Ecologists generally, and marine biologists in particular, do not spend sufficient time, at least according to the available literature, in introspection about the nature of the science that they do Underwood AJ, 1991. The logic of ecological experiments: a case history from studies of the distribution of macro-algae on rocky intertidal shores. J. mar. Biol. Ass. U.K., 71:841-866. 1
Underwood AJ, 1997. Experiments in ecology: their logical design and interpretation using analysis of variance. Cmbridge University Press 2
What this course is not: An intro to statistics An exhaustive description of available analytical techniques A primer on the available software (SPSS, Statistica, SAS, R, S-Plus, etc.) 3
What this course is about: Being able do devise experiments to test hypothesis about nature Understanding the logic of experimental science and its tools Developing a critical attitude towards results and conclusions 4
LOGIC 5
What is science? What is a scientific method? 6
Maya: astrologer Do not deny beforehand a science that you don t know Não negue à partida uma ciência que desconhece 7
Scientific inference: The process of generating explanations of data with hypothesis/theories 8
Methods of scientific inference: Induction Deduction Abduction Hypothetico-deduction 9
Induction Multiple observations (instances) of a phenomenon lead to a generalization Francis Bacon (1561-1626) 10
Hypothesis: all swans are white Cygnus olor (Gmelin, 1789) 11
Abduction The hypothesis that is most consistent with the empirical evidence is to be chosen Charles Peirce (1839-1914) The father of pragmatism 12
Deduction Build a series of logical statements into an argument (syllogism): if the premises are true, the conclusion must be true. 1st Premise (Major): All men are mortal 2nd Premise (Minor): Socrates is a man Socrates (469-399 BCE) Conclusion: Socrates is mortal 13
Hypothetico-Deduction Coined the term Was himself an inductivist William Whewell (1794-1866) 14
Hypothetico-Deduction Popularized hypotheticodeduction by extending and formalizing its principles and operations Falsifiability as a demarcation criterion Karl Popper (1902-1994) Refutation of scientific proof 15
All swans are white Cygnus olor (Gmelin, 1789) FALSE Cygnus atratus (Latham, 1790) 16
Hypothetico-Deduction Hypotheses have a central role H0 = Null hypothesis HA = Alternative hypothesis No hypothesis, no experiments, and consequently no science 17
HA: X Y H0: false H0: X = Y HA: corroborated If the null hypothesis is false, the only thing left is the alternative hypothesis as the best explanation for the observations (until new evidence is gathered based on a new set of observations) 18
H0 is not always in the form X=Y (no difference) For example: HA: X > Y H0: X Y 19
Observations Model (Explanation or theory) H0 retained Hypothesis HA (Prediction based on the model) Wrong model! Null hypothesis H0 (Negation of HA) H0 rejected Model corroborated! (Continue testing) Experiment (Critical test of H0) Statistics Interpretation Do not stop here! 20
Why statistics? 21
Uncertainty in natural phenomena Skin pigmentation 22
Uncertainty in natural phenomena How to measure skin pigmentation? 23
We hardly have access to the whole population So we use samples (small sets actually subsets of the population) 24
Skin pigmentation Colorimeter Highly variable among subjects and even within the same subject (individual) Complex measuring devices have limitations in their precision and accuracy 25
Precision and accuracy (the target analogy) 26
R. A. Fisher (1890-1962) "We may at once admit that any inference from the particular to the general must be attended with some degree of uncertainty, but this is not the same as to admit that such inference cannot be absolutely rigorous, for the nature and degree of the uncertainty may itself be capable of rigorous expression." R. A. Fisher (1966) The Design of Experiments 27
Statistics Allow us to summarize the data Allow us to deal with uncertainty However, be aware that: If you torture the data long enough, Nature will confess." Ronald Coase (1901- ) 28
Population parameters µ = Average (Mean) σ = Standard deviation σ² = Variance 29
Sample estimates 30