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Ecosphere
Volume 14, Issue 5 e4539
ARTICLE
Open Access
WRITING STATISTICAL METHODS FOR ECOLOGISTS
Amy J. Davis,
Corresponding Author
Amy J. Davis
* amy.j.davis@usda.gov
* orcid.org/0000-0002-4962-9753
United States Department of Agriculture, Animal and Plant Health Inspection
Service, Wildlife Services, National Wildlife Research Center, Fort Collins,
Colorado, USA
Correspondence
Amy J. Davis
Email: amy.j.davis@usda.gov
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Shannon Kay,
Shannon Kay
* orcid.org/0000-0001-8742-6570
United States Department of Agriculture, Forest Service, Rocky Mountain Research
Station, Fort Collins, Colorado, USA
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Amy J. Davis,
Corresponding Author
Amy J. Davis
* amy.j.davis@usda.gov
* orcid.org/0000-0002-4962-9753
United States Department of Agriculture, Animal and Plant Health Inspection
Service, Wildlife Services, National Wildlife Research Center, Fort Collins,
Colorado, USA
Correspondence
Amy J. Davis
Email: amy.j.davis@usda.gov
Search for more papers by this author
Shannon Kay,
Shannon Kay
* orcid.org/0000-0001-8742-6570
United States Department of Agriculture, Forest Service, Rocky Mountain Research
Station, Fort Collins, Colorado, USA
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First published: 24 May 2023
https://doi.org/10.1002/ecs2.4539
Handling Editor: John Humphreys
Amy J. Davis and Shannon Kay contributed equally to this study.
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* INTRODUCTION
* PITFALLS IN STATISTICAL WRITING AND HOW TO AVOID THEM
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ABSTRACT
The Methods section is a key component of any ecology research publication
containing detailed information on how the data were collected and analyzed.
However, descriptions of which statistical methods were used and how they were
applied can substantially vary and may not provide enough information for the
analyses to be reproducible. Computational and statistical programming advances
have allowed ecological researchers without a strong statistical or mathematical
background to access and use increasingly complex statistical methods. Thus,
statistical methods are written by and need to be accessible to researchers
across a range of quantitative expertise. Poorly written Methods sections can
incorrectly inflate the strength of or call into question the results of an
analysis. Although there are resources available, we have not found one that is
specific to writing statistical methods, includes all the elements we discuss,
and is targeted for ecologists. Here we provide guidelines for ecological
researchers when writing statistical methods and review frequent errors made in
Statistical Methods sections. We highlight some common dos and don'ts when
writing Statistical Methods sections and present a simple checklist to help
guide authors with their writing to ensure reproducibility. We illustrate the
use of this guidance with two examples.
INTRODUCTION
Statistics are a cornerstone of ecological research. Unfortunately there have
been high levels of anxiety associated with taking statistics courses
(Onwuegbuzie & Wilson, 2003) and many tend to dislike or avoid statistical or
mathematical courses (Hogg, 1991; Prayoga & Abraham, 2017; Slootmaeckers et
al., 2014). Ecological researchers have a diversity of statistical backgrounds
from having formal training to learning on the job. A survey of mostly
early-career ecologists found that 75% “were not satisfied with their
understanding of mathematical models” (Barraquand et al., 2014). For many
ecologists, Statistical Methods sections are challenging and time-consuming to
fully understand and may be skimmed, or skipped altogether, when reading
articles. If readers cannot comprehend the Statistical Methods sections as
written, they will likely be unable to repeat the analyses, and perhaps more
importantly, will be unable to judge the strength of the results. Many aspects
of a Statistical Methods section may be too “in the weeds” for some readers, and
it has been suggested (Fawcett & Higginson, 2012) and refuted (Fernandes, 2012)
that more equations in biological papers equate to fewer citations. However,
explaining the rationale for each statistical approach in a way that provides
context for all readers and refraining from relegating the “scary math” to
appendices is critically important and aids in the advancement of new theories
(Chitnis & Smith, 2012).
Recent statistical and computational tools have been developed to help broaden
the accessibility of different methods to a larger pool of ecological
researchers. The use of “Plug-and-play” statistical software (e.g., OpenEpi—Dean
et al., 2013) allows for analyses to be conducted by answering simple questions.
