Welcome to AP Statistics.

• AP Statistics - Fall Semester 2015• Mr. Schooleman• Room 320• 720-423-6145• William_Schooleman@dpsk12.org• http://mrschooleman.wikispaces.com• http://stattrek.com

Big Ideas of AP Statistics

1. Data analysis2. Data production3. Probability and Simulation4. Statistical Inference

Tack - ActivityWhat is the probability that a tack will land on its head?1. How can we produce data?2. What could we do to analyze the data?3. How could we run a simulation without tacks?4. What can we infer about the random phenomenon of rolling a tack and having it land on it’s head?

Chp. 5 Producing Data

Sec. 4.3 Establishing Causation

Non-Probability Sampling Methods

• With non-probability sampling methods, we do not know the probability that each population element will be chosen, and/or we cannot be sure that each population element has a non-zero chance of being chosen.

Voluntary Response Sample

• A voluntary sample is made up of people who self-select into the survey. Often, these folks have a strong interest in the main topic of the survey. This can lead to a biased sample.

• Read example 5.3, page 331 and discuss.

Convenience Sampling

• A convenience sample is made up of people who are easy to reach.

Consider the following example. A pollster interviews shoppers at a local mall. If the mall was chosen because it was a convenient site from which to solicit survey participants and/or because it was close to the pollster's home or business, this would be a convenience sample.

Bias.

The sampling method is biased if it systematically favors certain outcomes.

• Census

A census attempts to contact every individual in the entire population.

August 28th, 2015Objectives:1. Understand the difference between

Observational and Experimental studies.2. Population vs. Sample3. Explore different types of sampling methods.

Observational Study

• Observational study. Like experiments, observational studies attempt to understand cause-and-effect relationships. However, unlike experiments, the researcher is not able to control:

• (1) how subjects are assigned to groups and/or

• (2) which treatments each group receives.

Experimental Study

• Experiment. An experiment is a controlled study in which the researcher attempts to understand cause-and-effect relationships. The study is "controlled" in the sense that the researcher controls

(1)how subjects are assigned to groups and

(2) which treatments each group receives.

Population and Sample

• The information from the entire population is called a parameter.

• The information about a population taken from a sample is called a statistic.

• What methods could be used to obtain a parameter and statistic from a population?

Population parameter = actual % of what is being measured.Census : involves gaining information from every member (subject) of the population.

Population statistic = estimated % of what is being measured.Survey, experimental study…… : studying part of the population to estimate the whole of the population.

August 31, 2015• Objectives:1. Define “Simple Random Sample”.2. Identify different methods to obtain a SRS

from a population.

Sampling ?

Simple Random Sample (SRS)

• Simple random sampling refers to any sampling method that has the following properties. –The population consists of N objects.–The sample consists of n objects.–If all possible samples of n objects are

equally likely to occur, the sampling method is called simple random sampling.

Random Rectangles.Understanding the role of randomness is the key to understanding statistical sampling. This activity should help you see that judgmental samples tend to produce estimates that are more biased while random samples tend to be unbiased and better predictors of the population parameters.

Stem and Leaf plot:Hallux abducto valgus (call it HAV) is a deformation of the big toe that is not common in youth and often requires surgery. Doctors used X-rays to measure the angle (in degrees) of deformity in 38 consecutive patients under the age of 21 who came to a medical center for surgery to correct HAV. The angle is a measure of the seriousness of the deformity. Here are the data.

Make a stem & leaf plot and give a numerical description of this distribution. Are there any outliers?Hallux abducto valgus data:• 28 32 25 34 38 26 25 18 30 26 28 13 20• 21 17 16 21 23 14 32 25 21 22 20 18 26• 16 30 30 20 50 25 26 28 31 38 32 21

Generate 5 random numbers between 1 and 100.a. Open a calculator page and press Menu.

b. Enter the following and select 5 numbers.

September 1, 2015Objectives:

1. Identify different ways to randomly select individuals or subjects to a study.

2. Use the Random Number Table for any size population.

Choosing an SRS

• Names out of a hat.• Random number table.• Computer (calculator) generated sample.• 1- Label. Assign a number to each individual• 2-Hat, Table, Computer, select at random• 3- Stopping Rule. Indicate when you stop.• 4- Identify sample. Identify who is selected.

