Northern Prairie Wildlife Research Center

The standard deviation (SD) is a descriptive statistic, and the standard error (SE) is an inferential statistic. Accordingly, the SD can be used to portray the variation observed in a sample: = 100, SD = 25 suggests a much more variable population than does = 100, SD = 5. The expected value (i.e., an average over a large number of replicate samples) of the SD² equals σ² and depends very little on sample size (

When presenting results such as *a* ± *b*, always indicate if *b*
is a SD or a SE or is *t* × SE (indicating a confidence limit),
where *t* is from the *t* distribution (e.g., 1.96 if the degrees
of freedom are large). If a confidence interval is to be used, give the lower
and upper limits as these are often asymmetric about the estimate. Authors
should be clear concerning the distinction between precision (measured by
variances, standard errors, coefficients of variation, and confidence intervals)
and bias (an average tendency to estimate values either smaller or larger
than the parameter; see White et al. 1982:22-23).

The Methods section should indicate the (1 - α)%
confidence level used (e.g., 90, 95, or 99%). Information in tables should
be arranged so that numbers to be compared are close to each other. Excellent
advice on the visual display of quantitative information is given in Tufte
(1983). Provide references for any statistical software and specific options
used (e.g., equal or unequal variances in *t*-tests, procedure TTEST
in SAS, or a particular Bayesian procedure in BUGS). The Methods section should
always provide sufficient detail so that the reader can understand what was
done.

In regression, discriminant function analysis, and similar procedures, one should avoid the term independent variables because the variables are rarely independent among themselves or with the response variable. Better terms include explanatory or predictor variables (see McCullagh and Neider 1989:8).

Avoid confusing low frequencies with small sample sizes. If one finds only 4 birds on 230 plots, the proportion of plots with birds can be precisely estimated. Alternatively, if the birds are the object of study, the 230 plots are irrelevant, and the sample size (4) is very small.

It is important to separate analysis of results based on questions and hypotheses
formed before examining the data from results found after sequentially examining
the results of data analyses. The first approach tends to be more confirmatory,
while the second approach tends to be more exploratory. In particular, if
the data analysis suggests a particular pattern leading to an interesting
hypothesis then, at this midway point, few statistical tests or measures of
precision remain valid (Lindsey 1999 *a,b*; White 2000). That is, an
inference concerning patterns or hypotheses as being an actual feature of
the population or process of interest are not well supported (e.g., likely
to be spurious). Conclusions reached after repeated examination of the results
of prior analyses, while interesting, cannot be taken with the same degree
of confidence as those from the more confirmatory analysis. However, these
post hoc results often represent intriguing hypotheses to be readdressed with
a new, independent set of data. Thus, as part of the Introduction, authors
should note the degree to which the study was exploratory versus confrimatory.
Provide information concerning any post hoc analyses in the Discussion section.

Statistical approaches are increasingly important in many areas of applied science. The field of statistics is a science, with new discoveries leading to changing paradigms. New methods sometimes require new ways of effectively reporting results. We should be able to evolve as progress is made and changes are necessary. We encourage wildlife researchers and managers to capitalize on modern methods and to suggest how the results from such methods might be best presented. We hope our suggestions will be viewed as constructive.

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