Notes

Grammar means more generally, rules for art and science, as in the richly illustrated The Grammar of Ornament (Jones, 1856), and Karl Pearson’s The Grammar of Science Pearson, 1892).

Statistics vs. Probability:

What happened -> Statistics -> How the world works?

How the world works -> Probability -> What will happen?

Definition (Elements of Statistics):

The science of statistics may be described as exploring, analyzing and summarizing data; designing or choosing appropriate ways of collecting data and extracting information from them; and communicating that information. Statistics also involves constructing and testing models for describing chance phenomena. These models can be used as a basis for making inferences and drawing conclusions and, finally, perhaps for making decisions.

1. Motivation of using statistics: statistics as grammar of science: 

Statistics is necessary for making sound generalizations from particular observations. In other words, statistics helps us make sound inductive reasoning. We've already discussed that the scientific method has a largely inductive flavor in which observations are used to check the validity of an hypothesis. This makes statistics an ideal companion for science since scientific conclusions are mostly statistical in nature.

Probability, on the other hand, works from the general to the particular. Given that the probability of such and such is this (i.e., the general rule is given), find how many such and such occurs in a small sample (the particular observation is to be predicted). In this sense, probability is a perfect companion to statistics.

Probability guides us as to what we shall expect when we sample from a known population; Statistics guides us about the population by just observing a sample.

a. Pseudoscience vs. Science:

Which networking product in the market performs best? is Company A's product better, or company B's?

In network performance analysis and evaluation, such questions are settled through the usage of the 'scientific method' with evidence presented in the form of data and statistical conclusions rather than on the basis of anecdotal data and/ or opinion.

However, anecdotal data does seem to sway us to hasty generalizations and improper conclusions. This is due to our propensity to personalize and assume that our experience is typical for the general population. In general, this is not the case, and we would do well to remember the maxim: "the plural of anecdotes is not fact".

Karl Pearson, a famous British statistician whose contributions to science we will get an opportunity to study, stated that 'statistics is the grammar of science'; stated more simply, statistics is an integral part of good science and allows us to separate facts from myths.

b. Science of uncertainty:

The worldview scientists have today is essentially of a statistical nature in contrast to the prevailing idea in 19th and early 20th century of a clockwork universe in which everything is deterministic and determinable and the only reason we cannot predict how things will pan out is the fact that we have insufficient precision of information of our current state. This has, of course, taken a hit during the last century with the discovery of many classes of knowledge which are not only unknown but also are unknowable.

The works of Godel, Turing and recently Chaitin has shown that mathematics, or any formal system of logic, must contain some truths that are unprovable.

The field of quantum mechanics has shown that even at subatomic levels, reality pans out in a probabilistic sense and not in a deterministic system.

An old saying goes: "A person with a watch knows the time. A person with two watches is never sure.". Such an uncertainty is appreciated by a statisticians since it allows us to quantify how certain we can be about the conclusions we can draw from our data.

Good statistical education would also allow us to appreciate that all measurements (with the possible except of counting) is imprecise and has a sense of approximation. It seems to be a paradox, but as Bertrand Russel said, the foundations of science is based on a sense of approximation.

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