Author’s Comment
You may have heard someone say “You can
prove anything you want with statistics!” However, this is not true,
unless the audience is ignorant of how statistics works, or unless
the audience is not given essential information showing the validity—or
not—of important conditions and assumptions behind the statistical
techniques involved. In particular, you cannot be deceived,
unless you do not know how statistics works! Furthermore,
statistics cannot actually prove a particular conclusion, such as
a difference among different groups. The best statistics can do for you
is to tell you, within a formal, probabilistic framework, that an
observed difference among samples is probably different—or
not—from what would be expected to occur by chance if the samples came
from different groups having the same characteristics. Even though
statistics does not give you a proof, statistics does provide friendly
tools that give you conclusions based on real data and valid techniques,
so that, overall, you can be reasonably confident about the final
conclusions (while admitting the possibility of being wrong). However,
no matter how elegant the statistical analyses are, the conclusions of
the research may still be false, unless the data collected are valid
representations of the real world and all the components of the study
are properly designed and carried out.

The Intuitive Statistics Handbooklet
of Standard Deviation, Variance, et Cetera 
Simple Explanations
of the Measures of Variation and Their Associated Concepts,
Plus a Practical Exercise to Illustrate the Concepts
Ray L.
Winstead

Order this 55page handbooklet from Amazon.com
by clicking on either image of the cover of the book 
Book
Description
This 55page "handbooklet"
is intended for anyone at any level who wishes to have more intuitive
explanations of the concepts of standard deviation and variance, as well
as a better understanding of their formulas and associated concepts.
(Total of 66 pages.)
Part 1 explains the concepts of standard deviation and variance as
measures of variation.
Section I.1: Introduction and the Mean
Section I.2: Standard Deviation of a Population Characteristic
Section I.3: Standard Deviation of a Sample Characteristic
Section I.4: Variance
Part 2 explains some additional statistical concepts specifically
associated with standard deviation and variance, such as degrees of
freedom.
Section II.1: Unbiased and Biased Estimate
Section II.2: Degrees of Freedom
Section II.3: Distribution of Measurement Values
Section II.4: Point Estimate, Confidence Interval Estimate, and Standard
Error of an Estimate
Section II.5: Independent Variable and Dependent Variable
Part 3 provides a practical exercise to demonstrate the concepts of
standard deviation and variance, as well as simple statistical tests,
such as the ttest and Ftest, to compare the characteristics between
two groups. Strength of Association Measures are also examined.
Section III.1: Introduction to the Exercise and Calculations to Obtain
the Standard Deviation and Variance
Section III.2: Comparing Two Groups
Section III.3: Strength of Association Measure
Part 4 provides information about Research Procedure.
Section IV.1: Outline of Research Procedure
Section IV.2: Null Hypothesis and “p value”
In addition to the explanations of standard deviation, variance, and
some other concepts directly associated with these measures of
variation, additional statistical concepts are mentioned to lead and
encourage the reader to further explore the details of those useful
statistical tools that are beyond the scope of this little “handbooklet.”
