Experimental design and statistical methods in biology

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Experimental design and statistical methods in
biology

• Some practical information

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Teachers

• Lektor Anders Michelsen, Dept. of Terrestrial
  Ecology andersm_at_bi.ku.dk (responsible for
  practicals)
• Ph.D. student Kristian Albert, Dept. of
  Terrestrial Ecology kristiana_at_bi.ku.dk (assistant
  at the practicals)
• Lektor Gösta Nachman, Dept. of Population Biology
  gnachman_at_bi.ku.dk (responsible for the lectures
  and course organizer)

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Suggested further readings readings

• Biometry by Sokal, R.R. Rohlf, F.J.
• Biostatistical Analysis by Zar, J.H.
• A primer of Ecological Statistics by Gotelli,
  N.J. Ellison, A.M.
• Introduktion til SAS med statistiske anvendelser
  af Jensen, J.E. og Skovgaard
• SAS System for Linear Models by Littell et al.

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Kursets hjemmeside er
www.bi.ku.dk
Courses\Course home pages
Logon er Biologi
Password er biku
Kurset findes under B.Sc. Courses/ 3rd year
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Experimental design and statistical methods in
biology

• Lecture 1
• Introduction
• General linear models and design of experiments

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Why statistics?

• Because it is demanded by your supervisor or a
  scientific journal
• Because you want to make your arguments in favour
  of your hypothesis more convincing.
• Because your observations contain so much scatter
  that you cant see any clear pattern.
• Because you have so many factors simultaneously
  affecting your observations that you cant
  identify which one(s) are the most important.

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Problem
Observations
Scientific approaches
Conclusion
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What is a General Linear Model?
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Examples ofGeneral Linear Models (GLM)
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Simple linear regression  
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Polynomial regression  
Ex   y depth at disappearance x
nitrogen concentration of water
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Multiple regression  
Eks   y depth at disappearance x1
Concentration of N x2 Concentration of P
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Analysis of variance (ANOVA)
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Analysis of covariance (ANCOVA)
Ex   y depth at disappearance x1 Blue
disc x2 Green disc x3 Concentration of N
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Nested analysis of variance
Ex   y depth at disappearance ai effect of
the ith lake ß(i)j effect of the jth
measurement in the ith lake
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What is not a general linear model?

• y ß0(1ß1x)
• y ß0cos(ß1ß2x)

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Other topics covered by this course

• Multivariate analysis of variance (MANOVA)
• Repeated measurements
• Logistic regression
• Log linear models

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Topics covered if time allows

• Bayes statistics
• Maximum likelihood estimation
• Akaikes information index
• Power analysis
• Randomization methods (resampling, jackknife,
  bootstrap)

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Experimental designs

• Some examples

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Note
If you plan your experiments in a clever
way, i.e. use a standard experimental design, you
get the appropriate statistical methods served on
a silverplate!
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Randomised design

• Effects of p treatments (e.g. drugs) are compared
  
• Total number of experimental units (persons) is n
  
• Treatment i is administrated to ni units
• Allocation of treatments among units is random

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Example of randomized design

• 4 drugs (called A, B, C, and D) are tested (i.e.
  p 4)
• 12 persons are available (i.e. n 12)
• Each treatment is given to 3 persons (i.e. ni 3
  for i 1,2,..,p) (i.e. design is balanced)
• Persons are allocated randomly among treatments

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Drugs Drugs Drugs Drugs Drugs
A B C D Total
y1A y2A y3A y1B y2B y3B y1C y2C y3C y1D y2D y3D

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Source Degrees of freedom
Estimate of Treatments ( ) Residuals 1 p - 1 3 n-p 8
Total n 12
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Randomized block design

• All treatments are allocated to the same
  experimental units
• Treatments are allocated at random

B C B
A B D
D A A
C D C
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Treatments Treatments Treatments Treatments Treatments Treatments Treatments
Persons A B C D Average
Persons 1
Persons 2
Persons 3
Average
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Randomized block design
Source Degrees of freedom
Estimate of Blocks (persons) Treatments ( drugs ) Residuals 1 b - 1 2 p-1 3 n-(b-1)(p-1)1 6
Total n 12
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Double block design (latin-square)
Person Person Person Person Person
Sequence 1 2 3 4
Sequence 1 B D A C
Sequence 2 A C D B
Sequence 3 C A B D
Sequence 4 D B C A
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Latin-square design
Source Degrees of freedom
Estimate of Rows (sequences) Blocks (persons) Treatments ( drugs ) Residuals 1 a-1 3 b - 1 3 p-1 3 n-3(p-1)1 6
Total n p2 16