Random Digits.A table of random digits is a long string of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with these two properties:1. Each entry in the table is equally likely to be

any of the 10 digits 0 through 9.2. The entries are independent of each other.

That is, knowledge of one part of the table gives no information about any other part.

A. Flipping a coin a determining head / tails.B. Rolling a one die to simulate 1, 2, 3, 4, 5, or 6C. Rolling two dice to simulate 2, 3, …….. 11, 12D. Every person in our class is assigned a

number alphabetically and 5 students are selected.

E. A congressional district has 25 % democrat, 55% republican, and 20% independent.

September 3rd, 2015

Objectives:1. Define different methods of

sampling.• Stratified sample• Cluster sample• Multistage sample

Probability Sampling

• Probability sampling is a sample chosen by chance. We must know what samples are possible and what chance each sample has to be chosen.

• Types of Probability Samples:Stratified random sample, Cluster sample,

Multistage sample, and Systematic sample.

Stratified Sample

• Stratified sampling. With stratified sampling, the population is divided into groups, based on some characteristic. Then, within each group, a probability sample (often a simple random sample) is selected. In stratified sampling, the groups are called strata.

• Group: Discuss a situation of stratified sampling that would involve the South High student body.

Rolling Down the River Activity

A farmer has just cleared a new field for corn. It is a unique plot of land in that a river runs along one side. The corn looks good in some areas of the field but not others. The farmer is not sure that harvesting the field is worth the expense. He has decided to harvest 10 plots and use this information to estimate the total yield. Based on this estimate, he will decide whether to harvest the remaining plots.

Cluster Sample

• Cluster sample divides the population into groups, or clusters. Some of these clusters are randomly selected. Then all individuals in the chosen clusters are selected to be in the sample.

Bias Sampling

• Undercoverage is when some group in the population are left out of the process of choosing the sample.

Come up with an example from your group.

• Nonresponse occurs when an individual chosen for the sample can’t be contacted or does not cooperate.

Give a group example.

Response Bias• Response bias is when the respondent choses

to lie due to legal or social pressure.• Describe the response bias that Calvin is

demonstrating on the “Chewing” magazine survey.

Wording of the Question Bias.

• Confusing or leading questions can introduce strong bias, and even minor changes in wording can change a survey’s outcome.

MC about Bias

• We say that the design of a study is biased if which of the following is true?

(a) A racial or sexual preference is suspected.(b) Random placebos have been used.(c) Certain outcomes are systematically favored.(d) The correlation is greater than 1 or less than –1.(e) None of the above. The answer is _____________________________.

Sep. 10 Objectives

• How to carry out a well designed experiment.• Identify all elements of an experiment.• Identify the 3 principles of a well designed

experiment.1. Control2. Replication3. Randomization

The 10 top reasons to be a statistician.

1

• Estimating parameters is easier than dealing with real life.

2

• Statisticians are significant.

3

• I always wanted to learn the entire Greek alphabet.

4

• The probability a statistician major will get a job is > .99999

5

• If I flunk out I can always transfer to Engineering.

6

• We do it with confidence, frequency, and variability.

7

• You never have to be right – only close.

8

• We’re normal and everyone else is skewed.

9

• The regression line looks better than the unemployment line.

10

• No one knows what we do so we are always right.

Elements of an experiment.

• Experimental units: individuals that the experiment is performed on.

• Subjects: an experimental unit that is a person.

• Treatment: an specific experimental condition applied to the unit.

• Factors: explanatory variable.• Level: different values of a factor.

• Discuss: Example 5.14 on page 355 and discuss the different elements.

The goal of research is to establish a causal link between a particular treatment and a response. Experiments are much better at this than are observational studies. In observational studies, you cannot guarantee that you have controlled for the effects of lurking variables, but you can in a well-designed experiment.

Placebo Effect

• A placebo is a dummy treatment. Some subjects may respond favorably to any treatment, even a placebo.

• Group answer: problem 5.33 page 357

Identify the experimental units, the factors, the treatments, and the response variables.

3 Principles of Design

• Control• Replication• Randomization

• From the “Cookie” activity discuss where the three principles are in

(a) Describe the experimental units/subjects in the experiment. How many were there?

(b) Identify the explanatory variable(s).(c) How many treatments were there? ____ List them. (d) How many subjects were in each treatment

group? (e) What was the response variable?

Control

• By comparing two or more treatments an experiment has more control of the confounding effects of lurking variables on the response.

