STATS 13

Introduction to statistical methods
for the life and health sciences

Bonjour, I'm Guillaume

The administrative stuff

Lectures:
Tuesdays & Thursdays
3:30-4:45PM

Labs:
Mondays & Wednesdays
10:00-10:50AM

Grading:
Homeworks (25%)
Midterm (35%)
Final (35%)
Participation (5%)

No official textbook

Homeworks:
assigned Mondays (11:00AM)
due before the next Monday (10:00AM)

Office hours:
W/F: 1:30-3:30PM (MRL 3761)

Class-related communication:
Piazza forum (peer learning)

Understanding > knowing

Getting an answer is very different from knowing WHY we get this answer.

Understanding statistics implies understanding the underlying process leading to the answer we get.

This class is a bit different => RESAMPLING & SIMULATIONS.
We believe understanding how things work is far more interesting and useful, because it can be applied and tweaked to very specific situations.
Formula have been developed for a certain kind of data.
The problem is that we are living in a rapidly evolving world, with new kind of data being generated every day. We need to be able to analyze this new kind of data. Formula applies to a very narrow range of data. We are not living in a fantasy world.
I am not here to train you to be a bunch of robots who know how to apply some recipe by heart and just press a button and just read the results.
I am here is to train the next generation of scientists, the next generation of entrepreneurs, the next generation of leader, who will be able to understand to analyze any kind of new data they encounter.

Motivation for this class

What we teach is largely the technical machinery of numerical approximations based on the normal distribution and its many subsidiary cogs. This machinery was once necessary, because the conceptually simpler alternative based on permutations was computationally beyond our reach [...]

Before computers statisticians had no choice. These days we have no excuse. Randomization-based inference makes a direct connection between data production and the logic of inference that deserves to be at the core of every introductory course.”

George W. Cobb
(2005 USCOTS presentation)

Stats 13

Lecture 1

Introduction

Guillaume Calmettes

Statistics?

Making decisions based on Data!

Statistics is the science of

collecting,
organizing,
presentating,
analyzing,
and interpreting

data

to assist in
making more effective decisions.

Statistics is not an exact science

2017 NCAA Finale (Apr 3)

Statistics is not an exact science

2017 NCAA Finale (Apr 3)

Statistics:
Numbers (players' height, offensive points, opposite team score, ...)

Bookmakers:
Numbers + history
("team experience")

Statistics is not an exact science

2017 NCAA Finale (Apr 3)

There is no RIGHT or WRONG in Statistics,
there is only (most) likely or (most) unlikely

How statistics solved the Cholera transmission problem

Cholera outbreaks in the world

The mystery of Cholera's cause and transmission

Miasma theory
The theory of indirect and airborne transmission held that cholera was caused by the smell of the bad air (miasmata), a poisonous vapor with suspended particles of decaying matter and a foul smell

- 19$^{th}$ century prevailing dogma.
- It made sense to most as disease and epidemics were concentrated in poor, filthy and foul-smelling city neighborhoods.

John Snow

British physician, considered one of the fathers of modern epidemiology.

He was skeptical about Cholera being caused by pollution or a noxious form of "bad air".

He proposed that cholera was attributable to a self-replicating agent, probably ingested through the medium of water.
Hypothesis

(15 March 1813 - 16 June 1858)

Being skeptic, curious, not taking anything for granted is a good quality to have.

The first cases of cholera in England were reported in 1831, about the time Dr. Snow as finishing up his medical studies at the age of eighteen. Between 1831 and 1854, tens of thousands of people in England died of cholera. Although Dr. Snow was deeply involved in experiments using a new technique, known as anesthesia, to deliver babies, he was also fascinated with researching his theory on how cholera spread.
In the middle 1800s, people didn’t have running water or modern toilets in their homes. They used town wells and communal pumps to get the water they used for drinking, cooking and washing. Septic systems were primitive and most homes and businesses dumped untreated sewage and animal waste directly into the Thames River or into open pits called “cesspools”. Water companies often bottled water from the Thames and delivered it to pubs, breweries and other businesses.
Dr. Snow believed sewage dumped into the river or into cesspools near town wells could contaminate the water supply, leading to a rapid spread of disease.
In August of 1854 Soho, a suburb of London, was hit hard by a terrible outbreak of cholera. Dr. Snows himself lived near Soho, and immediately went to work to prove his theory that contaminated water was the cause of the outbreak.

Statistical hypothesis

A hypothesis is an assumption about certain characteristics of an object of interest/study. This assumption may or may not be true.

In Statistics, a hypothesis is a specific statement regarding the relationship between two variables.

- Does the association exist?
- Could it be by chance?
- Is there bias?

The River Thames, a (polluted) source for water companies

Soho cholera epidemics (Sept. 1854)

The most terrible outbreak of cholera which ever occurred in this kingdom.
- John Snow -

The first 10 days:
> 500 fatalities

John Snow's dataset

Snow tracked the numbers of cholera fatal attacks in the neighborhood.

