Lies, Damned Lies, and Health Physics

Report
Lies, Damned Lies,
and Health Physics
Some Random Comments About
Statistics in Health Physics
Tom LaBone
Savannah River Chapter of
the Health Physics Society
Aiken, SC
April 15, 2011
1
“There are three kinds of lies: lies, damned lies,
and statistics.”
Mark Twain
“It is easy to lie with statistics.”
“It is hard to tell the truth without statistics."
Andrejs Dunkels
2
Today

Informal, mostly apocryphal discussion of




Main message of talk



what statistics really is,
who practices statistics and how they do it, and
why all of this is important to you as a health physicist
A good working knowledge of statistics is essential in any
endeavor where data are collected and analyzed (e.g., health
physics)
Everyone in the room should become a statistician (of sorts)
No math is used in this presentation and no health
physicists were harmed during its preparation
3
Health Physics and Statistics

Some HP “stat” books I used in school
F. Knoll Radiation Detection and Measurement 1st
Edition 1979
 J. Shapiro Radiation Protection 1nd Edition 1972
 H. Cember Introduction to Health Physics 1st Edition
1969
 R. D. Evans The Atomic Nucleus 1955
 P. R. Bevington Data Reduction and Error Analysis for
the Physical Sciences 1st Edition 1969
 G.

Statistics was a tool, a “wrench to turn a nut”
 Is
that all it is?
4
What is Statistics?
“Humans are good, she knew, at discerning subtle
patterns that are really there, but equally so at
imagining them when they are altogether absent.”
Carl Sagan in Contact
5
Signals and Noise
Useful information comes to us in the form
of signals that form distinct patterns
 The signals are contaminated with varying
degrees of noise, which can make it
difficult to see the signal

6
Seeing Patterns

In our evolutionary history,
seeing patterns where none
existed may have been less
harmful than missing patterns
that did exist
noise in the grass – is it
just the wind or is it a lion?
 That

So, we as a species got very
good at seeing patterns, even
in the absence of a signal
7
Apophenia
Apophenia is the experience of seeing
meaningful patterns or connections in
random or meaningless data
 What do you see below?

8
Face on Mars
Viking 1 Orbiter
Mars Global Surveyor
9
Face in Food, et cetera
10
Face in Data
11
Statistics is …




… a science that helps us to differentiate signal
from noise and make decisions with a known
probability of being wrong
… a very practical, decision oriented
methodology developed to tame our natural
tendency to be Apopheniacs
… based on the idea that variability and noise
are natural and unavoidable
… a relatively modern science that is actively
evolving
 especially
since cheap, powerful computers became
available
12
Really, What is Statistics?
“Statistics is concerned with collecting,
analyzing, and interpreting data in the best
possible way, where the meaning of “best”
depends on the particular circumstances of
the practical situation”
Chris Chatfield
Problem Solving: A Statistician’s Guide
13
Exploratory Data Analysis

Look at data (usually with graphics) and use our
ability to see patterns in the data to
 Suggest
hypotheses to test
 Assess validity of assumptions on which statistical
inference will be based
 Support the selection of appropriate inferential tests
 Suggest ideas for further data collection
14
Air Filters
Fecal Samples
Kinectrics Filters All
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Fecals as of 3/5/2011
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15
15
Confirmatory Data Analysis

Use statistical tests to answer questions
about the data along with the risks of
reaching the wrong conclusion
 Is
the material on the filters the same material
that is in the fecal samples?
 Are the Pu-239 to Am-241 ratios in the fecal
samples and air samples the same once we
account for random noise?
16
Fecal Samples
10
5
95% CI = (1.33, 1.46)
0
Am-241 (mBq)
15
2
0
2
4
6
Pu-239 (mBq)
8
10
12
17
Data Dredging



Are the two Pu-239 to Am-241 ratios the same?
If this question was asked before we saw the
data we can proceed with the test to answer it
If this question was inspired by the data then we
should not test the same data to get the answer
 Referred
to as data snooping, data dredging, etc.
 Cancer clusters
18
Statistical Method

Define the problem
 Formulate
your questions in such a way that
unambiguous answers are possible

Collect data
 Collect


data capable of answering your question
Analyze the data
Present the results
 in
terms your audience can understand
19
Define the Problem
“An approximate answer to the right problem
is worth a good deal more than an exact
answer to an approximate problem.”
John Tukey
"It is better to solve the right problem the
wrong way than to solve the wrong problem
the right way".
Richard Hamming
20
Data Collection

Collect data that are capable of answering
the question asked (Data Quality
Objectives)
 Designed
experiments
 Observational studies

Sampling
 You
select samples from a population in order
to make inferences about the population
21
GIGO


The collection of data is often the most timeconsuming and expensive part of a study
Reverend Bayes and all of his horses can’t fix a
bum dataset
22
Analyze the Data


All statistical procedures have assumptions
In practice, the assumptions of any given
statistical procedure are violated to some degree
 Can
 Can



the validity of the assumptions be verified?
the validity of the answer be verified?
How robust is your statistical procedure to
violations of its assumptions?
Simple approximate solutions you can understand
may be better than complex exact solutions that
you can’t
Augment standard statistical analyses with
simulations
23
Present Results

Technical answer versus the functional
answer
 “the
null hypothesis is not rejected”
 technically “not rejected” “accepted”
 functionally “not rejected” = “accepted”

Statistical significance and practical
significance
 Apply
“so what” test to your answers
24
What is a Statistician?
“Powerful spirits should only be
called by the master himself”
Goethe
The Sorcerer's Apprentice
25
What is a Statistician?



