Stats 141

Stats 141/Bio 141: Lecture 1

Rajarshi Mukherjee

Stanford University

September 23, 2014

Stats 141/Bio 141: Lecture 1 September 23, 2014 1

Class Logistics


Overview

Instructor: : Rajarshi MukherjeeOffice: Sequoia Hall 202e-mail: [email protected]

Class Meetings: 2:15 pm – 3:30 pm, Tuesday and Thursday, 200-02.

Office Hours: Thursday 4:00 pm-6:00 pm, and by appointment. (RoomTBD)

Who am I? Stein Fellow/ Lecturer, Department of Statistics, StanfordUniversity.


Definitely Not a Professor!


Teaching Assistants

Sam GrossOffice Hours: Thursday 10 am - 12 pmRoom: Sequoia 227e-mail: [email protected]

Hera HeOffice Hours: Friday 1 pm – 3 pmRoom: Sequoia 232e-mail: [email protected]

Qingyuan ZhaoOffice Hours: Monday from 12 pm - 2 pmRoom: Sequoia 206e-mail: [email protected]

Xiaoying TianOffice Hours: Tuesday 10 am - 12 pmRoom: Sequoia 232e-mail: [email protected]


Sections

Wed 3:40 PM - 4:30 PM at 380-380X (Listed as 3:15 pm - 4:30 pm)

Friday 3:15 PM - 4:05 PM at 380-380W

You can come to any of these sections.

Sections are not mandatory but recommended.

Sections will be used to review course materials/ work through practiceproblems/discuss computing.


Prerequisites

Some background of algebra will be helpful.

There will be some theoretical developments more than Stats 60/Stats 160.

However, no prior knowledge of statistics will be assumed.


Homework and Exams

Homework: Assigned each week on Thursday. Due at the beginning ofclass on Thursday of the following week. The lowest of your homeworkscores will be dropped, so if you fail to turn one in, you will still be OK.

Quizzes: Quiz 1 Thursday October 9th; Quiz 2 December 2nd. (In class)

Midterm Exam: Wednesday, November 12th, in the evening (time andplace to be announced). It will roughly cover material from Lectures 1through 12.

Final Exam: Date, time and place are determined by the Registrar.Currently, we are listed as having our final on Thursday, December 11thfrom 7pm to 10pm. The location is TBA. The final will test knowledge fromall sections of the course.

All exams are open book. But no computers will be allowed. You can usehand scientific calculators.


Grading

Grades: Your class grade will be calculated as follows:

Homework: 20%

Quizzes: 10% each (total 20%)

Midterm exam: 25%

Final exam: 35%


Textbook and Class Notes

Textbook:Required: Statistics for the Life Sciences: Samuels, Witmer and Schaffner,4th Edition (Prentice Hall)Suggested: Introductory Statistics with R: Dalgaard, 2nd Edition (Springer)Using R for Introductory Statistics: Verzani, 1st Edition (Chapman &Hall/CRC)

Course Website URL:https://coursework.stanford.edu/portal/site/F14-BIO-141-01

Lecture Notes will be uploaded on the website before class and should bedownloaded/printed out in advance and brought to class.

I will try to post/mention the textbook section(s) being covered from thetext.

Today: General Introduction, Section 1.3, 2.1., Types of Variables.


Computing

For statistical computation and programming we will use environment R.

You can download it for free from http://cran.r-project.org/.

You can find extensive documentation for free on the Web, starting with thesame site/ suggested textbooks.

It is also suggested that you download an editor for R. We suggest RStudio,which can be downloaded from http://www.rstudio.com/.

Weekly sections will talk about computing and data examples.

Nice Introduction: https://www.codeschool.com/courses/try-r.


Teaching Schedule

A tentative schedule of things to be covered is given on the website in thesyllabus document.

I will not be teaching on October 16. Instead there will be a class long TAsection devoted towards review and questions.

October 10 Fri, 5:00 pm: Last day to add or drop a class.


Compare classes

Stats 60 : Stats for social sciences (mostly surveys).

Stats 110: A much more “mathy” class.

Stats 141: Understanding Tools used in Statistics.