Graphical user interface (GUI) options for common ecological analyses (e.g.,
Buckland et al., 2001; Rexstad & Burnham, 1991; White & Burnham, 1999) allow
users to conduct more complex analyses in a user-friendly manner. The rise of
freeware, coding-based statistical software (e.g., R; R Core Team, 2021) has
allowed for greater use of complex statistical approaches by researchers without
advanced statistical training. The use of R has become widespread in ecology,
with nearly 60% of articles published in ecology journals in 2017 reported using
R as their primary tool in data analysis (Lai et al., 2019). The availability of
freeware Bayesian analysis options (JAGS—Plummer, 2003; STAN—Gelman et
al., 2015; NIMBLE—de Valpine et al., 2017) has led to increases in the use of
Bayesian approaches in ecology (Anderson et al., 2021; Hooten & Hobbs, 2015).
There has been an increase in the use of sophisticated and computationally
intensive statistical approaches in ecology over time (Touchon & McCoy, 2016).
Despite this rise in the use of advanced statistical methods, many graduate
programs have not kept pace by requiring statistics coursework (Touchon &
McCoy, 2016). To ensure the statistical approaches in ecological publications
are comprehensible, repeatable, and properly cited, clear guidance is needed on
best practices for writing statistical methods.
Proper use of statistics is critically important and there are extensive
resources available for guidance on which methods are appropriate (e.g., Fox et
al., 2015; Gotelli & Ellison, 2004; McGarigal et al., 2013; Steel et al., 2013;
Zuur et al., 2010, 2007), but our focus is specifically for writing and
reporting Statistical Methods sections. There are resources that focus on how to
effectively communicate mathematical concepts to scientists in other fields
(Table 1). Recently, Shoemaker et al. (2021) provide general guidance for
writers and readers on communicating mathematics. Other resources provide
guidance on writing Methods sections in general or how to write and report
specific statistical details (Table 1). These publications provide some useful
overlap for our objective in terms of ensuring that mathematical elements are
clearly linked to the ecological concepts and to use illustrations and diagrams
to help convey ideas. However, there is a need for clear guidance on how to
comprehensively and clearly communicate statistical methods used by ecologists.
TABLE 1. References of interest for deeper dives into related concepts to
writing statistical methods (not an exhaustive list).
Reference Description Other sources on methods writing Adams-Huet and Ahn (2009)
A guide for writing statistical methods targeted at clinical investigators.
Azevedo et al. (2011) A guide for writing methods in general with a section on
data analysis, focusing on medical methods. Ghasemi et al. (2019) Guidance on
writing methods for biomedical fields, provides many useful tables, boxes, and
references. Lang and Altman (2015) Detailed guidance on statistical reporting
specific to analytical method used, targeted for biomedical researchers. Michel
et al. (2020) Specific guidance with examples on how to report data analysis and
statistical methods for experimental biology. Worthy (2015) Guidance on
statistical analysis and reporting for medical fields. Provides recommendations
on methods, results, tables and figures, and discussion. Sources on how to
effectively communicate mathematical concepts Crowe and Cash (2023) Short guide
to writing Methods sections for broad range of researchers with focus on common
pitfalls to avoid and pearls to include. Fallon (2016) Multidisciplinary writing
guide for researchers using a series of prompting questions with a final section
of examples. Scheinerman (2011) Descriptions of mathematical notation and usage,
how to produce mathematical symbols in LaTeX, and links to further reading on
topics. Shoemaker et al. (2021) Recommendations for both readers and writers of
mathematical ecology focusing on bridging the gap between advanced modeling
techniques and understandability. Sources for reviewers Triaridis and Kyrgidis
(2010) Provides guidance on how to review articles and particularly statistical
methods. Helpful when writing to see how methods may be critiqued. Parker et al.
(2018) A checklist to help reviewers ensure transparency.
