In The Design of Experiments, Ronald A. Fisher writes, “We may at once admit tha

Question

In The Design of Experiments, Ronald A. Fisher writes, “We may at once admit that any inference from the particular to the general must be attended with some degree of uncertainty, but this is not the same as to admit that such inference cannot be absolutely rigorous, for the nature and degree of the uncertainty may itself be capable of rigorous expression.”

Keeping in mind what you have learned this week, discuss the quotation. How “significant” should results be to be relied on? Are there situations or scenarios where the nature of the uncertainty affects the ability to infer from statistical results.

Explanation / Answer

We need statistics in order to know something about a large group of something after only studying a small group of that something. We take a sample of a population and study it, and then we can usually draw conclusions about the rest of the population without also studying each member of the population individually.
It helps us to be sure that when we try to generalize about some pattern in the weather, behavior of certain people, or the yield of a chemical reaction, that it is objective mathematics that is doing the calculating and not anecdotal evidence based only on human experience.
      We generalize about patterns and data every day, we just don't call it statistics when we do. We also count things every day, but we don't call it math when we do. Statistics and Multivariable Calculus are both just refined versions of the skills we already use. Understanding statistics makes you a more objective person and increases your ability to generalize about patterns and populations. Statistics is becoming increasingly more important in modern society with passing time. We are constantly being bombarded with charts, graphs, and statistics of various types in an attempt to provide us with succinct information to make decisions. Sometimes this information is presented in a manner so as to sway us toward a particular.

A few examples on how and where we use this type of math is as consumers and decision makers we use it for which drug should we take, or which car should we buy? We can even use it for the economy. These are all examples of questions which are usually relegated to the statistician for analysis and dissemination. This lecture will attempt to introduce the beginning to student some of the reasoning behind the necessity of statistical inference.  

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