Statistical Sampling SP 2015

Journal Prompt:Describe 5 things that might be wrong with Catbert’s claims

•When the next slide is shown

•Pick a number from those displayed

•Write it down on your journal page

1 2 3 4

•How many students in this class selected each number?

•What percentage selected each number?

How did your class compare?

Typically about:75% will choose 320% will choose 2 or 45% will choose 1

 The study of numerical data

(information) 

Statistics

A sample is a collection of data from some fraction of a population.

It allows us to learn about the entire population by studying a relatively small portion of the population.

Sample

A census is when every individual in the population is measured.

Not difficult if your population is Mrs. Otap’s 4th Block.

Imagine your population is all household in South Carolina.

What would happen by the them you collected data from the entire population?

(does the wording matter or did that last one make sense?) Would there be some households that could be

easily missed?

Census

Suppose you are interested in knowing the mean height for everyone in your school. ◦ What would a census tell you?

◦ How close would a sample size of one less student that the population be to the mean of the population?

◦ What about ten less students?

◦ If you took a sample of 100 and another sample of 10, which mean would be closer to the population?

Census vs. Sample

In general, a larger sample size will result in a more accurate estimate of the population.

When the population is very large, larger samples will not produce significantly better results and are usually more expensive or difficult to obtain.

A balance is usually made, not too small to sacrifice accuracy, and not too large to sacrifice cost.

For very large populations a sample size in the hundreds is normally sufficient.

Census vs. Sample

Making sure that a sample is truly random means that the person taking the sample has no control over who is selected.

When a sample is not random a bias could appear. This means that some individuals are somehow favored over others in the population.

Random

Each individual has an equal chance of being

selected

Example: High School Students Step 1: Write each student’s name on a slip

of paper Step 2: Mix the papers up in a box Step 3: Draw names/slips from the box

(Is this feasible for Wando? Other ideas?)

Simple Random Sampling (SRS)

Describe a method that would ensure your sample of 5 students from this class will be a simple random sample. Compare and discuss your method with others in the class.

Simple Random Sample

Random Numbers are a primary tool in selecting SRS.

You can get random numbers from your TI-84 calculator.

Books of random numbers have been published. Page 834

Websites exist which provide truly random numbers. http://www.random.org/

Simple Random Sample

Select random groups and interview every member of the selected groups

Example: High School Students Step 1: Randomly select classes Step 2: Interview every student in the

selected classes

Cluster Sampling

An appropriate rule or pattern is used to make

selectionsExample: Step 1: Sort students alphabetically by last

name, first name. Step 2: Select every 8th name on the list

Systematic Sampling

Population is divided into subpopulations or strata and a random

sample taken from each subgroupExample: High School Students Step 1: divide students by grade level Step 2: use an appropriate method to take a

random sample from each subgroup

Stratified Random Sample

Easy Example: Survey your friends

Convenience Sample

Def: Bias from people choosing if they participate

Example: Lunch Room ask each person if they want to take a quick survey

Voluntary Response Bias

Def: Bias resulting from a large number not responding

Ex: Chose 1234, only half the students gave answer

Nonresponse Bias

Def: Anything in a survey design that influences responses

Example: Raise your hand if you are failing this class

Do you want this ugly yellow or this pretty blue for our shirts?

Response Bias

Some part of population is under represented

Example: Lack of lower income individuals vote in presidential election

Undercoverage

1. Determinea) What information you need to gatherb) What size sample you want to usec) How you will collect the information

2. Create the Surveya) Brainstorm questionsb) Read through proposed questions and fine tune the wordingc) Put the questions in the order you want them to be on the surveyd) Review the survey and determine if questions should be removed

or addede) Construct your final list of survey questions

3. Identify the Sample to be Used4. Collect the data5. Organize data (table/chart)6. Analyze data & draw conclusions 

Statistical Study Steps - Survey

 1) As LARGE as possible, A study with 100 people is going to be a more authentic study than a

study with 10 people.

 2) REPRESENTATIVE of the larger population you are studying

If your study is favorite singer among 7th graders, only survey 7th graders! Don't ask 8th graders, your parents, baby cousins, etc.

 3) RANDOMLY selectedIf your study is favorite sports team, don't ask only Yankees fans.

4) UNBIASED (fair)

Valid SampleIn order to have the best sample possible, you want your sample to be...

CW 1 – 3 What type of sampling is described?

Question 1 – Do you like this ugly yellow shirt, or is blue a color for our T-shirt?

Question 2 – Which color do you prefer for our t-shirt? Yellow or blue? 

CW 4) The 12th graders at WHS are trying to decide what color their 12th grade T-shirts should be. Which question would be the better question to ask to get a valid sample? Explain your answer.

Plan 1 – Go to the supermarket and ask 50 people.

Plan 2 – Go to Hunter Mountain Ski Resort and ask 50 people.

CW 5) You want to conduct a study to determine the most popular sport at the Winter Olympics. Which plan would make for a more valid sample? Explain your answer.

CW 6) You want to conduct a study to determine the average student height at OMS. Determine if the potential sample is unbiased/fair or biased/unfair, explain your reasoning.

 Sample

Unbiased Biased

  Fair Unfair

a) Every 3rd student entering school on Monday.

b) The basketball team

c) The entire 8th grade class

d) Every 10th person selected from an alphabetical list of all students

e) All girls at OMS

f) The 1st three students who report to the nurse on Monday

CW 7) Do you want more pep rallies for sporting events?Determine whether or not the following locations would be good placesto collect data fromyour sample. Would a sample from each location beunbiased/fair orbiased/unfair? Explain

 Sample

Un-biased Biased

  Fair Unfair

a) The gym, after a game

b) The libraryc) The lunchroom

d) The cheerleaders’ meeting

e) The next meeting of the prom committee

f) An advisory class chosen at random