Recognizing that there are errors or inconsistencies in reporting statistical
methods (Michel et al., 2020; Worthy, 2015), there has been a push, particularly
in the biomedical fields, to develop uniform guidance on how to present
statistical methods and results (Crowe & Cash, 2023). This has led to more
detailed recommendations as to how to report statistical methods in these fields
(e.g., Indrayan, 2020; Lang & Altman, 2015; Worthy, 2015). Although Methods
sections in general have long been used to enable study replication, recent
understandings of the complexities of statistical methods have engendered new
standards to help ensure reproducibility in statistical work by putting a
greater emphasis on publishing data and corresponding code for analyses with
articles (Fidler et al., 2017; Peng, 2011). We support these efforts and
additionally recommend more uniformity in how statistical methods are presented
to improve clarity and reproducibility in ecological research.
Our objective is to provide recommendations for ecological researchers of all
levels of statistical knowledge on how to write clear, repeatable Statistical
Methods sections. We start by identifying common pitfalls in statistical
writing, then give guidance for authors describing what information should be
included in any account of statistical analyses performed. Like other resources
(e.g., Makin & Orban de Xivry, 2019; Parker et al., 2018; Zuur & Ieno, 2016), we
include a simple checklist for authors to help guide writing statistical methods
and include some simple dos and don'ts to aid in avoiding any oversights
(Schroter et al., 2008). Finally, we demonstrate how to use this guidance by
working through two ecological examples of Statistical Methods sections.
PITFALLS IN STATISTICAL WRITING AND HOW TO AVOID THEM
There are several common pitfalls ecologists make when writing Statistical
Methods sections in publications such as not clearly defining each test or
analysis, not providing enough information to make it reproducible, or not
properly citing methods or the software used to implement the analyses (Makin &
Orban de Xivry, 2019; Miller, 2006). Likely the most important consideration is
ensuring that each analysis appears in the Methods section and enough
information is provided so that others fully understand the results and could
repeat the same analysis. Results of analyses that were conducted post hoc are
sometimes presented in the Results section or even the Discussion section but
were never described in the Methods section, which does not allow readers to
replicate these analyses. Even if an analysis or hypothesis test was conducted
after the planned analyses, perhaps to test a specific follow-up question, the
approaches for these need to be described in the Methods section. This does not
equate to requiring one to narrate every bit of exploratory data analysis
conducted or to describe common statistical methods in detail. Novel statistical
methods need more detailed descriptions than more general or well-known methods,
and citations should be provided when available (Worthy, 2015).
Another pitfall is to use terminology incorrectly to describe statistical
methods or metrics. Precise terminology importantly avoids confusion in
statistical writing. Parameters can be either estimated directly from a model or
derived from model estimates. For example, we could say that we estimated
monthly survival rates from a survival analysis, and we derived annual survival
rates from the monthly survival estimates. If descriptions in the Methods state
“we estimated parameter X” but the parameter was derived from the model, the
reader may misunderstand the nature of the model. It is common for people to
refer to “running models”; however, it is more appropriate to say models are fit
to the data. It is appropriate to say “we run simulations” based on a model or
set of assumptions to aid in prediction. It is important to be mindful of which
terms are and are not interchangeable to avoid confusion.
Another pitfall is confusion between the statistical method and the tool or
program used to carry out the analysis. We often see authors reporting the
function itself (e.g., lm in R) rather than the actual analysis (e.g., linear
regression). Similarly, if equations are included, they should reflect the
mathematical form (e.g., ββεy=◂+▸β0+β1x+ε$$
y={\upbeta}_0+{\upbeta}_1x+\upvarepsilon $$) and not the software program's
function formula (e.g., y ~ x). However, both the method and the tool used to
implement the method should be reported and properly cited (Worthy, 2015).
GUIDANCE FOR AUTHORS
In Box 1 we provide some dos and don'ts for writing a Methods section for
ecologists. Box 2 has a checklist to guide statistical methods writing for each
analysis. We also provide examples of “sufficient” and “insufficient”
descriptions of methods and an example of how to use the checklist to guide
statistical methods writing. These guidelines should help authors ensure that
their analyses are clearly defined, understandable, and repeatable. Following
these guidelines will help ecologists be more effective in their communication,
which may lend more credence to their results and help readers make their own
conclusions regarding inferences made from the analyses.
