Statistical considerations in the analysis of minirhizotron data and a review of current practice in agronomic research

Abstract

A growing body of agronomic research seeks to understand the drivers of plant‐ and field‐scale patterns of crop root system distribution, and how root system distribution in turn affects crop performance. Minirhizotrons play an important role in this effort due to the unique opportunities they provide for collecting in situ root measurements, nondestructively, under field conditions, over a deep (albeit narrow) section of the soil profile. Alongside these advantages and opportunities, however, minirhizotron data also feature a number of idiosyncrasies with potentially important implications for their analysis, including (i) doubly repeated measures in time and space, (ii) non‐normal data with a potentially large number of zeros, and (iii) data subjected to spatial aggregation and, thus, the modifiable areal unit problem. Twenty years of peer‐reviewed journal articles from field trials using minirhizotrons to study cultivated species were reviewed to understand how these statistical issues are being addressed in contemporary agronomic research. The findings indicate that a large proportion of analyses make no effort to account for these issues; it is possible the authors are not aware of them or their implications. Furthermore, even where the analytical methods do reflect concern about one or more of these issues, many studies remain reliant on antiquated and potentially inefficient methods. Crop root systems researchers need to familiarize themselves with more modern, flexible approaches to statistical analysis appropriate to their data and their research objectives, while journals and reviewers need to redouble their efforts to enforce statistical rigor in the works they publish.

Full text

Received: 4 October 2024 Accepted: 28 November 2024
DOI: 10.1002/vzj2.20395
Vadose Zone Journal
REVIEW
Statistical considerations in the analysis of minirhizotron data and
a review of current practice in agronomic research
Simon Riley Edzard van Santen
Statistical Consulting Unit, Institute of Food
and Agricultural Science, University of
Florida, Gainesville, Florida, USA
Correspondence
Simon Riley, Statistical Consulting Unit,
Institute of Food and Agricultural Science,
University of Florida, Gainesville, FL, USA.
Email: simon.riley@ufl.edu
Assigned to Associate Editor Yingxue Yu.
Abstract
A growing body of agronomic research seeks to understand the drivers of plant-
and field-scale patterns of crop root system distribution, and how root system dis-
tribution in turn affects crop performance. Minirhizotrons play an important role in
this effort due to the unique opportunities they provide for collecting in situ root
measurements, nondestructively, under field conditions, over a deep (albeit narrow)
section of the soil profile. Alongside these advantages and opportunities, however,
minirhizotron data also feature a number of idiosyncrasies with potentially impor-
tant implications for their analysis, including (i) doubly repeated measures in time
and space, (ii) non-normal data with a potentially large number of zeros, and (iii)
data subjected to spatial aggregation and, thus, the modifiable areal unit problem.
Twenty years of peer-reviewed journal articles from field trials using minirhizotrons
to study cultivated species were reviewed to understand how these statistical issues
are being addressed in contemporary agronomic research. The findings indicate that
a large proportion of analyses make no effort to account for these issues; it is possible
the authors are not aware of them or their implications. Furthermore, even where the
analytical methods do reflect concern about one or more of these issues, many studies
remain reliant on antiquated and potentially inefficient methods. Crop root systems
researchers need to familiarize themselves with more modern, flexible approaches
to statistical analysis appropriate to their data and their research objectives, while
journals and reviewers need to redouble their efforts to enforce statistical rigor in the
works they publish.
Plain Language Summary
Minirhizotrons are clear plastic tubes that are buried in the soil so that plant roots
can be photographed and measured. They are important in research on how crop
roots are distributed in the soil and how that distribution changes over time. There
Abbreviations: GLM, generalized linear model; GLMM, generalized linear mixed model; LMM, linear mixed model; MANOVA, multivariate analysis of
variance; MAUP, modifiable areal unit problem.
This is an open access article under the terms of the Creative Commons Attribution- NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided
the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
©2025 The Author(s). Vadose Zone Journal published by Wiley Periodicals LLC on behalf of Soil Science Society of America.
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are a number of factors, though, which make the analysis of data from these studies
more complicated than for other types of experiments, and it is unknown how aware
researchers are of these issues or what they are doing to address them. This study
aimed to answer those questions and to find areas for improvement in how researchers
analyze their data by reading through descriptions of the statistical methods used in
minirhizotron studies conducted in the last 20 years. Some important findings are that
researchers are not reporting as much detail as they should be regarding the statistical
methods they are using, and that many researchers are analyzing their data in ways
that are likely to exaggerate the importance of some of their findings.
1INTRODUCTION
1.1 Minirhizotrons in modern crop root
systems research
The term “mini-rhizotron” was coined by Böhm (1974),
although the idea of using a transparent tube to observe roots
in the field was first proposed nearly 40 years earlier by
Bates (1937). Initially, tubes made of glass were installed
vertically into a hole augered in the soil and observations
of crop roots were made via an angled mirror lowered into
the tube at the end of a long shaft; photographs could not
be taken for subsequent measurement or other use. By the
year 2000, glass minirhizotrons had largely been supplanted
by acrylic, polycarbonate, or cellulose acetate butyrate tubes,
which were generally being installed at an angle of between
30˚ and 60˚ from horizontal, and roots were being recorded
using commercially available cameras and video cameras spe-
cially constructed for use in minirhizotron systems (Smit
et al., 2000; Vamerali et al., 2012). At that time, measur-
ing the length or diameter of individual root segments was
costly, time-consuming, and error prone because it had to be
done manually. It was thus common to instead record the
number of root segments appearing in each minirhizotron
image. Software for automating the identification and mea-
surement of washed roots placed on a uniform background
has existed since the mid-1980s, and the first effort to train an
artificial neural network to identify roots in a minirhizotron
images was made in 1992 (Richner et al., 2000). Today, there
are both proprietary and open-source versions of software,
which partially automate root tracing and measurement, and
there is considerable interest in leveraging recent advances in
machine learning algorithms to improve the accuracy of such
systems.
Minirhizotrons have proven useful in several broad lines
of inquiry, including research into root interactions with par-
asitic plants, Rhizobia, mycorrhizal fungi, nematodes, and
other soil organisms, and have also been extensively employed
in studies examining root longevity and processes of senes-
cence and decay, especially among tree crops and other
perennial species. Most frequently, however, minirhizotrons
are employed in research seeking to characterize the spatial
and temporal distribution of crop root production, how this
distribution is affected by genotypic, environmental, and/or
management conditions, and the degree to which such differ-
ences in root distribution are associated with differences in
yield or other measures of crop performance. Even in heavily
managed agricultural soils, there can be pronounced gradients
in temperature, pH, moisture, oxygen, and, of course, nutrient
concentrations. These gradients themselves are not necessar-
ily fixed, but may instead evolve and change throughout the
year (Adamchuk et al., 2010). The accessibility of both nutri-
ents and water as well as the avoidance of hypoxic or other
adverse soil conditions is thus subject to where and when a
plant’s roots are present in the soil and for how long they per-
sist (Lynch, 1995, 2007). Minirhizotrons are instrumental in
such research because they are nearly unique in providing the
ability to collect (comparatively) large numbers of in situ root
measurements, nondestructively, under field conditions, over
a deep (albeit narrow) section of the soil profile. Alongside
these advantages and opportunities, however, minirhizotron
data also feature a number of idiosyncrasies with potentially
important implications for their analysis, including (i) dou-
bly repeated measures in time and space, (ii) non-normal data
with a potentially large number of zeros (some of which are
true zeros and others non-detections), and (iii) data subject to
spatial (and temporal) aggregation and, thus, the modifiable
areal unit problem (MAUP).
The remainder of Section 1will describe in greater detail
each of these idiosyncrasies of minirhizotron data from a sta-
tistical perspective, including how they relate to the most
commonly employed analytical approaches used in agronomy,
the implications of ignoring them on the resulting estimates
and inferences, and a cursory review of existing methods
employed to address them. It should be noted that minirhi-
zotrons are distinctive, but hardly unique, in introducing this
particular combination of statistical complications. Those
who perform studies using pore-water sampling devices such

