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Classification of Statements in Science
Non-empirical
(Definitions, Applied Math)
vs.
pH is defined as – log of [H+]
Empirical
(Observations, Experiments)
vs.
For a given star, the angle of parallax
decreases as distance increases.
pH of pure water = 7
vs. The parallax angle of the nearest
star is less than 1/3600 of one degree.
An Important Distinction Within the Empirical Domain:
Universal Generalizations
(All A’s are B’s. If something is an A,
it definitely is a B.)
Examples of laws of nature:
Law of reflection, refraction, falling bodies
Boyle’s Law, Le Chatlier’s Principle
vs.
Statistical Generalizations
(80% of A’s are B’s. If something is an A
the odds are 4 to 1 it’s a B.)
Statistical laws seem to be rarer:
Mendel’s Laws of Inheritance, the
half-life of C14 is 5730 years.
Laws (Nomic) vs. Contingent (Accidental):
Some generalizations under both universal and statistical appear to be true, but only
“accidentally” so – we can easily imagine a world very like ours in which things were
different.
Contingent (as opposed to law-like):
All dinosaurs are extinct. All samples
of gold weigh less than 2 trillion tons.
Contingent statistical claims:
Most swans are white. Carbon, oxygen,
and nitrogen make up 1.5% of our sun.
Dichotomous vs. Continuous Variables:
Our Venn diagrams could only represent two-valued categories (e.g., A and not-A). To
simplify the math most of our statistical examples will also work with only two or three
categories. Scientists, however, frequently use continuous variables.
All of the examples of laws of nature
above have continuous variables.
A correlation between the height and
weight of children would likely use
continuous variables.
An example using dichotomous variables
would be: All metals conduct electricity.
Statistical claims about Democrats
vs. Republicans would use
dichotomous variables.
Different Testing Strategies
Although all branches of science pose problems, formulate hypotheses, and test them
empirically, in statistical sciences the typical testing strategies are different.
Tests of universal generalizations
focus the search on the most likely
domains in which to find refutations.
Small sample size is often O.K.
Tests of statistical generalizations
ideally use large, random samples.
What gets refuted is typically the
so-called Null Hypothesis.
Often the number of variables required
to make good predictions is small and
causal connections are apparent.
Many causal factors may play a role
and it may be difficult to quantify the
contribution of each.
Example: Gravitational attraction depends
only on the masses of bodies and the
distance between them.
Example: Causal factors mentioned
for depression range from a recent
loss to hormones, drugs, and genes.
Key Concepts
Relationship between sample size, statistical significance and margin of error
Statistical significance vs. practical significance (what Giere calls effectiveness)
Relationship between correlation and causation
Varieties of causal structures – proximate vs. ultimate causes, common cause, screenedoff causal factors
Randomized controlled test (RCT) vs. prospective study vs. retrospective study
Advantages and disadvantages of each
Miscellaneous: single blind, double blind, placebo, “natural” experiment