JV Stats #5Surveys and Experiments

Sampling Design

Good sampling must be done randomly

You cannot choose the people to sample

Small samples are not good

Samples should not be larger than 10% of the population

Poor sampling leads to Bias.

Good Sampling Methods

Simple Random Sample(SRS) – every combination of size n has the same chance of being picked. Best method is putting all names of the population in a hat and draw out the desired amount randomly.

Stratified Sample – place people in similar groups called strata then do an SRS of that group. Example. Split up people in California by their area codes then choose an SRS 50 people from each area code.

Cluster Sample – divide people into clusters or groups then sample everyone in that group.

Systematic Sample – choose every kth person that enters or leaves a certain area

Bad Sampling

Convenience Sampling – choosing samples that are easiest to use. Example. Friends, coworkers, people in your class, etc.

Voluntary Sampling – Using volunteers to be your sample. People with strong opinions will usually volunteer and most likely will lead to bias.

Telephone Sampling – only uses people with landline phones or people willing to be surveyed. Leads to undercoverage bias.

Judgement Sampling – when you choose who you think is best to be sampled. Definitely biased.

Be aware of “Poorly Worded Questions” in surveys – lead to response bias

A medical laboratory technician counts the # of white blood cells in a drop of a patients blood.

Identify the population, sample, and variable.

Population: all the patients blood

Sample: drop of blood

Variable: # of white blood cells.

Survey Practice

Let’s say that there are 1,823 students at Rancho.

What would be the maximum sample size we should take?

1. Give an example of how to take an SRS.

2. Give an example of how to use a stratified sample.

3. Give an example of how to use a cluster sample.

4. Give an example of how to use a systematic sample.

Rancho Stadium

Mr. Pines has designed a new football stadium to be built on campus this summer. As you can see it has seating for thousands including luxury suites. The stadium also includes bleacher seating for those “Old School” fans who like the feel of cold hard aluminum underneath them.

Design a Survey

On the opening night of the stadium Mr. Pines would like to distribute a survey to some of the people that came to watch the game.

Since Rancho spent all their money on the stadium they can only afford to survey 300 people.

Your job is to design this survey.

Design a Survey

Use proper sampling techniques.

Be detailed.

I do not want to know your survey question.

I want to know who you will give the survey to, how you will give it to them.

Try to avoid bias

Keep in mind that all peoples opinions matter in a survey.

Be creative

Each group will present their survey to the class today.

Random Digit Table

Use line 105 from the random digit table to select 5 of the people below. Make sure to assign your digits.

Erik Tammi Gracie Julie Matt Landry Tim Buddy

Lyla Tyra Jason Billy Luke J.D. Mac Mindy

Brian Vince Jess Becky Joe Wade Santiago Pam

D.A.R.E

D: Determine the number of digits you will take at a time

A: Assign digits

R: Repeats? What will you do with them?

E: Ending rule. When do you stop?

D: We will take 2 digits at a time 01-99 & 00

A: Let 01 = Erik, 02 = Tammi, …..24 = Pam

R: Skip repeats numbers because we cannot take the same person twice. Numbers larger than 24 will be ignored

E: End the simulation once you have selected 5 unique numbers(people)

Random Digit Table

Suppose we have 1000 people.

How many digits do you take at a time?

Random Digit Table

Suppose we have 823 students, and 10 are to be selected for a survey.

Explain your method for randomly selecting an SRS of 10 students using a random digit table.

Use line 111 on your random digit table.

Class Sampling

Assume that there are 42 students in class today.(exactly 6 in each group)

Explain in DETAIL! How to take a random sample of 6 students using the following methods:

1. Simple Random Sample

2. Stratified Sample

3. Cluster Sample

Lincolns Gettysburg Address

Choose 5 words that are good examples of the typical length of the words in Lincoln’s speech.

Find the mean length of these 5 words

Create a dotplot as a class

Lincolns Gettysburg Address

Use a random digit table to select an SRS of 5 words. Use the line number according to YOUR class number.

Find the mean length of these 5 words

Create a dotplot as a class

The true mean length of the words in the Gettysburg Address is.…………….

4.29

River Problem

Convenience Sample….terrible estimate

River Problem

ACTUAL YIELD = 5004

Experimental Design

3 major components of experimental design. Control

Randomization

Replication

Control

What are we trying to control? Lurking variables.

Example: To test which tires work or wear best on a car, what things to we have to control?

Tire pressure, weight of car, speed of car, road conditions…the list is endless.

Control--continued

Example 2: New medicine to help with headaches. They want to compare it with the old. Lurking variables?

Gender, body size, age of participant to name a few.

Methods of control Direct control---in car example have the exact

same car for each type of tire and drive the same speed, with the same road, etc. Tough to do!

Control--continued Methods of control.

Blocking: You block to control a known lurking variable. Example: Headache

medicine—gender could be a factor. We will separate men and women into 2 blocks Then half are given

new medicine and half are given the old medicine to compare results.

500 subjects

Men Women

Randomly assign half

To new medicine

Randomly Assign half to old

medicine

RandomlyHalf to newmedicine

RandomlyHalf to old medicine

Control--continued

Same problem but medicine is for prostate cancer.

Direct control is used in that only men 50-60 are studied.

Blocking is used for more control because they believe that these medicines work differently with various races.

Let’s say there are three medicines being tested (A,B,C) they are randomly assigned after the blocks.

NOTE: BLOCKS ARE NOT RANDOM> YOU CONTROL.

Men age 50-60

in study

Caucasians Blacks Asians Hispanics

A B C A B C A B C A B C

Control—Blocks—matched pair

Blocks that are size two are called “matched pair.” Twins are the best

example of a matched pair.

If two people have the same blood pressure.

Sometimes the matched pair is the same person.

Three major designs

1 Group split into two or more groups for your experiment.

Blocks

Matched pair—a form of a block.

The reality is Blocking is used almost every time. Either you have 1 big block, blocks of your choosing, or blocks of size 2 called matched pairs.

Randomization

Concept is treatment groups are randomly assigned.

Randomization, or the theory behind it, is to eliminate bias.

There are many, unlimited ways to randomize.

Other ways to randomize

Dice

Names in a hat

Random numbers.

Count 1-3 and put in groups.

Flip coin.

Replication

There are two meanings of replication. The First is that there are an adequate number of

samples in your study.

The next is that similar studies looking for the same relationship done by different parties yield the same result consistently.

Notes Double blind

The subjects AND the evaluators both do not know the treatments given.

WHY?

Who must know the treatments?

Beware of observational studies that are passed on as experiments—see notes.

Completely Randomized

Mr. Pines has come up with two new studying techniques designed to help students on their AP Test, 90 students have volunteered to participate.

The techniques are:

A new Note Taking Method

An App

Your job is to come up with a proper design for this experiment.

Block Design

Peter Griffin has designed a new energy drink that hopes to increase production of the workers at his job site.

Typically drinks similar to these have different effects on Men and Women.

60 women and 40 men are available for this experiment.

Your job is to come up with a proper design for this experiment.