Information Technology Reference
In-Depth Information
Tables dealing with two-factor arrays are straightforward, provided that
confidence limits, least standard deviations, and standard errors are clearly
associated with the correct set of figures. Tables involving three or more
factors are not always immediately clear to the reader and are best
avoided.
Are the results expressed in appropriate units? For example, are parts
per thousand more natural in a specific case than percentages? Have we
rounded off to the correct degree of precision, taking account of what we
know about the variability of the results and considering whether they will
be used by the reader, perhaps by multiplying by a constant factor or by
another variate—for example, % dry matter?
Dyke [1997] also advises us that “Residuals should be tabulated and
presented as part of routine analysis; any [statistical] package that does not
offer this option was probably produced by someone out of touch with
research workers, certainly with those working with field crops.” Best of
all is a display of residuals aligned in rows and columns as the plots were
aligned in the field.
A table of residuals (or tables, if there are several strata) can alert us to
the presence of outliers and may also reveal patterns in the data not con-
sidered previously.
STANDARD ERROR
One of the most egregious errors in statistics—one encouraged, if not
insisted upon by the editors of journals in the biological and social
sciences—is the use of the notation “mean ± standard error” to report
the results of a set of observations.
Presumably, the editors of these journals (and the reviewers they select)
have three objectives in mind: To communicate some idea of
1. The “correct” result
2. The precision of the estimate of the correct result
3. The dispersion of the distribution from which the observations
were drawn
Let's see to what degree any or all of these objectives might be realized
in real life by the editor's choice.
For small samples of three to five observations, summary statistics are
virtually meaningless; reproduce the actual observations; this is easier to
do and more informative.
For many variables, regardless of sample size, the arithmetic mean can
be very misleading. For example, the mean income in most countries is
far in excess of the median income or 50th percentile to which most of
us can relate. When the arithmetic mean is meaningful, it is usually equal
