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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