BOX 1. DOS AND DON'TS IN WRITING STATISTICAL METHODS FOR ECOLOGISTS
Dos
1. Do imagine a nonscientist reading your article—would they understand what
the objectives/rationale were for each analysis?
2. Do include enough information for reproducibility: could another researcher
repeat the statistical analyses you performed from your description?
3. Do describe EVERY analysis used in the paper, including post hoc analyses or
tests
4. Do clearly describe which data or subset of data are used in each analysis.
5. Do review guidance for authors from journals for standards specific to their
audiences
Don'ts
1. Don't include results or discussion of statistical approaches that were not
first described in the Methods section.
2. Don't equate a software function with a statistical method.
3. Don't forget to give credit where it is due! Be sure to cite statistical
methods, software, and packages.
BOX 2. STATISTICAL METHODS WRITING CHECKLIST FOR ECOLOGISTS
Items in boldface are necessary; items in italics are helpful to include when
appropriate.
For each analytical approach be sure to include:
1. Objective: Describe the rationale for the analysis and how it relates to the
study objective.
2. Variables: Define the experimental unit and the response and predictor
variables clearly.
* Response: Specify the response variable distribution, why it is
appropriate, and any link functions.
* Predictors: Specify which predictor variables were examined and which were
fixed or random effects.
* Meaningful difference: State what is an ecologically meaningful difference
in the response variable.
3. Statistical method: Describe the statistical method (e.g., t-test,
generalized linear model).
* Model fit: Specify how model fit was assessed.
* Model comparison: Specify the model comparison approach and how many
models were fit.
4. Implementation: Describe the function, package, and software used and
include any appropriate citations (e.g., glmer in package lme4, in R).
* Cite: Cite software and packages.
The first step is to consider the target audience and the typical analytic
background of the intended readers. It can be helpful to consult a journal's
Guidance for Authors section to determine if there are specific recommendations
for statistical methods. If there is no specific advice from the journal, then
looking at previous publications from the journal will give the author an idea
of what may be expected. However, published articles are not without faults
(Michel et al., 2020; Nuijten et al., 2016) and lack of detail in published
articles should not be treated as justification not to include detail in one's
own writing. Even when targeting a highly quantitative audience, statistical
methods should be written with sufficient justification and context to allow a
general reader to follow the logic of the approach even if the technical details
are beyond their training. Ultimately, the Results section should flow clearly
and directly from the Methods section. If many analyses were conducted, consider
adding subheadings to aid the reader in matching each analysis with its result.
CHECKLIST
Our checklist for statistical methods writing is designed to guide ecologists on
how to write comprehensive statistical methods. For each analysis included in a
study, the author should include these four primary components: the objective or
rationale of the analysis, the variables used in the analysis, the statistical
method, and how the analysis was implemented. Details for each element are
described below. Once authors have a clear understanding of each element, they
can use the checklist (Box 2) to help guide them in their writing. Some
statistical methods have elements of the checklist implied (e.g., logistic
regression implies a binomial response variable) or elements that are not
applicable (e.g., model selection is not needed for a t-test) and therefore they
do not need to be explicitly stated. In the checklist, we distinguish between
necessary elements (our four primary components) and helpful elements that
should be included when appropriate. The order of elements does not always have
to follow the order in which we present them; it is more important that all
elements are included. We do recommend starting with the objectives to orient
the readers and ending with how the analyses were implemented to not confuse the
tool (program/package) with the statistical method, but this is not essential.
OBJECTIVES
Every statistical approach used in a study should be conducted to help achieve
the study objectives. Writers should take care to connect the statistical method
that is described to the biological/ecological metric of interest and its
relevance in the study (Lang & Altman, 2015; Worthy, 2015). Making these
connections clear helps both scientists and nonscientists understand the Methods
sections. Additionally, the better these sections are explained and connected to
the implications of the study, the easier it is for the reader to assess the
inferences made. By making sure you can clearly articulate the rationale for
your statistical approaches, and link them to the study objectives, the
statistical approach will be more comprehensible, and your results will be more
impactful.
