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BIO 4118 Applied Biostatistics

• Scott Findlay
• Vanier 306, 313, 314
• sfindlay_at_science.uottawa.ca
• 562-5800 x4574

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About me

• Not a statistician
• So, emphasis will be on practical knowledge and
  application of statistics, rather than theorems
  and proofs.

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Why you should be here

• you have an interest in statistical reasoning
• you have a desire to learn to use statistics
  properly in experimental design and data analysis
• you want to develop your ability to critically
  assess scientific (or pseudo-scientific) arguments

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What is expected of you

• attendance at most lectures
• attendance at most laboratory sessions
• feedback to me on what you like and dislike about
  the course, especially how it can be improved

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Objectives

• Understand the fundamental principles of
  statistical inference.
• Understand the general principles underlying the
  most common tests.
• Know the assumptions of common tests and
  understand impact of violations.
• Be able to perform standard statistical analyses
  with SYSTAT.

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Evaluation

• 60 Problem assignments
• 40 Term projects

• All assignments are open-book, and can be done
  in groups of three people or fewer.
• Remember, plagiarism is not acceptable!

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Texts

• Morin, A. C.S. Findlay 2001. Course Notes for
  BIO 4118 Applied Biostatistics. University of
  Ottawa, Ottawa.
• Findlay, C.S. A. Morin 2001. Lecture
  Presentations for BIO 4118 Applied Biostatistics,
  Vol. 1. University of Ottawa, Ottawa.
• Sokal, R.L. F.J. Rohlf. 1995. Biometry (3rd
  edition), W.H. Freman Co., New York, or
• Zar, J.H. 2000. Biostatistical Analysis (4th
  edition), Prentice-Hall, Upper saddle River, New
  Jersey.

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Class preparation

• Read appropriate chapter(s) in lecture notes
  beforehand and bring questions to class.
• If youve got a question, ask it immediately!
  There is no such thing as a stupid question!
• For labs, read appropriate section(s) in lecture
  notes beforehand.

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Extended classroom structure
Lectures
Me
Laboratory
Course Web
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Accessing the course web

• Obtain account for one of campus servers (e.g.
  for Proktor (Faculty of Science)).
• Log on using your user ID and password, then
  launch Netscape.
• Enter www.edteched.uottawa.ca in the location
  field.
• At the Teaching Technologies home page, click on
  Course Webs (under Applications), then Science (a
  yellow box on the left).
• Click on BIO 4118 - youre there!

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Remote access

• Launch Netscape and follow the same procedures,
  except...
• ...you will be asked for a user ID and password
  to get into the Course Webs home page.
• UserID is bio4118 Password is Findlay.

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Components of Course Web

• Syllabus and outline (Course info)
• Lectures and summaries (PPT images) (Lectures)
• Laboratory solutions (Laboratories)
• Old exams solutions, problems solutions
  (Problem-solving)
• Incidental info, commentary, responses to
  questions (Whats new)

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Lecture 1 The role of statistics in the
scientific method

• The hypothetico-deductive approach
• Falsification of hypotheses
• Evaluation criteria for scientific hypotheses
• Uses of statistics
• What statistics can do
• What statistics cant do
• Selection criteria for statistical tests

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Some opinions of statistics
If your experiment needs statistics, you should
have done a better experiment. Ernest Rutherford

• There are three types of lies lies, damn lies,
  and statistics!
• Benjamin Disraeli

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Some opinions of statistics

• To call in a statistician after the
  experiment is done may be no more than asking him
  to perform a postmortem

• The purpose of models is not to fit the data,
  but to sharpen the questions.
• Samuel Karlin

examination he may be able to say what the
experiment died of. Sir Ronald Fisher
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The hypothetico-deductive approach
Hypothesis
Deduction
Induction
Predictions
Question
Experiment
Observations
Conclusions
Inference
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Falsification of hypotheses

• Scientific hypotheses can only be corroborated or
  falsified, not confirmed.
• Hypotheses that have been rigorously tested come
  to be regarded as a fact, but should not be
  considered true.

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Evaluation criteria for scientific hypotheses

• Generality
• Accuracy
• Precision
• Simplicity

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Hypothesis generality

• A more general hypothesis eliminates more
  possibilities and applies to more situations.
• e.g. in lakes, primary production is controlled
  by nutrient levels, versus
• in small temperate lakes, primary production
  depends on the relationship between nutrient
  levels and consumption by zooplankton.

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Hypothesis accuracy

• Two theories y is a (1) linear or (2) non-linear
  function of x.
• Observations are, on average, closer to
  predictions for the more accurate theory.

More accurate theory
Observed
Less accurate theory
Expected
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Hypothesis precision

• Two theories H1 y is a linear function of x1,
  or H2 y is a linear function of x1 and x2.
• Since for given x, the difference between
  replicate measurements of y is smaller for H2, it
  is the more precise theory.

Less precise theory
More precise theory
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Simplicity

• Better hypotheses are simpler, easier to
  understand, or more economical or practical to
  use.
• e.g. D 15 W-1.16
• D a bWc c sin(x1) fx2- gx3

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The uses of statistics
Description
Design
Hypothesis-testing

• Provide a data summary
• Help discover trends and patterns.
• Evaluate magnitude and direction of experimental
  effects

• Assist in the design of experiments and field
  studies
• A priori decisions about usefulness of
  experiments.

• Evaluate biological hypotheses by testing to see
  whether observed patterns are consistent with
  predictions.

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Use of statistics inference

• Are observed differences real or simply due to
  chance?
• To answer this question, we need to know the
  probability that observed results are in fact due
  to chance.
• Statistical tests allow us to estimate this
  probability and draw a conclusion.

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Use of statistics description synthesis

• Provide a data summary.
• Help discover trends (induction) through
  examination of summary statistics for patterns.
• Remember in statistical summaries, information
  is lost. So retain your raw data!

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Use of statistics experimental design

• Allocation of effort
• A priori decisions about usefulness of experiments

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What statistics can and cant do

• provide objective criteria for evaluating
  hypotheses
• help optimize effort
• help you critically evaluate arguments

• tell the truth (probabilistic conclusions only!)
• compensate for poor design
• indicate biological significance statistical
  significance does not mean biological
  significance, nor vice versa!

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Four important questions to ask yourself before
beginning any statistical analysis

• Is there any reason to believe that your
  observations are independent and that in fact the
  data represent a random sample? And if so,
  random with respect to what?
• Is it even possible to answer your question with
  the data you collected?
• Can the contemplated analysis even answer your
  question, assuming there is an answer?
• Are there alternate ways of analyzing the data?

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The four ages of statistical man
Age Defining characteristics Comment
Stone Total ignorance Ignorance is not bliss!
Bronze Nodding familiarity, but understanding purely superficial Statistics a (small) sidebar to scientific investigation (See Rutherford, Ernest)
Silver Moderate familiarity coupled with a strong desire to demonstrate same statistical reach exceeds grasp Overwhelming concern with statistical minutae scientific forest often obscured by statistical trees.
Gold Knows when statistical issues are (and are not) important recognizes limitations (of self and statistical science) That to which we can/should all aspire.
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Selection criteria for statistical tests

• The question (hypothesis to be tested) and the
  nature of the data
• The extent to which the assumptions of the test
  are met, and how sensitive the test is to
  violation of these assumptions
• The power of the test