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as the one described by Bertolin et al. (1995), for example, will
face nearly identical concerns, as might some of those con-
ducting research using electrical resistivity tomography (de
Franco et al., 2009), among others. It is the authors’ hope that
this work may thus also prove of interest to others in agron-
omy, soil science, and beyond, whose research instruments
introduce a similar suite of issues.
Section 2then describes the structured literature search
employed in this review, along with the protocol employed
for article screening and retention. Finally, a brief outline
is provided of how the methods used in the retained arti-
cles are classified for subsequent reporting. Section 3reports
the results of the literature search, aiming primarily to char-
acterize current statistical practice in minirhizotron research
in the field of agronomy. Section 4, in contrast, discusses
those findings with specific focus on the agronomic implica-
tions of those statistical and data analytic choices. Section 5
concludes the work with a review of the findings and pro-
vides recommendations for researchers, journal editors, and
reviewers.
1.2 Statistical considerations in the analysis
of minirhizotron data
In order to make the ensuing discussion more concrete, it will
be presented in the context of a specific minirhizotron study
originally published by Zurweller et al. (2018). That study (the
complete details of which are provided in the original pub-
lication), sought to understand how root system growth and
distribution differed among various peanut (Arachis hypogaea
L.) cultivars grown in the Southeastern United States when
cultivated under different irrigation regimes. The four cul-
tivars included in the study represented two Valencia-type
cultivars (A. hypogaea L. subsp. Fastigiate Waldron) and
two runner-type cultivars (A. hypogaea L. subsp. hypogaea),
while the irrigation treatments in the study included, in
ascending order of the volume of water provided to the crop:
rain-fed (i.e., no irrigation), deficit irrigation, primed accli-
mation, and full irrigation (see the original publication for
the specific definitions of each irrigation treatment within
the context of that particular study). The experiment had a
full factorial treatment structure and was established as a ran-
domized complete block design with a split-plot restriction
on randomization, with irrigation as the main-plot factor and
cultivar as the sub-plot factor. Shortly after planting, a single
minirhizotron tube was installed into a row of peanuts within
each subplot at an angle of approximately 60˚ from horizontal.
Root imaging was then performed at five different timepoints
throughout the growing season (namely, 21, 28, 35, 56, and 75
days after planting), with approximately 83 images (spanning
a depth of approximately 800 mm) being collected from each
minirhizotron on each sampling date. The study included four
Core Ideas
∙Many minirhizotron studies rely on antiquated,
inefficient, or inappropriate statistical methods.
∙Minirhizotron studies often generate doubly
repeated measures data but are almost never
analyzed as such.
∙The modifiable areal unit problem has impor-
tant implications for studies of crop root system
distribution.
blocks and was conducted at a single location in each of two
successive years.
1.2.1 General issues of experimental design
If we contrast the root measurements just described with,
for example, the yield data that emerge from the same study
(there are more than 400 minirhizotron images collected from
each plot in which a single yield measurement is taken), it
can be seen that the use of minirhizotrons in such field trials
constitutes the addition of a particular sampling framework
onto an underlying experimental design. Thus, in addition to
those statistical issues, discussed below, which are specific
to minirhizotron studies as a result of that sampling frame-
work (among other factors), there are also the general issues
of proper design that are common to all designed experiments.
These basic principles are violated (sometimes subtly) with
enough regularity to warrant their brief reiteration here; those
interested in a fuller treatment of the topic are referred to Lent-
ner and Bishop (1993), Casella (2008), and Dean et al. (2017).
The fundamental tenets of experimental design are
randomization, which ensures that estimates are unbiased;
replication, which ensures that there is a valid error term from
which to calculate confidence intervals and perform tests;
and blocking, which can improve the precision of estimates
and the power of tests. This implies, in our example, that the
delineation of blocks would have been made based on known
variation in edaphic conditions, management history, or other
conditions at the research site, and not simply arbitrarily
defined (using what Stroup [2013b, p. 475] referred to as
“convenience blocking”). It furthermore means that the
experimental unit for the irrigation treatments was defined
by the smallest physical area to which an irrigation treatment
could be independently applied, and it was at this scale that
irrigation treatments were replicated, regardless of the size of
the experimental unit and appropriate scale of replication for
cultivar (Casler et al., 2015). Zurweller et al. also took care
to re-randomize the allocation of treatments to experimental
units within each main plot, block, and year, and avoided

