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Philosophy of Science: the Scientific Method

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Philosophy of Science: the Scientific Method Philosophy of science: the scientific method Philosophy How we understand the world Science A “method” for achieving this goal Development of theory Formulation of hypotheses - predictions Tests of predictions Design & Analysis How we test predictions of hypotheses Statistics Tool for quantitative tests Definitions Theory: a set of ideas formulated to explain something Hypothesis: general – supposition or conjecture put forth in the form of a prediction according to a theory, observation, belief, or problem specific – formulation of a general hypothesis for application to a specific test (observational OR experimental) Null hypothesis: expected outcome if supposed mechanism is not manifested (i.e. “no effect”) Predictions: expected outcomes if both assumptions and conjecture are correct Definitions (examples) Theory: species distributions determined by dispersal of offspring Hypothesis: general – larval settlement of mussels determines adult distribution (i.e. is restricted to the area inhabited by adults) specific – if we sample larval settlement of mussels in and out of adult distribution, then settlement will only occur within area inhabited by adults Null hypothesis: if we sample larval settlement of mussels in and out of adult distribution, there will be no difference in settlement (i.e. density of settlers) Predictions: theory predicts that larval settlement will only occur where adults are Definitions Induction (or inductive reasoning): reasoning that general laws exist because particular cases that seem to be examples of it exist Deduction (or deductive reasoning): reasoning that something must be true because it is a particular case of a general (universal) law known to be true induction specific general deduction 5 swans seen, all are white all swans are white Examples Induction (or inductive reasoning): Every swan I have seen is white, therefore all swans are white (if) (particular/observation), (then) (universal/ inference) Deduction (or deductive reasoning): All swans are white, therefore next swan I see will be white (if) (universal/ theory), (then) (particular/observation) “DIGS”: deductive is general to specific Comparison: 1. Which is more testable? What if next swan is not white? 2. Which is normally used in everyday experience? 3. Which is more repeatable by different people? Hypothetico-deductive reasoning Deduction (or deductive reasoning): formalized and popularized as basis of scientific method by Karl Popper (in readings) Two phases: conception and assessment Conception: how one comes up with a new idea or insight (“rules” of formulation are not obvious). -- theory, observation, belief, problem -- creative, difficult to teach, but often inductive! Assessment: deductive phase, should be repeatable Together, hypothetico-deductive reasoning Hypothetico-deductive reasoning Perceived Problem I. Conception Largely inductive reasoning Previous Observations Belief *Note: General hypothesis INSIGHT stated as alternative HA to null H O Existing Theory General hypothesis* rejection II. Assessment Specific hypotheses Deductive reasoning Confirmation (and predictions) Falsification H “supported (confirmed)” A H rejected H rejected A O H “supported (confirmed)” Comparison with O new observations or experimental results Hypothetico-deductive reasoning Platt’s (1964) “Strong Inference” 1) Is there provision for “accepting” general hypothesis? Why not? Because it is easy to find confirmatory observations for almost any hypothesis, there is always the possibility of a negative result yet to be tested, and only one negative result refutes it absolutely 2) Propositions not subject to rejection (not falsifiable) are not “scientific”. 3) Progress made by repeated testing (rejection or confirmation) of alternative hypotheses until all reasonable ones have been tested (“last man standing”). Copyright 2016 Jason Matthias Mills Coyote bush (Bacchar Copyright 2012 Jean Pawek Western Water Hemlock (Cicuta) Copyright 2010 Vernon Smith Rush (Juncus) Pickleweed (Salicornia) Younger Lagoon from outlook by OHB 1-7-2019 Copyright 2016 Neal Kramer Example – Platt’s (1964) “Strong Inference” 1) Observation: discrete distributions of vegetation along elevation gradient (zonation) adjacent to Younger Lagoon (S) (R) (H) Hemlock (H) 100 percent Rush (R) cover 50 Salicornia (S) 0 02468 elevation (m) above mean water level Example – Platt’s (1964) “Strong Inference” 1) Observation: discrete distributions of vegetation along elevation gradient (zonation) adjacent to Younger Lagoon Is there any existing theory to explain this pattern? Limits of species distributions often set by their relative tolerance to physical factors: -- water immersion -- salinity -- desiccation -- soil characteristics Insight: distribution limits set by tolerance to water immersion 2) General hypothesis: (HA) lower limit of rush set by tolerance to immersion [alternatively, “null hypothesis” (Ho) of no effect of immersion on lower limit of rush distribution] Example – Platt’s (1964) “Strong Inference” 2) General hypothesis: lower limit of rush set by tolerance to immersion (alternatively, “null hypothesis” of no effect of immersion on lower limit of rush distribution) 3) Specific hypotheses: Observational – if we measure the water and plant levels, then… HA: average water level coincides with lower limit of rush; Ho: no relationship between water level and lower limit. Experimental – if we transplant… then… HA rush plants transplanted to clearing below lower limit will die. Ho: no difference in survival between transplants and controls Example – Platt’s (1964) “Strong Inference” 4a) Test of prediction: repeatedly observe water levels and find that lower limit of rush coincides with mean water level ( confirm hypothesis that lower limit set by immersion). Consider other tests (e.g., other species) of general hypothesis 4b) Test of prediction: repeatedly observe water levels and find that lower limit of rush does NOT coincide with mean water level ( reject hypothesis that lower limit set by immersion). Consider other alternative hypotheses until you can’t reject one. 5a,b) Parallel results and conclusions from experimental tests of predictions – Why?? correlation vs. causation Example – Platt’s (1964) “Strong Inference” 1) Observation (or theory) Question 2) General hypothesis (question rephrased as testable statement) 3) Specific hypothesis (that state testable predictions that are directly related to how you would test the general hypothesis) 4) Test(s) of prediction(s) confirm hypothesis consider other tests of general hypothesis to possibly reject or further substantiate reject hypothesis consider other alternative hypotheses until you can’t reject one. Problems 1) This process leads to “paradigms”, a way of thinking that has many followers, with great inertia. Contrary evidence considered an exception rather than evidence for falsification. 2) Some (e.g., Roughgarden) argue that this is not how we do science, but rather by building a convincing case of many different lines of evidence (i.e. inductive conception and assessment) 3) Others (e.g., Quinn & Dunham) argue that ecology, in particular, is too complex (many variables that interact with one another) to devise unequivocal tests. Examples: importance of process (e.g., competition) is context dependent (e.g., environmental harshness or recruitment limitation) 4) In ecology, we’re often interested in relative effects and strengths of effects (rather than mere presence – absence of effects). Rigorous Science Based on absolute or probability values? The linkage between Popperian science and statistical analysis Absolute vs. measured differences A) Philosophical underpinnings of Popperian Method is based on absolute differences. E.g., All swans are white, therefore the next swan I see will be white. If the next swan is not white, then the hypothesis is refuted absolutely. B) Instead, most results are based on comparisons of measured variables not really true vs. false but degree to which an effect exists (recall Quinn and Dunham) Absolute vs. measured differences Example: General or working hypothesis: larval settlement determines adult distribution Specific hypothesis: if we count the number of mussel larvae settling inside and outside the adult distribution, then counts will be higher inside the the adult distribution Observation 1: Observation 2: Number outside Number inside Number outside Number inside 010310 01557 01829 012812 01378 Mean 013Mean 5 9.2 What counts as a difference? Are these different? Statistical analysis - cause, probability, and effect Specific hypothesis HA: if we count the number of I) What counts as a difference - this is mussel larvae settling in areas a statistical & philosophical inside and outside the adult question of two parts distribution, then counts will be higher inside than outside A) How shall we compare measurements - statistical Conception - Inductive reasoning methodology? Perceived Problem Previous Observations Belief INSIGHT B) What will count as a significant Existing Theory difference? philosophical question General hypothesis and as such subject to convention Specific hypotheses Confirmation(and predictions) Falsification HA rejected HA supported (accepted) H O supported (accepted) HO rejected Comparison with new observations Assessment - Deductive reasoning Statistical analysis - cause, probability, and effect II) Statistical Methodology Specific hypothesis HA: General Hypothesis testing if we count the number of 1) In most sciences, we are faced with: mussel larvae
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