Based on Chatfield’s definition of statistics, anyone who
makes decisions based on the analysis of data might be
called a statistician
However, the title statistician is usually reserved for a
professional who has specialized training in the concepts,
theoretical bases, and methodologies of statistics
Key difference between the sorcerer and his apprentice


Contrary to what you might think, there is a lot of subjectivity and
professional judgment in the practice of statistics
Statistics is vast in scope and detail, and the apprentice does not
know what he does not know
“It ain't what you don't know that gets you into trouble. It's what you
know for sure that just ain't so.”
Mark Twain
26
The Sorcerer’s Apprentice


We may not be statisticians, but we are clearly
doing statistics, often without adult supervision
Doing our own statistics is a good thing, but we
need to become better students of the black arts
and consult the master before the brooms get
out of control
“Should I refuse a good dinner simply because I do not understand
the processes of digestion?”
Oliver Heaviside
[On being criticized for using formal mathematical manipulations without understanding
how they worked]
27
How We Can be Better Statisticians
Master the basics
 Learn the language
 Play with your data
 Use better software
 Perform reproducible work
 Consult with a real statistician

28
Master the Basics
Kahn Academy
http://www.khanacademy.org/
29
Statistics MS/Certificate
Distance Programs
University of South Carolina
 Colorado State University
 Texas A&M University
 Penn State University

30
Concepts and Terminology

Specialized Concepts


Statistics has a very precise language all its own



“the null hypothesis is not rejected”
“not rejected” “accepted”
Questions and answers are not right unless you use the
proper language to convey the proper concept


Population versus sample for example
some statisticians can be intolerant of laymen who misuse the
language of statistics
Learn to phrase questions and interpret answers
properly
31
Exploratory Statistics
Learn to play with
your data and see if it
is trying to tell you
something new
 Study graphs of your
data

“There is no data that can be
displayed in a pie chart, that cannot be
displayed BETTER in some other type
of chart.”
John Tukey
32
Software used for Statistics

I use the following software for statistical
calculations (in order of usage)
R
 Minitab
 SAS
 Spreadsheet

(e.g., MS Excel, Gnumeric)
There are many others
33
Spreadsheets (Excel)

What some people can do in Excel is nothing
short of amazing (but should they be doing it?)
 Amarillo
Slim beat tennis champ Bobby Riggs at PingPong, using a frying pan instead of a paddle

Spreadsheet Addiction by Patrick Burns
 http://lib.stat.cmu.edu/S/Spoetry/Tutor/spreadsheet_ad
diction.html

Problems with spreadsheet implementation
 Excel

has a long history of doing bad stats
Problems with spreadsheet paradigm
 Reproducible
science
34
http://www.msnbc.msn.com/id/21033161/from/RS.1/
9/28/2007
M. G. Almiron et al. On the Numerical
Accuracy of Spreadsheets, Journal of
Statistical Software (34) 4, 2010
35
Reproducible Research

Reproducible research refers to the idea that the ultimate
product of research is the paper along with the full
computational environment used to produce the results
in the paper such as the code, data, etc. necessary for
reproduction of the results
Raw Data
Data
Massaging
Calculations
Plots and
Tables
Final
Paper
36
The R Project for
Statistical Computing




R is a language and environment for statistical
computing and graphics
R is available as Free Software under the terms
of the GNU General Public License in source
code form
It compiles and runs on a wide variety of UNIX
platforms and similar systems (including
FreeBSD and Linux), Windows and MacOS
Download from http://www.r-project.org/
37
Advantages of R

Command line interface rather than a GUI
 Promotes

reproducible statistics
Open source
 Flexible licensing
 Availability of source
code for peer review
 Bugs are public knowledge and are fixed quickly
 New tests and methods tend to appear first in R


Many dozens of recently published books
devoted to R
Free (and very good) community support
available
38
Consult with a Statistician

If you are going to involve a statistician, do
it at the study design and data collection
phases
 If
not, at least estimate how much it will cost
to collect the data all over again

Anybody can analyze compelling data
“To call in the statistician after the experiment is done
may be no more than asking him to perform a postmortem examination: he may be able to say what the
experiment died of.”
Sir Ronald Fisher
39
Twisted Answers to
Crooked Questions


As health physicists there are times when a
decision will be made, with or without good data
and a proper statistical analysis
In such situations we base our decisions on
professional judgment, often augmented with
“statistics”
 We must not fool ourselves about what we are doing
 … of all the wrong answers we have to choose from, this one
is the best
 We
have no right to expect a statistician to endorse
such mischief
40
The Apprentice Should Beware of …
The Management Prior
 Being bamboozled by other people’s
statistics
 “The only right way to do this is X [insert
statistical method here]”
 Being seduced by complexity

41
Statistics in the Workplace:
Musings of a Sorcerer's Apprentice
Presentation to USC Stat Club
March 26, 2009

Main message
 A degree
in statistics is a “Swiss Army Knife” that is
very useful in any endeavor where data are collected
and analyzed
 Everyone in the room should become a health
physicist (I had no takers)
42

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