Stats 202: “Cutting edge” data mining and visuals. (akin to bioinformatics)

Stats 300A: Very theoretical. For PhD students with lots of mathbackground.


Introduction


Let’s begin with the Following

1 Describe the range of applications of statistics.

2 Identify situations in which statistics can be misleading.

3 Define “Statistics”.


Range of applications of statistics

Statistics include numerical facts and figures.

Earth Sciences: The largest earthquake measured 9.2 on the Richter scale.

Social Sciences: Men are at least 10 times more likely than women tocommit murder.

Public Health: One in every 8 South Africans is HIV positive.

Biology: ANGPTL 3,4 and 5 genes might be associated withHypertriglyceridemia in Europe.

Statistical Physics, History, Anthropology,...

http://en.wikipedia.org/wiki/List of fields of application of statistics.


Be Cautious against Misleading Statistics

The study of statistics involves math and relies upon calculations ofnumbers.

But it also relies heavily on how the numbers are chosen and how thestatistics are interpreted.

For example, consider the following three scenarios and the interpretationsbased upon the presented statistics.

You will find that the numbers may be right, but the interpretation may bewrong.


Example 1

A new advertisement for Ben & Jerry’s ice cream introduced in late May of lastyear resulted in a 30% increase in ice cream sales for the following three months.Thus, the advertisement was effective.

A major flaw is that ice cream consumption generally increases in themonths of June, July, and August regardless of advertisements.

Example where one interpretes outcomes as the result of one variable (Ben& Jerry advertisment) when another variable (Time of the Year) is actuallyresponsible.


Example 2

The more churches in a city, the more crime there is. Thus, churches lead tocrime.

A major flaw is that both increased churches and increased crime rates canbe explained by larger populations.

In bigger cities, there are both more churches and more crime.

A third variable (number of people) can cause both situations.

However, people erroneously believe that there is a causal relationshipbetween the two primary variables rather than recognize that a third variablecan cause both.


Example 3

75% more interracial marriages are occurring this year than 25 years ago. Thus,our society accepts interracial marriages..

A major flaw is that we don’t have the information that we need. What isthe rate at which marriages are occurring?

Suppose only 1% of marriages 25 years ago were interracial and so now1.75% of marriages are interracial (1.75 is 75%higher than1).

But this latter number is hardly evidence suggesting the acceptability ofinterracial marriages.

In addition, the statistic provided does not rule out the possibility that thenumber of interracial marriages has seen dramatic fluctuations over the yearsand this year is not the highest.

Again, there is simply not enough information to understand fully the impactof the statistics.


”Definition” of Statistics

As a whole, these examples show that statistics are not only facts and figure.

They are something more than that.

In the broadest sense, “statistics” refers to the ”art” (techniques andprocedures) for analyzing, interpreting, displaying, and making decisionsbased on data.


Why Study Statistics

Statistics Encountered in Daily Life

4 out of 5 dentists recommend Dentine.

Almost 85% of lung cancers in men and 45% in women are tobacco-related.

A surprising new study shows that eating egg whites can increase one’s lifespan.

People predict that it is very unlikely there will ever be another baseballplayer with a batting average over 400.


Why Study Statistics

Statistics are often presented in an effort to add credibility to an argumentor advice.

Hopefully studying statistics will make us into an intelligent consumer ofstatistical claims.

It can be a claim made by an Biologist about collected data or claim madeby a business company about their product.

Charles Frederick Mosteller:

“While it is easy to lie with statistics, it is even easier to lie without them..”


Population and Sample

Statistics is the art of dealing with ”Data”.

However, as we said earlier, one of the most important things to understandis the context.

In statistics, we always want to study certain characteristics of individuals(people/animals/organisms/objects....) in a population of interest.

It is important to identify the population of interest and the characteristicsof interest/ objectives of the study before embarking on statistical analysis.

Example

1 Height of Basketball Players: Population- All Basketball Players,Characteristics of interest- Height.

2 Rate of Cell Division of a Skin Cancer Tissue: Population- All SkinCancer Tissues, Characteristics of interest- Rate of cell division.

