Empiricism rests on the idea that nature is governed by laws or principles that create predictable patterns which can be discovered through careful observation.
Statistics is the quantitative technology for empirical science.
Most of the “evidence” you will evaluate will be a story derived from data interpreted in statistical form.
Deductive Reasoning
You start with a general principle(s)—similar to axioms in mathematics—as a starting point and use logic to deduce a conclusion. It is the kind of reasoning you used when developing proofs in your geometry course in high school.
Syllogism is an example of simple deductive reasoning. There is a first and second premise and finally a conclusion which follows logically from these premises.
Major Premise: All dogs are friendly.
Minor Premise: Your new neighbor has a dog.
Conclusion: Your neighbor’s dog is friendly.
The problem is the overgeneralization in the major premise—some might call it naiveté.
Inductive reasoning
i.e.t. a prediction
The process of deriving general principles (conclusions) from repeated facts or observations—that is, the particular to the general.
Down syndrome (DS) is a relatively common disorder in humans. Geneticists tell us that individuals with DS have three copies of chromosome 21 instead of two. How did they reach this conclusion? A French geneticist in 1959 analyzed chromosomes of individuals with what was believed to be Down syndrome and observed an extra copy of chromosome 21 in each of them. This discovery was later confirmed by further studies using more advanced techniques.
Is this absolute proof that an extra copy of chromosome 21 is the only cause of DS? No.
Unlike deductive reasoning, induction is not guaranteed to produce absolutely true conclusions.
Basic Statistical Concepts
A population is the total set of subjects or things we are interested in studying.
A list containing all members of the population is referred to as a frame.
A strict definition of a census is a survey that includes all the elements or units in the frame.
A measurement that describes some aspect of the entire population is called a population parameter. A population can have many parameters.
A sample is a subset of the population which is used to gain insight about the population. Samples are used to represent a larger group, the population.
A statistic is a fact or characteristic about the sample.
Descriptive Statistics
i.e.t. a claim with facts
The emphasis in descriptive statistics is analyzing observed measurements, usually from a sample. Descriptive methods provide a powerful means of summarizing and simplifying data sets. We use descriptive statistics to begin telling the data’s story by answering questions like what is a typical value for the measurements?
Descriptive statistics is the collection, organization, analysis, and presentation of data.
Inferential Statistics
i.e.t. an educated guess
Historically, the ozone layer over most of the Earth’s surface is about 3 millimeters thick. A problem such as trying to assess the ozone thickness over the entire surface of the earth at a point in time would be an impossible sample space to measure. There is no way to know the actual thickness of the ozone layer except by an inductive process: namely sampling, data collection, and statistical inference.
The objective of inferential statistics is to make reasonable estimates of population characteristics using sample data.
Review
I am a little confused on identifying inductive vs deductive reasoning