Variables

Observational
Units

House	Address	Population	Fatalities
House #1	45 Lexington St	8	5
House #2	15 Broadwick St	21	7
House #3	61 Poland St	4	1
House #4	37 Broad St	27	16
House #5	48 Carnaby St	11	3
House #6	46 Beak St	8	0
House #7	43 Broad St	44	9

Observational units & variables

An observational unit (or case) is the individual entity of interest on which data are recorded.

The recorded characteristics of the observational unit are the variables of interest. Those variables can be quantitative (numerical values) or categorical (category designation).

John Snow's dataset

Snow tracked the numbers of cholera fatal attacks in the neighborhood.

Categorical

Quantitative

Variables

Observational
Units

House	Address	Population	Fatalities
House #1	45 Lexington St	8	5
House #2	15 Broadwick St	21	7
House #3	61 Poland St	4	1
House #4	37 Broad St	27	16
House #5	48 Carnaby St	11	3
House #6	46 Beak St	8	0
House #7	43 Broad St	44	9

Categorical & Quantitative variables

A categorical variable divides the observational units into groups.

A quantitative variable measures a numerical quantity for each observational unit.

Name	Year	Gender	GPA	Sibling	Height	Weight	TV	Award
Paul	Senior	M	3.1	2	71	180	3	Olympic
Nicole	Somophore	F	3.4	0	66	140	1	Nobel
Maria	Senior	F	2.9	4	64	135	0	Academy
John	First Year	M		1	68	160	2	None
Chris	Junior	M	3.8	3	72	173	1	Nobel

What are the observational units & variables?

Does louder music cause people to drink more beer?

Do males find females more attractive if they wear red?

Are lions more likely to attack after a full moon?

To put everything together. What are the observational units and variables?
Are the variables Categorical or Quantitative?
1- We would record data on people. And define different level of music volume (high/low ... in this case CATEGORICAL) or (direct volume number ... in this case QUANTITATIVE). And we would observe the number of beer people would drink (Quantitative).
2- Women would be our observational unit. For each women, we would record if she was wearing red or not as a variable (categorical). Another variable would be the level of attractiveness felt by men (could just be "Attractive/Not attractive" or a value).
Lions attacks would be what we observe. For each lion attack we would store the time information (full moon or not).

John Snow's dataset

House	Address	Population	Fatalities
House #1	45 Lexington St	8	5
House #2	15 Broadwick St	21	7
House #3	61 Poland St	4	1
House #4	37 Broad St	27	16
House #5	48 Carnaby St	11	3
House #6	46 Beak St	8	0
House #7	43 Broad St	44	9

Subset of the dataset.

Tracking down the outbreak's source

Snow analyzed the spatial pattern of the disease based on:

Cholera fatal attacks
Water sources

"Anomalies":
Workhouse
(535 inmates)
Brewery
(70 workers)

It is likely that the epidemic had a common source
To better see what was happening, snow placed the data on a map of Soho. Within 250 yards of the spot where Cambridge Street joins Broad Street there were upwards of 500 fatal attacks of cholera in 10 days.
He also added the water sources locations (blue points)
Deaths concentrated around Broad Street pump. Dr. Snow worked around the clock to track down information from hospital and public records on when the outbreak began and whether the victims drank water from the Broad Street pump. Snow suspected that those who lived or worked near the pump were the most likely to use the pump and thus, contract cholera.
But they are also data that are a bit different. Anomalies.
None of the workers at the Broad Street brewery had cholera: they were very close to Broad street pump.
Likewise the Poland Street Workhouse only recorded five deaths among its 535 inmates.

Outliers

An outlier is an observed value that is notably distinct from the other values in a dataset. Usually, an outlier is much larger or much smaller than the rest of the data values.

Outliers in Snow's Soho investigation

The information given by the outliers was important: it helped Snow rule out other possible sources of the epidemic besides pump water.

A workhouse had 535 inmates but almost no cases of cholera.
=> Snow discovered the workhouse had its own well

The 70 workers of the brewery on Broad Street also escaped cholera.
=> Mr. Huggins (owner) told Snow that the men drank the liquor they made or water from the brewery’s own well.

An elderly widow in West Hampstead (an area some distance away, which was free of cholera) and her niece died from cholera.
=> She liked the taste of Broad Street water, and she had a bottle brought to them every day from the pump

The Broad street pump area

Area for which the Broad Street pump is the fastest trip to water
(on foot).

From data to administrative action

On Sep 7, 1854, Snow took his research to the town officials and convinced them to take the handle off the pump.

Still, the scientific community was reluctant to believe his theory

What would be alternative explanations for the decrease in cholera fatal attacks?

Snow's "Grand Experiment"

Despite the success of Snow’s theory in stemming the cholera epidemic in Soho, public officials still thought his hypothesis was nonsense.
=> He needed stronger evidence.

Research question:
Is there a causal relationship between water supply and cholera?

