Unit 1: Introduction to data Lecture 1: Data collection ...nmd16/courses/Summer15/sta101... · For...

U 1: I L 1: D , ,

S 101

Nicole DalzellDuke University

May 13, 2015

Welcome to Stat 101!

Welcome!

Professor: Nicole Dalzell

Sta 101 (N.Dalzell– Duke University) U1 - L1: Data coll., obs. studies, experiments May 13, 2015 2 / 1

Welcome to Stat 101! Introduction to Inference

So...what is statistics?

Statistics is the art and science of learning from data.

Data are a set of measurements taken on a set of individual units

Steps for Statistical Inference/ Scientific Inquiry1 Identify a hypothesis or research question2 Collect relevant data3 Analyze the data4 Form a conclusion5 Communicate the Results6 Present your data



Step 1 : Identify a Hypothesis or Research Question

A well formed hypothesis will clearly identify a population andassociated parameters of interest.

Population: group of individuals or subjects to whom we can makeinference.Parameters: “True” values of characteristics in the population wewant to study.

How many names given to newborn babies in 2012 in the UnitedStates begin with the letter ”j”?

Population ?Parameter ?



Step 2: Collect the data

Each year the Social Security Administration collects andreleases data on the how many babies are given a certain name.

They released these data for years 1880 to 2013 for eachgender.

For privacy reasons they restrict the list of names to those with atleast 5 occurrences.

We often store and present such data in data sets , comprised ofvariables measured on individual cases.



Data Sets

dataset ordatamatrix⇒

variable↓

type price · · · weight

1 small 15.9 · · · 27052 midsize 33.9 · · · 3560 ← observation...

......

......

54 midsize 26.7 · · · 3245



Baby Names Data Set

Besides looking at the frequency of first initials, what else could welearn from this data set?



Visualize the Data: Rank Table

Top Baby Names in 2012Rank Male Female1 Jacob Sophia2 Mason Emma3 Ethan Isabella4 Noah Olivia5 William Ava6 Liam Emily7 Michael Abigail8 Jayden Mia9 Alexander Madison10 Aiden Elizabeth

http:// www.ssa.gov/ oact/ babynames


http://www.ssa.gov/oact/babynames


Visualize the Data: Rank Table

Top Baby Names in 2013Rank Male Female1 Noah Sophia2 Liam Emma3 Jacob Olivia4 Mason Isabella5 William Ava6 Ethan Mia7 Michael Emily8 Alexander Abigail9 Jayden Madison10 Daniel Elizabeth

http:// www.ssa.gov/ oact/ babynames



Visualize the Data: Time Dependencies

How has the popularity of a name changed over time?http:// www.babynamewizard.com/ voyager#prefix=\&sw=both\&exact=false



Visualize the Data: Time Dependencies

http:// www.babynamewizard.com



What about the first initials?

1 Obtain data from SS website: name, gender, frequency.d <- read.csv("yob2012.txt")

2 Use an R function (substring) to extract the initial of the name.d$initial = substring(d[,1],1,1)

3 Make a barplot of the initials, by gender if desired.barplot(table(d$initial))

barplot(table(d$initial[d$gender == "M"]))

barplot(table(d$initial[d$gender == "F"]))


http://www.ssa.gov/oact/babynames

http://www.babynamewizard.com/voyager# prefix=\& sw=both\& exact=false

http://www.babynamewizard.com/voyager# prefix=\& sw=both\& exact=false

http://www.babynamewizard.com


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Initials − All names in 20120

1000

2000

3000

4000




Initials − All names in 201 (M)

020

040

060

080

012

00


Initials − All names in 2012 (F)

050

010

0015

0020

0025

0030

00



Step 4: Form a conclusion

In 2012, newborn babies in the US were given 3,000 unique namesthat began with the letter ”j” based on the data from the SocialSecurity database

The list of babies from the Social Security data set is a sample, agroup of individuals taken from the entire population.

The number of individuals in the sample is usually denoted withthe letter n.

A statistic is any function of the data collected in the sample(e.g., mean, median, etc).

So, the count of the names in the Social Security data set for2012 which begin with ”j” is a statistic.


Welcome to Stat 101! Populations and Samples

Data Collection

Be aware that there exist “bad” samples.“There are three kinds of lies: lies, damned lies, andstatistics.”

If poor sampling techniques are utilized, then the observedstatistics will not be applicable to the true population of interest.

Example Data Collection:

Raise your hand if you have been on an airplane in the past twoyears.What does this tell us about how many 17-30 year olds haveridden an airplane in the past two years?


