Introduction to Statistics

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 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 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

Population Data or Sample Data?

Population Data or Sample Data?The US Government takes a census of its citizens every 10 years to gather information.

A. PopulationB. Sample


You want to know what sports teens prefer so you send out a survey to all the students in your high school.


A. Population DataB. Sample DataA. [Default]

B. [MC Any]C. [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.



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.



You want to know the average GPA of a Parkland student, so you ask all of the students in all of your classes.



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.

Parameter or statistic?You want to know the mean income of the people who subscribe to People magazine, so you question 100 subscribers.

A. ParameterB. Statistic

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.

A. ParameterB. Statistic

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 person’s 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 Data• 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?

You want to know the average GPA of a football player at school this year.

A. SurveyB. Observational StudyC. Experiment

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.


Which method would you choose?

Does working with computers improve student performance in school?


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 .


Which method is used?

Medical records were used to determine if there is a correlation between inducing labor and autism in children.


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• Random 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 animals

• Stratified 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 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 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 rabbits

Which sampling method is used in the scenario below?

A. RandomB. StratifiedC. SystematicD. Cluster

[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.




A principal goes to one classroom in each department and chooses two students from each classes to participate in a school climate survey.




WSFCS sends out a survey to parents by generating a list of student numbers from PowerSchool.

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 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.

A. Biased B. Unbiased

A person asks, “Do you prefer delicious pancakes or cold soggy cereal?



Asking people shopping at a farmer’s market if they think locally grown fruit and vegetables are healthier than supermarket fruits and vegetables.



A survey about whether or not teachers who earn their master’s 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 population

Random Selection

No Random Selection

Random Assignment

CausalityPopulation

CausalityOnly to sample

No Random Assignment

No causalityPopulation

No 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

Introduction to Statistics

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