Unit 8: Introduction to Statistics
What 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 data
Population Data or Sample Data?
• Population data is used when you are
gathering data from every individual of
interest.
• Ex: Asking the entire football team a question
• Sample 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 team
Identify Population Data or Sample Data?
1) The US Government takes a census of its citizens
every 10 years to gather information.
A. Population
B. Sample
2) You want to know what sports teens prefer so you
send out a survey to all the students in your high
school.
A. Population
B. Sample
3) You want data on the shoe size of all West
students, so you interview every student at school.
A. Population
B. Sample
4) You want to know how long people in WinstonSalem visited the beach last summer, so you polled
50 random people at the Dixie Classic Fair.
A. Population
B. Sample
5) You want to know the average GPA of a student,
so you ask all of the students in all of your classes.
A. Population
B. Sample
Parameter vs. Statistic
• A 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.
Identify as Parameter or Statistic?
1) You want to know the mean income of the
people who subscribe to People magazine, so
you question 100 subscribers.
A. Parameter
B. Statistic
2) 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.
A. Parameter
B. Statistic
What the Process Looks Like
START
1.
2.
POPULATION
SAMPLE
3.
5.
4.
POPULATION
PARAMETERS
SAMPLE
STATISTICS
The Process of Statistical Study
Ways to Gather Data
#1: 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
person’s GPA.
#2: OBSERVATIONAL 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.”
#3: (Controlled) Experiment – 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 80’s 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?
1) You want to know the average GPA of a football
player at school this year.
A. Survey B. Observational Study C. Experiment
2) The Gallop Poll questions a sample of about 1500
adult U.S. residents to determine national opinion
on a variety of issues.
A. Survey B. Observational Study C. Experiment
3) Does working with computers improve student
performance in school?
A. Survey
B. Observational Study
C. Experiment
4) 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 .
A. Survey
B. Observational Study
C. Experiment
5) Medical records were used to determine if there
is a correlation between inducing labor and autism
in children.
A. Survey B. Observational Study C. Experiment
SAMPLING
• When 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 Methods
Example if selecting 10 animals from 25 dogs, 15 cats, and 10 rabbits
• SIMPLE RANDOM sampling: when everyone in a
population has an equal chance of being chosen in
the experiment.
Randomly selecting 10 from all 50 animals
• STRATIFIED sampling: when the population is first
divided into similar categories (stratas) and the
number of members in each category is
determined.
Select 5 from 25 dogs, 3 from 15 cats and 2 from the
rabbits
Example if selecting 10 animals from 25 dogs, 15 cats, and 10 rabbits
• 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)
Give every animal a random number and then choose
every 5th number
• CLUSTER sampling: when you randomly put the
population into clusters (groups) 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.
Which sampling method is used in the
scenario below?
1) A Gallop poll surveyed 1,018 adults by telephone in 2 of
the 6 regions of the country, and 22% of them reported that
they smoked cigarettes within the past week.
A. Simple Random
C. Systematic
B. Stratified
D. Cluster
2) A principal goes to one classroom in each department and
chooses two students from each classes to participate in a
school climate survey.
A. Simple Random
C. Systematic
B. Stratified
D. Cluster
3) WSFCS sends out a survey to parents by generating a list
of student numbers from PowerSchool.
A. Simple Random
C. Systematic
Cluster
v.
Clusters, Groups, Stratas
B. Stratified
D. Cluster
Stratified
Data
Random Sample Population
***NON-RANDOM Sampling Methods:
1. Volunteer
2. Convenience
Biased Questions
• Some 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 master’s degree?
• Phrased awkwardly:
– Do you disagree with people who oppose the ban on
smoking in public places?
Sampling Bias
• Sampling Bias occurs when one or more
subgroups 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.
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: TI83/84/89 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
– Jeffrey Williams – West Forsyth High School