3 Relationship between Work Hours and Blood Pressure in Texas:Population- All people in Texas, Characteristics of interest- Work Hours,Blood Pressure.


Population and Sample

However, most of the time the population is too big (it can even beinfinite!), or impossible to census.

In that case we need to work with a sample.

A sample is a collection of selected individuals chosen from the populationwe want to study.

Data is collection of measurements made on the these selected individualson the sample.

Hopefully, the sample is a representative of the population.

Aim of Statistics: Summarize data characteristics (Statistic) to give usidea about population summaries (Parameter): a process called inferenceInference.


Importance of Representative Sample: Random Sample

It is very important that the sampled data is a representative of thepopulation we are trying to study.

Random Sample: Subjects are selected from a population so that eachindividual has an equal chance of being selected.

Random samples are representative of the source population.

Non-random samples are not representative. If not, the inference drawn ispotentially false and misleading- Problem due to Sampling Bias.

Section 1.3 is a good read.

From now onwards, we will always assume that the data is a valid randomsample from the population.


Central Dogma of Statistics


In This Course...

1 Descriptive Statistics: Given data, how to perform initial description andvisualization of it.

Identifying different types of data.Tabular and Graphical Representation.Numerical summaries of the data.

2 Probability and Inferential Statistics:

Data as a “sample” from a larger population of interest.Given population variability how to quantify sample variability?(Probability)Given sample variability how to quantify population variability?(Inferential Statistics)

Estimation (Sampling Distribution, Means, Proportions, ConfidenceIntervals etc.)Hypothesis Testing (Testing for means, proportions, group homogeneityand equality etc.)


Take Home Messages

Statistics is about drawing inference from data about a population ofinterest.

Importance of Context: Ask the right questions to understand what is thepopulation of interest and what is the characteristics of the population weare interested in.

Make sure data is representative of the population of interest and measuresthe characteristics of the individuals of the population- Random Sample.


Statistics Does Not Prove Anything !

You only observe data once.

What if someone else does another study on the same population withanother random sample drawn from the population?

Different random samples will include different subjects, with differentobservations.

Each new random sample/data will lead to(slightly) different conclusions,implying that, sometimes, not so precise conclusions will be drawn.

Absolute certainty cannot be expected as conclusions are based on only asmall part (the sample) from the total, infinitely large, population.

Statistics is about quantifying this uncertainty from data.


Data and Variables

Data and Variables

Data is collection of characteristics/measurements of sampled units from anunderlying population.

A variable is a characteristic/measurement of a sampled unit.

Usually data is stored and presented in a dataset, comprised of variablesmeasured on sampled units.

Setting Up Data: Make a table with

One Sample unit per Row.

One Variable per Column.

Data with n sampled units and p variables measured for each sampled unitis therefore represented in a n × p table.


Patient Data from a City Hospital:n = 25, p = 6

Sampled Individual Var 1 Var 2 Var 3 Var 4 Var 5 Var 6Subject Index Gender Blood Gr. Health # Siblings Ht.(m) Wt.(Kg)

1 M A Fair 5 1.53 63.832 M B Excellent 4 1.16 92.983 F B Very Good 3 1.85 65.194 M A Poor 1 1.51 63.585 M B Fair 1 1.94 66.376 F B Very Good 1 1.62 61.697 F O Poor 4 1.22 87.518 F AB Very Good 3 1.09 64.839 F O Excellent 5 1.52 93.1310 M A Excellent 0 1.09 87.9111 F O Excellent 0 1.66 64.7212 F A Good 2 1.4 64.2213 M O Very Good 6 1.18 93.7114 M A Good 3 1.48 89.2215 M O Fair 0 1.72 65.5716 F A Very Good 3 1.72 66.4317 M O Good 2 1.87 65.1118 F AB Poor 4 1.42 65.6719 M B Very Good 4 1.53 66.7320 M A Excellent 3 1.28 89.7921 M O Excellent 4 1.86 92.0822 M B Good 3 1.53 65.2723 M O Excellent 8 1.42 65.5424 M O Good 5 0.58 63.825 M O Excellent 1 2.53 90.91


Types of Variables

In order to describe and summarize different variables of observed data, it isimportant to first identify the different types of commonly appearingvariables.