Replication

• Replicate each treatment on many units to reduce variation in the results.

• The purpose of replication is not to eliminate chance variation but to reduce its role and increase the sensitivity of the experiment to differences between treatments.

Randomization

• Randomization is to use impersonal chance to assign experimental units to treatments.

• It can be argued that randomization is the most important principle of experimental design since it is what allows us to assert that treatments groups are essentially similar.

Sep. 11 Objectives

• Design a completely Random Design and describe the process.

• Design a Block Design and state why blocking is used.

Answer: “ What are we controlling for?”

• Statistical Significance – An observed effect is so large that it would rarely occur by chance.

• Completely randomize design – When all experimental units are allocated at random among all treatments.

September 14, 2015Objectives:1. Define and apply Block Designs and Matched

Pair designs.2. Vocabulary group quiz.

Block Design

• In a Block Design experiment the units are divided into subgroups called blocks. Each block has something in common. From each block, the random assignments of units to treatments is carried out separately from each block.

• We Block to control for the variables you know about, we randomize to control for variables we do not know about.

• We Block to control for the variables you know about, we randomize to control for variables we do not know about.

• Mantra: “Control what you can, block on what you can’t control, randomize the rest.”

• Examples 5.20, 5.21, StatTrek Video.

Matched Pairs Design

• Matched pairs design is a form of block design in which just two treatments are compared.

• 1. Two subjects are matched(age, gender, income, ect.) and one of two treatments are randomly assigned to each subject.

• 2. One subject is given two treatments at different times. Treatments are randomly assigned in which goes first (cookie expt.).

Matched Pair Problem

• Design an experiment that compares old and new waterproofing treatments on the boots of 20 volunteers.

• Present your groups design on the large white board. Describe the steps so that others may carry out the design.

• Identify the 3-priciples: Control, Replication, and Randomization.

Double-Blind

• Neither the subject or those who measure the response variable know which treatment a subject received.

JPG

Causation-Common Response-Confounding

Establishing Causation.Objectives:1. Identify the three ways in which the

association between two variables can be explained.

2. Explain what process provides the best evidence of causation.

3. Define what is meant by a common response.4. Define what is means to say that two

variables are confounded.

• Establishing Causation. When we study the relationship between two variables, we often hope to show that changes in the explanatory variable causes changes in the response variable. A strong association between two variables in not always enough to draw conclusions about cause and effect.

Put into two groups

X Response variable

Input Y

Explanatory variable Output

The following are some examples of observed associations between x and y:

1. X = mother’s body mass index y = daughter’s body mass index

2. X = amount of the artificial sweetener saccharin in a rat’s diet

y = count of tumors in the rat’s bladder

3. X = a high school senior’s ACT score y = the student’s firs-year college GPA

4. X = monthly flow of money into stock mutual

funds y = monthly rate of return for the stock market

5. X = whether a person regularly attends religious services.

y = how long the person lives

6. X = the number of years of education a worker has

y = the worker’s income

1. X = mother’s body mass index y = daughter’s body mass index

2. X = amount of the artificial sweetener saccharin in a rat’s diet

y = count of tumors in the rat’s bladder

3. X = a high school senior’s ACT score y = the student’s first-year college GPA

4. X = monthly flow of money into stock mutual

funds y = monthly rate of return for the stock market

5. X = whether a person regularly attends religious services.

y = how long the person lives

6. X = the number of years of education a worker has

y = the worker’s income

Blocking

What’s the Big Deal?

must do hands up

-160 -150 -140 -130 -120 -110 -100 -90 -80 -70

Simulation 2 – Blocked by Breed

Data A B C D

Raw EX

Ca

Co

ave.

New Ex

Ca

Co

We must standardize the score to fairly make a comparison.

Simulation 2 – Blocked by Breed

Data A B C D

Raw EX

Ca

Co

ave.

New Ex

Ca

Co

average the 6 scores of your breed

subtract average from each score

We must standardize the scores to fairly make a comparison.

Simulation 2 – Blocked by Breed

Simulation 3 – Blocked by Clinic

Data Paw Pooch Tree Bark

Raw EX

Ca

Co

ave.

New Ex

Ca

Co

Simulation 3 – Blocked by Clinic

sample data

Simulation 2 – Blocked by Breed

sample data

Simulation 3 – Blocked by Clinic

sample data