Northern Prairie Wildlife Research Center

# Suggestions for Presenting the Results of Data Analyses

*Introduction*

For many years, researchers have relied heavily on testing null hypotheses in
the analysis of fisheries and wildlife research data. For example, an average
of 42 *P*-values testing the statistical significance of null hypotheses
was reported for articles in *The Journal of Wildlife Management* during
1994-1998 (Anderson et al. 2000). This analysis paradigm has been challenged
(Cherry 1998, Johnson 1999), and alternative approaches have been offered (Burnham
and Anderson 2001). The simplest alternative is to employ a variety of classical
frequentist methods (e.g., analysis of variance or covariance, or regression)
that focus on the estimation of effect size and measures of its precision, rather
than on statistical tests, *P*-values and arbitrary, dichotomous statements
about statistical significance or lack thereof. Estimated effect sizes (e.g.,
the difference between the estimated treatment and control means) are the results
useful in future meta-analysis (Hedges and Olkin 1985), while *P*-values
are almost useless in these important syntheses. A second alternative is relatively
new and based on criteria that estimate Kullback-Leibler information loss (Kullback
and Leibler 1951). These information-theoretic approaches allow a ranking of
various research hypotheses (represented by models) and several quantities can
be computed to estimate a formal strength of evidence for alternative hypotheses.
Finally, methods based on Bayes' theorem have become useful in applied sciences
due mostly to advances in computer technology (Gelman et al. 1995).
Over the years, standard methods for presenting results from statistical
hypothesis tests have evolved. The Wildlife Society (1995*a,b*), for
example, addressed Type II errors, statistical power, and related issues.
However, articles by Cherry (1998), Johnson (1999), and Anderson et al. (2000)
provide reason to reflect on how research results are best presented. Anderson
et al. (2000) estimated that 47% of the *P*-values reported recently
in *The Journal of Wildlife Management* were naked (i.e., only the *P*-value
is presented with a statement about its significance or lack of significance,
without estimated effect size or even the sign of the difference being provided).
Reporting of such results provides no information and is thus without meaning.
Perhaps more importantly, there are thousands of null hypotheses tested and
reported each year in biological journals that are clearly false on simple
a priori grounds (Johnson 1999). These are called "silly nulls" and account
for over 90% of the null hypotheses tested in *Ecology* and *The Journal
of Wildlife Management* (Anderson et al. 2000). We seem to be failing by
addressing so many trivial issues in theoretical and applied ecology. Articles
that employ silly nulls and statistical tests of hypotheses known to be false
severely retard progress in our understanding of ecological systems and the
effects of management programs (O'Connor 2000). The misuse and overuse of
*P*-values is astonishing. Further, there is little analogous guidance
for authors to present results of data analysis under the newer information-theoretic
or Bayesian methods.

We suggest how to present results of data analysis under each of these 3
statistical paradigms: classical frequentist, information-theoretic, and Bayesian.
We make no recommendation on the choice of analysis, instead, we focus on
suggestions for the presentation of results of the data analysis. We assume
authors are familiar with the analysis paradigm they have used; thus, we will
not provide introductory material here.

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