
Tabor High School Christina Holst Parkland High School Wendy
Bartlett Parkland High School