VARIABLES
All relevant variables should be clearly described in the Methods section
including the units of measurement (e.g., km2, %, mm) and the scale at which
each variable is measured (e.g., an individual, a site, a population; termed the
experimental unit). The experimental unit of each variable should clearly link
back to the experimental design. The response variable (also called the
dependent variable), the characteristic you are interested in predicting or
investigating relationships with, should be identified in addition to all the
predictor variables (also called independent variables, covariates, or
explanatory variables), the characteristics that may relate to the response
variable. If using a parametric model (i.e., a model that makes distributional
assumptions), the distribution that is appropriate for the response variable and
any link functions should be stated and which variables were used as random or
fixed effects should be included (Gelman & Hill, 2006). For simple linear
regression, the response variable is modeled as a normal or Gaussian
distribution, which is implied in simple linear regression and does not need to
be reiterated. However, for generalized linear models or other modeling
approaches (e.g., Bayesian), the appropriate distribution may be one that only
allows for positive data or discrete data. Describing the distribution of the
response will ensure the approach is repeatable and explaining the rationale for
the distribution will help lay people follow the logic of the analyses.
All predictor variables should be explicitly listed with their justification for
inclusion in the analyses; and, if relevant, their data sources should be
provided (e.g., remote sensing data, habitat data, or climate data).
Understanding the motivation for including certain predictor variables will help
the reader follow the story the authors are trying to tell and allow the readers
to consider any additional predictor variables that may be lacking in an
analysis. The assumed functional form of the predictor variables (linearity,
interactions, etc.) should also be stated. For Bayesian models, in addition to
the distributions for the variables in the model, the distributions for the
priors should be specified. Explaining which predictor variables or combinations
of predictors are considered, the approach can be replicated, and readers can
better assess the strength of the approach.
An often-overlooked feature that should be included in the Methods section is to
identify what magnitude of a difference in the response variable is ecologically
meaningful (Lang & Altman, 2015). There is an important difference between
statistical significance and biological/ecological significance (Nakagawa &
Cuthill, 2007). Reporting effect sizes (e.g., Cohen's d; Cohen, 1988) is a good
way to evaluate whether a statistically significant result is also relevant in a
practical sense. Relatedly, the range of values of the predictor variables used
is helpful to provide. It is possible to not detect a relationship with a
predictor that is frequently considered important by other research, but the
range examined in a study might not be wide enough to make a meaningful
difference. A power analysis could be conducted to determine the likelihood of
detecting a biologically meaningful difference, if so, the rationale and
approach should be described. By priming the reader with what type of difference
is ecologically meaningful, the reader will be better prepared to interpret the
results appropriately.
STATISTICAL METHOD
An important element to include for each analysis is the statistical method
being used. As mentioned previously, there can be confusion between the
statistical method (e.g., linear regression) and the tool that is used to
implement the statistical method (e.g., lm in R). It is important to distinguish
the statistical method from the tool used to conduct the analysis. By conflating
the method and the tool, it may come across as a lack of foundational
understanding of the approaches used and may lead to lack of confidence in the
work.
For most Statistical Methods sections, equations do not need to be provided.
Mathematical equations are the basis for statistical analyses, but, depending on
the audience, they may not be the most effective ways of describing an approach.
Do include equations when modifications are being made to standard approaches or
for custom Bayesian hierarchical models. If a novel statistical approach is
being used, then equations are usually necessary to demonstrate the fundamentals
of the approach. Similar to others (e.g., Cronin & Schoolmaster, 2018; Shoemaker
et al., 2021), we encourage the use of diagrams or directed acyclic graphs
(i.e., a visual representation of model specification and parameter
relationship) to help convey novel mathematical/statistical approaches to
general audiences. However, for established statistical approaches, references
to those approaches or even equations in other publications are usually
sufficient.
In addition to model specifics, it is important to describe which models were
fit, how models were compared, and how model fit was assessed. There are many
good guides on how to conduct model selection in ecology (Doherty et al., 2012;
Hooten & Hobbs, 2015; Johnson & Omland, 2004; Tredennick et al., 2021). It is
important to be mindful of how parameters from models are interpreted (Arif &
MacNeil, 2022; McElreath, 2020; Tredennick et al., 2021). If any model selection
was performed, make sure to identify the approach used, explain why it is
appropriate for the situation, describe what a meaningful difference in model
metrics would be (e.g., delta 2 AICc suggests a meaningful difference in model
parsimony), and provide a citation for the approach used (e.g., Burnham &
Anderson, 2002). It should also be clear how model selection uncertainty would
be addressed (e.g., model averaging, cumulative covariate weights; Burnham &
Anderson, 2002).
