Editor's Note:
Because of difficulties in displaying a square root
symbol on the web, we have used exponential notation.
Whenever you see X^{0.5} we are expressing
the square root of X. |

If you
have taken a statistics course, or just tried to read a
statistics book, you will remember how confusing the
terms can be. There seem to be a lot of them, but
there are really only a few. The problem is that
every special form of each term has its own name. While that
may be handy once you understand all this, it is a terrific
hassle when you are just trying to learn the material. We would
like to talk about 4 "new" terms in this short
article, they are:- Variance (V)
- Variance of the mean (V
_{ xbar}) - Coefficient of Variation (CV)
- Standard error in percent (SE%)
These are Lets consider the first term, the "Variance" (V).
This is just the Standard Deviation (SD) squared. What As you might expect, the Variance of the Mean (V The last two terms are more frequently used, and again are
just different ways of expressing the terms you are
already familiar with. These really do have a Suppose you were measuring both trees and logs in some
sort of study. You want an "equally good" answer
in each case. You know that the trees have a standard deviation
of ±0.3 cubic meters, while the logs have a SD of ±130
board feet. Which is the most variable? Clearly the most reasonable
way to express these terms would be in percentages. We therefore divide
the SD by the mean, and are able to express the
"spread" of the data in a way that is easy to understand
and to compare to other types of distributions. We give
this If we now say that trees have a CV of ±25%, and logs have a CV of ±17%, it is clear that trees are "more variable" than logs and will need to be measured more often to get the same relative answer. The same situation applies to the Standard Error. We are
more likely to get a reasonable reaction to a statement
like "we know the stand volume within ±7.3%" than
if we say "we know the stand volume within 12,300 Board
Feet". The standard error is divided by the mean,
and given the special term " . |
These
percentage terms themselves are also squared at times,
but luckily we are not plagued by special terms for these "squared percentage
versions". The Coefficient of Variation (CV) is
often seen in statistics, and is a The chart below summarizes all these terms and shows
how they are related. Note that they are broken down into
terms that discuss
As you would expect, the central terms are therefore: - Standard Deviation (things)
- Standard Error (averages)
When you square each of these you move up one level.
If you want to express them as a percentage, you move
down one level. To move from a description of the
population (left side) to a description of the sample average (right
side), you can just divide by the square root of the
sample size (or by "n" itself for the variance where
it has been squared already). This is because of the SD / n The chart makes it clear that you are only dealing
with 2 terms, which are either being squared for math
purposes or being expressed as percentages for easier understanding.
The special names given to these terms may make you think
something really different is being created, but this is
an illusion. One of the hard parts of statistics is to
tell when something really different is being introduced.
This Now that we have covered all these terms, and how they relate, the next discussion will be on sample size. There are a few logical ideas (and a few cheap tricks) that will make it much easier for you to calculate and understand sample size. |