Philosophy of science: the scientific method

Philosophy How we understand the world

Science A “method” for achieving this goal

Design & Analysis How we test predictionsof hypotheses

Development of theoryFormulation of hypotheses - predictionsTests of predictions

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)

Predictions: expected outcomes if both assumptions and conjecture are correct

Null hypothesis: expected outcome if supposed mechanism is not manifested (i.e. “no effect”)

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

Predictions: theory predicts that larval settlement will only occur where adults are

Null hypothesis: if we sample larval settlement of mussels in and out of adult distribution, there will be no difference in settlement

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

specific general

induction

deduction

all swans are white5 swans seen, all 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)

1. Which is more testable? What if next swan is not white?

Comparison:

2. Which is normally used in everyday experience?

3. Which is more repeatable by different people?

“DIGS”: deductive is general to specific

Hypothetico-deductive reasoning

Deduction (or deductive reasoning): formalized and popularized as basis of scientific method by Karl Popper (in readings)

-- theory, observation, belief, problem

Conception: how one comes up with a new idea or insight (“rules” of formulation are not obvious).

Together, hypothetico-deductive reasoning

-- creative, difficult to teach, but often inductive!

Two phases: conception and assessment

Assessment: deductive phase, should be repeatable

INSIGHT

Existing Theory

General hypothesis*

Previous Observations

Perceived Problem

Belief

Comparison withnew observations

or experimental results

Specific hypotheses

(and predictions)

I. ConceptionLargely inductive reasoning

Deductive reasoning Confirmation

H “supported (confirmed)”

H rejectedO

A

II. Assessment

Hypothetico-deductive reasoning

*Note: General hypothesis

stated as alternative HA

to null HO

Falsification

rejection

H rejected

H “supported (confirmed)”O

A

Hypothetico-deductive reasoningPlatt’s (1964) “Strong Inference”

1) Is there provision for “accepting” general hypothesis?Why not?

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”).

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

Example – Platt’s (1964) “Strong Inference”

1) Observation: discrete distributions of vegetation along elevation gradient (zonation) adjacent to Younger Lagoon

Anise (A)

Rush (R)

Salicornia (S)

elevation (m) above mean water level

percentcover

00 2 4 6 8

50

100

(S) (R) (A)

Example – Platt’s (1964) “Strong Inference”

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]

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

Example – Platt’s (1964) “Strong Inference”

3) Specific hypotheses:

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)

Observational – HA: average water level coincides with lower limit of rush; Ho: no relationship between water level and lower limit.

Experimental – 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).

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 tests (e.g., other species) of general hypothesis

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”

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)

1) Observation (or theory) Question

reject hypothesis consider other alternative hypotheses until you can’t reject one.

confirm hypothesis consider other tests of general hypothesis to possibly reject or further substantiate

Problems

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)

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.

4) In ecology, we’re often interested in relative effects and strengths of effects (rather than mere presence – absence of effects).

Rigorous ScienceBased on absolute or probability values?

The linkage between Popperian science and statistical analysis

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)

Example - General or working hypothesis – larval settlement determines adult distribution

Specific hypothesis – number of mussel larvae settling is higher in areas inside the adult distribution than in areas outside it

Absolute vs. measured differences

Number inside

Observation 2:

Number outside Number inside 3 10 5 7 2 9 8 12 7 8

Mean 5 9.2

What counts as a difference?Are these different?

Observation 1: Number outside 0 10 0 15 0 18 0 12 0 13

Mean 0 13