Welcome to Stat 101! Sampling from a population

Census

Wouldn’t it be better to just include everyone and “sample” the entirepopulation, i.e. conduct a census?

Some individuals are hard to locate or hard to measure. Andthese difficult-to-find people may have certain characteristics thatdistinguish them from the rest of the population.Populations rarely stand still. Even if you could take a census,the population changes constantly, so it’s never possible to get aperfect measure.

http:// www.npr.org/ templates/ story/ story.php?storyId=125380052Sta 101 (N.Dalzell– Duke University) U1 - L1: Data coll., obs. studies, experiments May 13, 2015 17 / 1

Welcome to Stat 101! Sampling from a population

Exploratory analysis to inference

Sampling is natural.Think about sampling something you are cooking - you taste(examine) a small part of what you’re cooking to get an ideaabout the dish as a whole.When you taste a spoonful of chili and decide the spoonful youtasted isn’t spicy enough, that’s exploratory analysis.If you generalize and conclude that your entire chili needs chilipowder, that’s an inference.For your inference to be valid, the spoonful you tasted (thesample) needs to be representative of the entire pot (thepopulation).

If your spoonful comes only from the surface and the chili powderis collected at the bottom of the pot, what you tasted is probablynot representative of the whole pot.If you first stir the chili thoroughly before you taste, your spoonfulwill more likely be representative of the whole pot.


Welcome to Stat 101! Sampling bias

Landon vs. FDR

A historical example of a biased sample yielding misleading results:

In 1936, Landonsought theRepublicanpresidentialnomination opposingthe re-election ofFDR.



The Literary Digest Poll

The Literary Digest polled about 10 millionAmericans, and got responses from about2.4 million.

The poll showed that Landon would likelybe the overwhelming winner and FDRwould get only 43% of the votes.

Election result: FDR won, with 62% of thevotes.

The magazine was completely discredited because of the poll,and was soon discontinued.


http://www.npr.org/templates/story/story.php?storyId=125380052


The Literary Digest Poll - what went wrong?

The magazine had surveyed

its own readers,registered automobile owners, andregistered telephone users.

These groups had incomes well above the national average ofthe day (remember, this is Great Depression era) which resultedin lists of voters far more likely to support Republicans than atruly typical voter of the time, i.e. the sample was notrepresentative of the American population at the time.



Large samples are preferable, but...

The Literary Digest election poll was based on a sample size of2.4 million, which is huge, but since the sample was biased, thesample did not yield an accurate prediction.

Back to the chili analogy: If the chili is not well stirred, it doesn’tmatter how large a spoon you have, it will still not taste right. Ifthe chili is well stirred, a small spoon will suffice to test the chili.



A few sources of biasNon-response: If only a (non-random) fraction of the randomlysampled people choose to respond to a survey, the sample mayno longer be representative of the population.Voluntary response: Occurs when the sample consists of peoplewho volunteer to respond because they have strong opinions onthe issue, and hence is not representative of the population.

edition.com, Aug 29, 2013

Convenience sample: Individuals who are easily accessible aremore likely to be included in the sample.

What type of bias do reviews on Amazon.com have? What about re-views on RateMyProfessor.com?



Participation question

A school district is considering whether it will no longer allow high schoolstudents to park at school after two recent accidents where students wereseverely injured. As a first step, they survey parents by mail, asking themwhether or not the parents would object to this policy change. Of 6,000 sur-veys that go out, 1,200 are returned. Of these 1,200 surveys that were com-pleted, 960 agreed with the policy change and 240 disagreed. Which of thefollowing statements are true?

I. Some of the mailings may have never reached the parents.

II. The school district has strong support from parents to move forwardwith the policy approval.

III. It is possible that majority of the parents of high school studentsdisagree with the policy change.

IV. The survey results are unlikely to be biased because all parents weremailed a survey.

(a) Only I (b) I and II (c) I and III (d) III and IV (e) Only IV



A picture’s worth a lot, but...

A lot of the time we only have part of the story.