What should Snow do to get "stronger" evidence?

- Bigger scale study? (generalization)
- More systematic comparison? ("Control" population)

Collecting a dataset

The population is the entire collection of observational units we are interested in. A sample is a subset of the population on which we record data.

Numerical summaries about a population are called parameters, and numerical summaries calculated from a sample are called statistics.

The London waterworks landscape

2 major water supply companies

	1849 epidemics	1853-1854 epidemics
Lambeth Waterworks	London intake	Seething wells intake
Southwark Vauxhall	London intake	London intake

What are the two groups tested?
What are the different variables?
What results are we anticipating?

London was without cholera from the latter part of 1849 to August 1853.
During this interval an important change had taken place in the water supply of several of the south districts of London. The Lambeth Company removed their water works in 1852 from opposite Hungerford Market to Thames Ditton [actually Seething Wells]; thus obtaining a supply of water quite free from the sewage of London.
The experiment, too, was on the grandest scale. No fewer than three hundred thousand people of both sexes, of every age and occupation, and of every rank and station, from gentlefolks down to the very poor, were divided into two groups without their choice, and, in most cases, without their knowledge; one group being supplied with water containing the sewage of London, and, amongst it, whatever might have come from the cholera patients, the other group having water quite free from such impurity.

Experiment & Observational study

An experiment is a study in which the researcher actively controls one or more of the explanatory variables.

An observational study is a study in which the researcher does not actively control the value of any variable but simply observes and record the values as they naturally exist.

Snow compared different exposure groups, but did not assign the exposure (contaminated water or not).
What kind of study is it?

Snow's "Grand Experiment"

Despite the success of Snow’s theory in stemming the cholera epidemic in Soho, public officials still thought his hypothesis was nonsense.
=> He needed stronger evidence.

Research question:
Is there a causal relationship between water supply and cholera?

Observational units:
"Groups" of people

Variables:
- Occurence of cholera fatal attacks (outcome)
- Type of water supply (explains difference in outcome)

Explanatory & Response variables

A response variable is the variable about which questions are asked, it measures the outcome of the study.

An explanatory variable is any factor that can influence, explain or predict the response variable.

The response variable is usually called dependent, while the explanatory variable is sometimes called independent.

Does meditation help reduce stress?

Does sugar consumption increase hyperactivity?

Snow's analysis of deaths data

Data

Analysis

Water supply and cholera occurence

	Number of houses	Deaths from cholera	Deaths in each 10,000 houses
Southwark & Vauxhall	40,046	1,263	315
Lambeth Waterworks	26,107	98	38
Rest of London	256,423	1,422	55

8 times more likely to die

On the basis of these figures, which company is more likely to be transmitting "morbid matter" causing cholera?

Cannot tell!
(we need to normalize the data)

On the basis of these figures, which company is more likely to be transmitting "morbid matter" causing cholera?
Cannot tell: Correct. Although there were more deaths in houses supplied by the Southwark and Vauxhall Company, this could just be because this company supplied water to a greater number of people. In order to know whether one company is more likely to transmit contaminated water, we need to know, for each company, the number of deaths as a proportion of the number of people supplied with water. => Need to normalize to be able to directly compare data.
In order to estimate the denominator, Snow obtained information on the number of houses in London whose water was supplied by each of the two water companies.
Are there are problems with using a general total of houses supplied by each company as a denominator?
- Ideally, the denominator should be all people supplied by water from each company, not houses. Different houses may contain different numbers of people. If, for example, the Lambeth company supplied an area where there were consistently more people per house than the area supplied by the Southwark and Vauxhall company, then we might be misled by using the number of houses as a denominator.
- Ideally, the denominator should be houses in the areas of mixed supply only, not all households supplied by the companies, because the patrons could differ substantially over the larger area.

New prevention measures enforced

Less people started to question the relevance of the germ theory to cholera.

New prevention and control measures developed to prevent cholera outbreaks (boiling water)

Improving the London waterworks

The S&V company was forced by the Metropolitan Water Act to move its intake to a location far upriver near Hampton.

6 steps of a statistical investigation

Could water supplied to South London residents by private companies be a principal vector for the transmission of cholera?

Large scale study of cholera fatal attacks in South London (water supply randomly "assigned")

Looking for patterns by comparing the occurence of cholera fatal attacks in the different population groups

People served by sewage-contaminated water seem more affected by fatal cholera attacks

Contamined water is most likely a source of cholera infection. Cholera is a waterborne disease.

Need for analyzing water samples (identify "germ").
Boiling water mandatory during cholera epidemics.

Summary

Data are everywhere.
A dataset is usually comprised of variables measured on observational units.
Variables can be
Categorical
Quantitative
Response
Explanatory
Data can be used to provide information about essentially anything we are interested in and want to collect data on!
Statistics is a powerful tool to draw inferences and make decisions.
Don't say that the hypothesis has been proven right or wrong, but rather say that evidence is either strong or weak.