Model selection methods often provide relative measures of goodness of fit
(e.g., AIC, BIC, WAIC, cross validation; Burnham & Anderson, 2002; Hooten &
Hobbs, 2015). That is, they compare the fit of the set of models considered but
do not provide an absolute measure of how well the “best” model fits the data.
Essentially, a goodness-of-fit metric is one that compares the expected values
from a model to the observed data. Goodness-of-fit metrics are important to
include to demonstrate to the reader how good the model is at fitting the data
and, therefore, how reliable the results are. Goodness-of-fit metrics are
specific to the model being used (e.g., R2 for simple linear regression, area
under the curve for logistic regression), and in many cases there are no
predefined goodness-of-fit metrics available. There are options to assess the
goodness of fit even when a predefined metric does not exist for an analysis,
including bootstrapping, simulations, or a type of cross validation to assess
model fit (Bonett & Bentler, 1983; Boyle et al., 1997; Stute et al., 1993). For
Bayesian models, researchers can use posterior predictive checks (Gelman et al.,
2013).
In addition to model fit specifications, for Bayesian models, authors should
describe how convergence was evaluated. The reliability of Bayesian models
depends on good mixing and convergence in the posterior distributions.
Understanding how convergence was assessed allows readers to have confidence in
the results. For nonparametric models, the values of tuning parameters should be
reported—especially if not using defaults (e.g., “mtry” in a random forest, the
number of variables selected at each split, defaults to p$$ \sqrt{p} $$ for
classification and p/3 for regression where p is the number of predictor
variables). Similarly, in a simulation study, all the specific parameter values
used should be reported. Note that including some of the more detailed method
information in a Supplementary section is generally an option.
IMPLEMENTATION
Not only is it important to describe and cite the statistical methods used, but
also the tools used to implement the analysis. This is critical for ensuring
reproducibility as there can be differences in optimization routines and the
presentation of results across programs. If there are different options for
estimation approaches and an author uses a nonstandard approach, for example,
using restricted maximum likelihood (REML) instead of maximum likelihood (ML) in
fitting a generalized linear model, authors should report the method used. As
mentioned previously, if unique code was developed as part of a study, authors
should provide the code along with the manuscript (Culina et al., 2020;
Filazzola & Lortie, 2022). Many readers find it useful to walk through analyses
with the code provided, leading to a better understanding of what was done.
Furthermore, credit should not just be given for the statistical method being
used, but also for the tools used to apply the method including any software,
packages, and functions. Even within the same software, there can be many ways
to perform the same analysis using different functions that may have options for
means of estimation. Additionally, it is important to include the version number
for programs and packages used as estimation approaches may vary by version. By
properly reporting and citing these tools, the analyses will be reproducible.
The citations associated with programs/packages can also be great references to
provide background on the statistical methods being used.
EXAMPLES
Here we present ecological research examples and demonstrate how to effectively
write a Statistical Methods section using the guidance we have provided. We
start with general design setups but recognize that a true Methods section would
be more in-depth; our objective is simply to provide context for the statistical
methods writing guidance.