BabyCenter: ”Our data comes from nearly half a million parentswho shared their baby’s name with us in 2014.”http:// www.babycenter.com/ top-baby-names-2014

1 ”The Netflix effect”Orange is the new Black : Galina, Piper, Nicky, Alex, GloriaHouse of Cards : Garrett, Claire, Robin, Wright

2 ”A blizzard of Frozen names” (Elsa, Hans, Kristin)

Are we comfortable making decisions about these name trends basedon this data? The ”name Elsa soared 29 percent on our list of namesfor baby girls”. Is this sample statistic enough for us to conclude thatthe population parameter of the percent of newborn girls in the UnitedStates who are named Elsa has increased from 2013 to 2014?http:// www.babycenter.com/ top-baby-names-2014


Welcome to Stat 101! Observational studies and experiments

Causality versus Correlation

1 Is there an increase in the popularity of the number of baby girlsnamed Elsa from 2013 to 2014?

2 Has the popularity in Frozen caused an increase in the numberof baby girls that were named Elsa?

Causal Effect3 Is the popularity in Frozen related to the increase in the number

of baby girls that were named Elsa?Correlation, or relationship

We collect our data differently depending on the type of relationship(causal or correlation) that we are interested in.



Observational studies and experiments

An experimental study is a controlled study in which theresearchers impose treatments upon the subjects.

Experiments are the preferred method of data collection becauseoften results can be attributed as causal. I.e., we can concludethat the treatments caused the response of the study.Subjects are assigned to control and treatment groups usingrandom assignment.



Blocking

We would like to design an experiment toinvestigate if energy gels makes you run faster:

Treatment: energy gelControl: no energy gel

It is suspected that energy gels might affect proand amateur athletes differently, therefore weblock for pro status:

Divide the sample to pro and amateurRandomly assign pro athletes to treatment andcontrol groupsRandomly assign amateur athletes totreatment and control groupsPro/amateur status is equally represented inthe resulting treatment and control groups

Why is this important? Can you think of other variables to block for?


http://www.babycenter.com/top-baby-names-2014

http://www.babycenter.com/top-baby-names-2014


Observational studies and experiments

An experimental study is a controlled study in which theresearchers impose treatments upon the subjects.

Subjects are assigned to control and treatment groups usingrandom assignment.Experiments are the preferred method of data collection becauseoften results can be attributed as causal. I.e., we can concludethat the treatments caused the response of the study.In some cases experiments are not always feasible or ethical.

An observational study is a study in which the researchers didnot assign the subjects to treatments.

Observational studies retain the notion of treatment and controlgroups.Observational studies still require the researcher to clearly definea research question. This requires identification of the responsevariable that they will measure on each subject in the study.


Welcome to Stat 101! Cereal breakfast



What type of study is this, observational study or an experiment?“Girls who regularly ate breakfast, particularly one that includes cereal, were slimmer

than those who skipped the morning meal, according to a study that tracked nearly

2,400 girls for 10 years. [...] As part of the survey, the girls were asked once a year

what they had eaten during the previous three days.”

What is the conclusion of the study?

Who sponsored the study?



3 possible explanations:

1 Eating breakfast causes girls to be thinner.

2 Being thin causes girls to eat breakfast.

3 A third variable is responsible for both. What could it be?An extraneous variable that affects both the explanatory and theresponse variable and that make it seem like there is arelationship between the two are called confounding variables.



Observational studies and experiments (Recap)

Observational study: Researchers collect data in a way that doesnot directly interfere with how the data arise, i.e. they merely“observe”, and can only establish an association between theexplanatory and response variables.Experiment: Researchers randomly assign subjects to varioustreatments in order to establish causal connections between theexplanatory and response variables.If you’re going to walk away with one thing from this class, let itbe “correlation does not imply causation”.

http:// xkcd.com/ 552/



Random assignment vs. random sampling

Random assignment

No random assignment

Random sampling

Causal conclusion, generalized to the whole

population.

No causal conclusion, correlation statement

generalized to the whole population.

Generalizability

No random sampling

Causal conclusion, only for the sample.

No causal conclusion, correlation statement only

for the sample.No

generalizability

Causation Correlation

ideal experiment

most experiments

most observational

studies

bad observational

studies


Welcome to Stat 101! Observations and variables

Types of variables

all variables

numerical categorical

continuous discreteregular

categorical ordinal

measured counted unorderedcategories

orderedcategories


Welcome to Stat 101! Observations and variables

Types of variables (cont.)

type: small, midsize or large.

price: average price in $1000’s

mpgCity: cite mileage per gallon

drivetrain: front, rear, 4WD

passengers: passenger capacity

weight: car weight in pounds


http://xkcd.com/552/

Welcome to Stat 101! Principles of experimental design


A study is designed to test the effect of light level and noise level onexam performance of students. The researcher also believes that lightand noise levels might have different effects on males and females,so wants to make sure both genders are represented equally underdifferent conditions. Which of the below is correct?

