Epistemology of Statistics

Statistical and Neural Classifiers

Andrius: We are collecting and systematizing the ways of figuring things out in statistics. Thank you for helping us!

The insights we gain may, in general, help us understand the assumptions that experimental science depends upon, and in particular, help us interpret and analyze the Raudys hierarchy of

Statistical and Neural Classifiers⁠

as expressing how a single layer perceptron grows in conceptual sophistication.

Sources of Examples

⁠

Wikipedia: Statistics⁠

⁠

Anderson, Norman (2001). Empirical Direction in Design and Analysis.

Huff, Darrell (1954).

How to Lie With Statistics⁠

Collection of Examples

Andrius: I am starting by collecting very basic examples inspired by the Wikipedia article.

Defining a population Simply defining a population gives us a first step in formulating what we are interested in.

Classification Distinguishing categories amongst a population.

Ranking Ordering elements. Determining the median and percentiles.

Measuring, adding, substracting using an

interval scale⁠

As with temperature on a Fahrenheit scale. Addition and substraction may be meaningful but there is no meaningful zero with regard to which multiplication or division could be performed.

Measuring, multiplying, dividing, using a

ratio scale⁠

Where zero is meaningful, and thus multiplication and division of values is meaningful.

Sampling Establishing and characterizing a representative sample allows us to draw conclusions about the entire population.

Averaging Averaging reduces a population to a single, typical individual.

Deviation Deviation allows us to consider the extent to which a particular individual resembles or not a typical individual.

Bounding errors Calculating error bounds distinguishes what is believable from what is not.

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