EXAMPLE 1: COMPARISON OF SUFFICIENT AND INSUFFICIENT STATISTICAL METHODS WRITING
Suppose we are interested in identifying influential environmental factors and
habitat characteristics associated with the number of eggs laid by a particular
raptor species. We conducted annual surveys of 100 randomly selected historic
nest locations across the species' breeding range. We recorded the number of
eggs laid at each nest and then added climate data (i.e., average annual
temperature and average precipitation) and habitat data (i.e., dominant habitat
type) around each nest to use in fitting a model to determine which of these
weather or habitat factors may be significantly affecting clutch size. Assuming
we have already described in the general methods how the nest data were
collected (e.g., site selection, sampling protocols, details of data recorded,
experimental unit) and how the study design relates to the objectives (e.g., we
designed a study to examine how a range in environmental and habitat variables
relate to clutch size to help understand potential impacts of climate change on
species X), we start off our Statistical Methods section by defining our
objectives and type of study design along with the variables we are going to
include:
> We analyzed the effects of climate variables and habitat variables on nest
> data of bird X,
but this does not clearly articulate our objective or provide specific
information about the variables we are using. We revised the text as follows:
> We were interested in identifying whether climate variables, specifically,
> annual precipitation (mm) and the average annual temperature (°C), as well as
> the dominant land cover type (including shrub, deciduous forest, evergreen
> forest, grassland, and wetland), were significantly related to the number of
> eggs laid by bird species X. Based on population viability analyses for this
> species ([citation]), an increase in 0.5 eggs per nest would be a meaningful
> difference.
Now that we added the specifics on which climate variables and habitat
variables, we included and what differences would be ecologically meaningful, we
need to define what statistical method was used and how each variable was
treated.
> We used glm in R to run a model on precipitation, temperature, and land cover
> type.
This sentence is not appropriate because it is confusing the statistical method
with the tool, we incorrectly refer to “running” a model instead of “fitting” a
model, and we do not define what distribution was used in the GLM or the
functional form of variables. We also need to specify whether any variables were
included as random effects. Updating the text, we have:
> We used a generalized linear mixed model (GLMM) to examine the relationship of
> our response variable, the number of eggs laid in each nest, and the fixed
> effect predictor variables of precipitation, temperature, and land cover
> class. We used a Poisson distribution for our response variable as the number
> of eggs must be a discrete number and a log link because the number of eggs
> cannot be negative. We included a polynomial term for temperature because we
> hypothesized that the number of eggs laid by bird X may increase with
> temperature to a certain point before decreasing at higher temperatures.
> Additionally, we hypothesized that an interaction may exist between
> precipitation and land cover class where precipitation may have a greater
> effect on the number of eggs laid in some habitats compared to other land
> cover classes. We included a random effect for a mated pair to account for
> multiple nesting attempts by the same pair over time.
Notice how we included the rationale for using the polynomial term on
temperature and the interaction between precipitation and land cover class. Now
we need to describe how we assessed model fit, whether we did model selection,
and how we implemented our analyses.
> We used simulated residuals (Dunn and Smyth 1996) to visually assess model fit
> by plotting residuals against each predictor variable. We used 10-fold cross
> validation to evaluate the goodness of fit of the model. Analyses were
> implemented using the statistical software package R (R Core Team 2021) using
> the lme4 (Bates et al. 2015) and DHARMa (Hartig 2022) packages.
Note that not only did we cite what software was used, but we also included a
citation for each package we used within the software.
In summation, we have touched on (1) our objective, (2) what variables were
included and how they were treated in the analysis, (3) what type of statistical
method was used and how we assessed fit, and (4) how we implemented the analysis
with proper citations (Box 2).
EXAMPLE 2: USING THE CHECKLIST TO GUIDE STATISTICAL METHODS WRITING
THE SETUP
Suppose we are interested in investigating the presence/absence of an amphibian
species across a wetland landscape. We want to know if this species occurs more
often in large or small ponds to help inform management. We also suspect that
ponds with higher pH levels will be less hospitable to this species. We think
that precipitation may impact detection. We conducted an occupancy analysis.
Post hoc, we conducted a likelihood ratio test to corroborate if pond size was
an important factor. We will use the checklist to ensure we have clearly
described both the occupancy analysis and the likelihood ratio test. Starting
with the occupancy analysis, follow along in Figure 1 as we provide the elements
needed (right side) that correspond with the checklist items (left side).
Elements in brackets are implied by or unnecessary for the approach and do not
need to be written out in a Methods section. We have included them in the
checklist for completeness.
FIGURE 1
Open in figure viewerPowerPoint
Checklist applied to writing statistical methods for occupancy analysis in
Example 2.
The checklist should be used for each analysis. The only other analysis in our
study is the likelihood ratio test. Follow along in Figure 2 to see how we
develop the write-up for the likelihood ratio test.
