What Is Statistics?
    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 view. As consumers and decision makers we
    must be aware of this.
    Which drug should we take? Which car should we buy?
    Where will the economy
    go? Who is infected with a particular deadly disease? 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.
     

    In order to realistically understand
    the subject of statistics
    it is important to
    appreciate the rationale behind why
    and how statistics is used by the world, at large.
    That is, why do we need statistics anyway?
    This, perhaps, is a bit
    philosophical, yet I can not over emphasize
    the need for thinking along these lines.  Without
    proper perspective, statistics
    becomes a  mere a mathematical exercise, diverging
    from the true nature of the subject.

    In order to begin our analysis as to why statistics is
    a necessary type of reasoning we must begin by addressing
    the nature of science and experimentation. A characteristic
    method used by Scientists is to study a relatively small collection of
    objects, say 2500 people, and a characteristic, say longevity,
    and through experimentation
    or observation, draw a conclusion appropriate for
    the entire class of objects (i.e., people, in general).
    For example,
    suppose a study published results suggesting
    people who own pets live longer.
    Would this mean that
    all people who own pets
    are likely to live long lives?
    Does owning a pet cause longevity?
    Suppose the people in the study, by chance, were on the
    whole, very healthy people, and therefore lived long lives:
    Would this invalidate the researcher's assertion that people who own
    pets live longer?
    The obvious problem with this type of reasoning is that these issues
    can never be proved absolutely. This type of scientific reasoning is called
    inductive reasoning and is inherently flawed. One can never study a
    sample and expect conclusions to hold true for the entire population with
    absolute certainty. This is exactly why statistics is needed.

    In contrast to the lack of certainty associated with  inductive reasoning,
    the type of logic used in Mathematics is absolutely certain. The
    mathematician begins with  general principles and logically concludes
    more specific relationships.
    This type of reasoning from the general to the particular is called
    deductive reasoning.
     A rather simplistic
    (but nevertheless correct)
    example is based on the principle that  two numbers can be added in any
    order, thereby giving the same sum.
    This is called the axiom of commutativity.
    An example of deductive reasoning would
    be to assert that since this holds for any two numbers, surely this
    must hold for
    the numbers
    two and three, in particular. We are, therefore,
    absolutely certain that
    2 + 3 = 3 + 2, given the axiom of commutativity.
     

    In its applied form,
    statistics
    then becomes a bridge between the inductive uncertainty
    of science and the deductive certainty of mathematics. In his classic book,
    The Design of Experiments,
    Sir Ronald A. Fisher expresses this idea beautifully:

    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 natureand degree of the uncertainty may itself be capable of rigorous expression.
     
     

    Statistics, therefore, is the mathematical method by which the
    uncertainty inherent in the
    scientific method is rigorously quantified.