(a) There are 3 explanatory variables (light, noise, gender) and 1response variable (exam performance)

(b) There are 2 explanatory variables (light and noise), 1 blockingvariable (gender), and 1 response variable (exam performance)

(c) There is 1 explanatory variable (gender) and 3 response variables(light, noise, exam performance)

(d) There are 2 blocking variables (light and noise), 1 explanatoryvariable (gender), and 1 response variable (exam performance)



Difference between blocking and explanatory variables

Factors are conditions we can impose on the experimental units.

Blocking variables are characteristics that the experimental unitscome with, that we would like to control for.

Blocking is like stratifying, except used in experimental settingswhen randomly assigning, as opposed to when sampling.



Principles of experimental design

Reading: Open Intro Chapter 1.5: Experiments

1 Control: Compare treatment of interest to a control group.2 Randomize: Randomly assign subjects to treatments.3 Replicate: Within a study, replicate by collecting a sufficiently

large sample. Or replicate the entire study.4 Block: If there are variables that are known or suspected to affect

the response variable, first group subjects into blocks based onthese variables, and then randomize cases within each block totreatment groups.



More experimental design terminology...

Placebo: fake treatment, often used as the control group formedical studies

Placebo effect: experimental units showing improvement simplybecause they believe they are receiving a special treatment

Blinding: when experimental units do not know whether they arein the control or treatment group

Double-blind: when both the experimental units and theresearchers do not know who is in the control and who is in thetreatment group


Welcome to Stat 101! Recap


What is the main difference between observational studies and exper-iments?

(a) Experiments take place in a lab while observational studies donot need to.

(b) In an observational study we only look at what happened in thepast.

(c) Most experiments use random assignment while observationalstudies do not.

(d) Observational studies are completely useless since no causalinference can be made based on their findings.


Welcome to Stat 101! Recap

More...

Want more baby name analysis?

Freakonomics podcast: How Much Does Your Name Matter?

http:// freakonomics.com/ 2013/ 04/ 08/how-much-does-your-name-matter-a-new-freakonomics-radio-podcast/


Syllabus & policies Logistics

General Info

Instructor: Nicole Dalzell - [email protected] Chemistry 214

Lecture: MTuWThF 12:30 AM - 1:45 PMPerkins Classroom 5

Lab: TuWTh 2 PM - 3 PMOld Chemistry 101

OH: Tentative: Monday 2:30 PM - 3:30 PMWednesday 10-11 AMOr by appointment



Required materials

Textbook OpenIntro StatisticsDiez, Barr, Cetinkaya-RundelCreateSpace, 2nd Edition, 2012ISBN: 978-1478217206

Calculator (Optional) You might need a four function calcu-lator that can do square roots for this class. Nolimitation on the type of calculator you can use.


http://freakonomics.com/2013/04/08/how-much-does-your-name-matter-a-new-freakonomics-radio-podcast/

http://freakonomics.com/2013/04/08/how-much-does-your-name-matter-a-new-freakonomics-radio-podcast/

mailto:[email protected]

http://www.openintro.org/stat/down/OpenIntroStatSecond.pdf


Webpage

https:// stat.duke.edu/∼nmd16/ courses/ Summer15/ sta101.001-1/


Syllabus & policies Goals and topics

Inference

Design of studies

Probability

Bayesian inference

Frequentist inference(CLT & simulation)

Modeling (numerical response)

1 explanatory

numerical

categorical

one mean & median

one proportion

many explanatory

Exploratory data

analysistwo means & mediansmany means

two proportionsmany proportions


Syllabus & policies Details

Course structure

Seven learning units.

Set of learning objectives and required and suggested readings,videos, etc. for each unit.

Prior to beginning the unit, complete the readings and familiarizeyourselves with the learning objectives.

Class time: split between lecture, discussion/application.

Computing labs.



Class - duration of unit

Slides will be posted on the course webpage (under schedule)on the day of the course.

Discussion of concepts as well as hands on activities andexercises to complement them.

Attend class to keep up with the pace and not fall behind + tocontribute to application activities completed in teams.

You are responsible for all the material covered in all componentsof the course, not just the class. Please ask questions in class,office-hours or by e-mail if you are struggling (or just curious), donot wait until just before an exam when it may be too late.


https://stat.duke.edu/~nmd16/courses/Summer15/sta101.001-1/


Participation questions: attendance and participation

Objective: Make you an active participant and help me pace the class.