FIGURE 2
Open in figure viewerPowerPoint
Checklist applied to writing statistical methods for the likelihood ratio test
in Example 2.
Putting it all together, we decided that describing the statistical method
before the variables flowed better. We also edited to eliminate any redundancies
that resulted from writing out each component of the checklist and omitted any
elements implied by the method.
> We wanted to understand the spatial patterns of presence and absence of
> amphibian species Y in ponds across our study area. We used an occupancy
> analysis which simultaneously estimates the probability of occurrence and
> accounts for imperfect detection typical of wildlife species (MacKenzie et al.
> 2017). We used a categorical variable specifying if the pond was large (x = 1)
> or small (x = 0) to examine if pond size was an important predictor of species
> Y occupancy. We considered a difference of 0.1 in occupancy meaningful in our
> study. We included a continuous variable for pH level as we expected a linear
> relationship within the narrow range of pH levels observed. We included an
> indicator variable for an effect of precipitation on detection to account for
> potential declines in detectability when it was raining.
> We compared models using Akaike Information Criterion corrected for small
> sample size (AICc; Burnham and Anderson 2002). Models within 2 delta AICc
> values from the top model were considered competitive (Burnham and Anderson
> 2002). If there was model uncertainty (i.e., if more than one model was within
> 2 AIC of the top model), we used model averaging (Burnham and Anderson 2002).
> We assessed goodness of fit using a bootstrapped χ2 statistic outlined by
> MacKenzie and Bailey (2004). Occupancy analyses were conducted in program MARK
> (White and Burnham 1999).
> We used a likelihood ratio test to specifically test if pond size was an
> important factor in species Y occupancy. We conducted the likelihood ratio
> test on the fully parameterized model and the full model without the pond size
> factor. We used a significance level of 0.05 as our cutoff. The likelihood
> ratio test was conducted in the program MARK (White and Burnham 1999).
CONCLUSION
Writing clear, comprehensive, and repeatable Statistical Methods sections is an
important skill for ecological researchers. We want our research to be
accessible; therefore, it is important to write our articles to be digestible
regardless of the educational background of the reader. Statistical components
of a manuscript can often deter some from wanting to read an article or prevent
some from understanding what was done. For authors, writing Statistical Methods
sections can be daunting. Herein, we provide clear guidance for ecologists to
ensure their methods are interpretable by a broad audience—by clearly explaining
the objectives of each analytical approach—and their methods are repeatable—by
describing statistical methods, defining the variables, and stating the
program/packages used to implement the analyses.
ACKNOWLEDGMENTS
We want to thank the multiple researchers who provided comments on previous
drafts of this manuscript, including S. Baggett, E. Beval, F. Buderman, A.
Burns, M. Combs A. Feuka, R. Giglio, E. Helmer, J. Morisette, C Pierce, S.
Shriner, and S. McKee. The findings and conclusions in this report are those of
the author(s) and should not be construed to represent any official USDA or U.S.
Government determination or policy. This research was supported [in part] by the
U.S. Department of Agriculture, Forest Service. Any use of trade, firm, or
product names is for descriptive purposes only and does not imply endorsement by
the U.S. Government.
CONFLICT OF INTEREST STATEMENT
The authors declare no conflicts of interest.
OPEN RESEARCH
DATA AVAILABILITY STATEMENT
No data were collected for this study.
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* FIGURES
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DETAILS
Published 2023. This article is a U.S. Government work and is in the public
domain in the USA. Ecosphere published by Wiley Periodicals LLC on behalf of The
Ecological Society of America.
This is an open access article under the terms of the Creative Commons
Attribution License, which permits use, distribution and reproduction in any
medium, provided the original work is properly cited.
* Check for updates
RESEARCH FUNDING
* U.S. Department of Agriculture, Forest Service
KEYWORDS
* ecological communication
* quantitative ecology
* scientific writing
* statistical methods
* statistics education
* writing clarity
PUBLICATION HISTORY
* Issue Online: 24 May 2023
* Version of Record online: 24 May 2023
* Manuscript accepted: 30 March 2023
* Manuscript received: 20 March 2023
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