These are:

1 Categorical/Qualitative Variables

Nominal variablesOrdinal variables

2 Numeric Variables

Discrete variablesContinuous variables

We will now go through each of them and try to understand how to suitablysummarize them.


Nominal Variables

The simplest type of variable is nominal variable, in which the observed values fallinto specific unordered categories/classes

Examples

Gender — Male(M), Female(F).

Survival Status — alive, deceased

Blood Group — O, A, B, AB.

Race/ Ethnicity- Asian, Caucasian, African.

Cause of Death- natural, accident.

Political Affiliation- Republican, Democrat.



Nominal NominalSubject Index Gender Blood Gr. Health # Siblings Ht.(m) Wt.(Kg)



Properties of Nominal Variables

Numbers are often used to represent the categories for convenience, butthese numbers are merely labels.

Examples:- Gender: Male = 1 and Female = 0.- Race/ Ethnicity: Asian = 1, Caucasian=2, African= 3.

Nominal variables that take on one of two distinct values are said to bedichotomous/binary. (Example: Survival Status: alive(=1), deceased(=0).)

Both the order and the magnitude of the numbers are unimportant.

Most arithmetic operations do not make sense for nominal data.

Examples: It does not make sense to take average.


Ordinal Variables

Variables are ordinal if the observed values fall into specific categories/classes butthe order among the categories is important.

Examples

patient satisfaction with care received in the hospital — poor, fair, good,very good, excellent

injury status — none, minor, moderate, severe, fatal

level of education- Bachelor, Masters, PhD.



OrdinalSubject Index Gender Blood Gr. Health # Siblings Ht.(m) Wt.(Kg)



Properties of Ordinal Variables

As with nominal variables, categories might again be represented bynumbers.

Example: injury status — none (0), minor (1), moderate (2), severe(3),fatal(4).

The order of the numbers is important, while interpretation.

We are still not concerned with the magnitudes.

Example: injury status — none (0), minor (1), moderate (2), severe(3),fatal(4) means the same thing while interpreting as none (5), minor (10),moderate (15), severe(20), fatal(50).

In particular, does not make sense to do most arithmetic operations such asaddition, subtraction, division, average etc.


Categorical Variables

Together, nominal and ordinal variables are called categorical variables.

Discrete Variables

Variables are discrete if it can take specific set of values but the order andmagnitude matter.

Numbers are not merely labels; they are actual measurable quantities.

However, these quantities are restricted to taking on specified values only —usually integers or counts.

Examples

number of siblings a person has - (0, 1, 2, 3, . . .).

number of motor vehicle accidents in the city of Boston in a given week -(0, 1, 2, 3, . . .).

number of new cases of diabetes diagnosed in the United States over aone-year period - (0, 1, 2, 3, . . .).

Number of days it rained in Palo Alto in the first week of November -(0, 1, 2, 3, 4, 5, 6, 7).



DiscreteSubject Index Gender Blood Gr. Health # Siblings Ht.(m) Wt.(Kg)



Properties of Discrete Variables

Both order and magnitude of the values of the variable matter.

Arithmetic rules can be applied.

However, the result of the arithmetic operation might not be a discretevariable itself.

Example: I person 1 has 2 siblings and person 2 has 3 siblings, then onaverage they have (2 + 3)/2 = 2.5 siblings, but 2.5 is not a valid value forthe number of siblings.


Continuous Variables

Variables are continuous When both order and magnitude are important, butquantities are not restricted to taking on specified values/counts.

Examples

Height.

Birth Weight.

Length of time a lung cancer patient survives after diagnosis.

Concentration of mercury in a particular fish.



Continuous ContinuousSubject Index Gender Blood Gr. Health # Siblings Ht.(m) Wt.(Kg)



Properties of Continuous Variables

Most arithmetic operations make sense.

Result of adding, subtracting, dividing etc. is again valid continuous variable.

The difference between any two values can be arbitrarily small.

Therefore fractional values are possible.

The accuracy of the measuring instrument is the only limiting factor


Numeric Variables

Together, discrete and continuous variables are called numeric variables.

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