On new material being discussed in class that day.

Credit for participation, regardless of whether you have thecorrect answer.

Up to two unexcused late arrivals or absences will not affect yourparticipation grade.

While I might sometimes call on you during the class discussion,it is your responsibility to be an active participant without beingcalled on.



Problem sets and labs

Problem sets:Objective: Help you develop a more in-depth understanding ofthe material and help you prepare for exams and projects.

Individual: collaborate but don’t copy! – submit in class, show allwork.

Labs:Objective: Give you hands on experience with data analysisusing a statistical software and provide you with tools for theprojects.

In partners – turn in lab report on Sakai by the following day at 5PM.

Lowest score dropped for both.



Project

Objective: Give you independent applied research experience usingreal data and statistical methods.

individual

statistical inference exploring the distributional characteristics ofone variable or relationship between two variables

choose a research question, find data, analyze it, write up yourresults



Exams

Midterm: Monday, June 1, in class

Final: Wednesday, June 24th (9:00 AM - 12:00 PM) (Cumulative)

Exam dates cannot be changed. No make-up exams will begiven. If you cannot take the exams on these dates you shoulddrop this class.

You must bring a calculator to the exams (no cell phones, iPods,etc.) and you are also allowed to bring one sheet of notes(“cheat sheet”). This sheet must be no larger than 81

2” × 11” andmust be prepared by you (no photocopies). You may use bothsides of the sheet.



Grading

In Class Participation/Activities:5%

Quizzes: 5%

Problem sets: 15%

Labs: 10%

Project: 20%

Midterm: 20%

Final: 25%


Syllabus & policies Support

Email

I will regularly send announcements by email, so make sure tocheck your email daily.

While email is the quickest way to reach me outside of class, it ismuch more efficient to answer most statistical questions inperson.



Piazza on Sakai

Content related questions should be posted on Piazza, whichyou may access through the course Sakai site.

Title your questions.

Check if your question has already been answered beforeposting a new question.

I will be answering questions on Piazza daily and all students areexpected to answer questions as well.

“Watch” to be notified when a new question is posted.



Office hours

Instructor Mondays 2:00 - 3:00 PMWednesdays 10-11am

You are highly encouraged to stop by with any questions orcomments about the class, or just to say hi and introduceyourself.

You must attempt problems sets before office hours.


Syllabus & policies Policies

Policies

Late work policy for problem sets and labs reports:

late but submitted duringclass: lose 10% of pointsafter class on due date: lose20% of points

next day: lose 40% of points

later than next day: lose allpoints

Late work policy for project: 10% off for each day (24-hourperiod) late.

No make-ups

Regrade requests: within one week, no regrade for number ofpoints deducted for a mistake, no regrade after the final


Syllabus & policies Policies

Academic Dishonesty

Any form of academic dishonesty will result in an immediate 0 on thegiven assignment and will be reported to the Office of StudentConduct. Additional penalties may also be assessed if deemedappropriate. If you have any questions about whether something is oris not allowed, ask me beforehand.

Some examples:

Use of disallowed materials (including any form ofcommunication with classmates or accessing the web) duringexams and readiness assessments.

Plagiarism of any kind.

Use of outside answer keys or solution manuals for thehomework.

If you have any questions about whether something is or is notallowed, ask me beforehand.


Syllabus & policies Tips

Tips for success

1 Complete the reading before a new unit begins, and then reviewagain after the unit is over.

2 Be an active participant during lectures and labs.3 Ask questions - during class or office hours, or by email. Ask me

and your classmates.4 Do the problem sets - start early and make sure you attempt and

understand all questions.5 Start your project early and and allow adequate time to complete

it.6 Give yourself plenty of time to prepare a good cheat sheet for

exams. This requires going through the material and taking thetime to review the concepts that you’re not comfortable with.

7 Do not procrastinate - don’t let a unit go by with unansweredquestions as it will just make the following unit’s material evenmore difficult to follow.


To do

To do

1 Download or purchase the textbook.www.openintro.org

2 Read the syllabus and let me know if you have any questions.3 Start reviewing the resources for Unit 1 – .

https:// stat.duke.edu/∼nmd16/ courses/ Summer15/ sta101.001-1/ resources/ unit1.html


www.openintro.org

https://stat.duke.edu/~nmd16/courses/Summer15/sta101.001-1/resources/unit1.html

https://stat.duke.edu/~nmd16/courses/Summer15/sta101.001-1/resources/unit1.html

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