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either using systematic treatment allocations (van Santen &
West, 2012) or “recycling” randomization schemes (Nelson
& Rawlings, 1983). Finally, the experimental design, in this
instance the blocking structure and split-plot restriction on
randomization, along with the treatment structure, all need
to be reflected in the model employed in the analysis (Frey
et al., 2024; Littell et al., 2006).
1.2.2 Singly repeated or doubly repeated
measures and anisotropic correlation
When the same measurement is taken on each experimen-
tal unit at different points in time, the data are said to be
repeated measures. The same is true when a measurement is
taken at a series of different locations or positions within each
experimental unit, as when a single soil core is segmented,
and measurements are recorded separately for each depth.
Where measurements are repeated in both time and space,
the data are said to be doubly repeated measures (Piepho
et al., 2004). Minirhizotron studies often generate such data,
as exemplified in the Zurweller study: for any given minirhi-
zotron, each point below the soil surface was photographed on
five separate occasions over the course of the study (repeated
measures in time), while each sampling day entailed collect-
ing 80 or more photographs from physically adjacent regions
of the soil profile (repeated measures in space). Repeated
measures data inherently violate the linear model assumption
of independence among observations, although the degree
of residual correlation as well as its form or structure may
differ depending on the specific context. Ignoring this correla-
tion during an analysis constitutes pseudoreplication, defined
by Hulbert (1984, p. 187) as “the use of inferential statis-
tics to test for treatment effects with data from experiments
where either treatments are not replicated (though samples
may be) or replicates are not statistically independent.” It
results in invalid standard errors (generally too small) and,
consequently, greatly inflated type I error rates (Littell et al.,
2000). Historically, several approaches have been developed
to address this, the simplest of which is to reduce the repeated
measures to a single summary statistic (Piepho et al., 2004).
A minirhizotron study could, for example, sum or average
(for each minirhizotron) the measures taken over time, space,
or both. But this approach, of course, makes it impossible
to examine the temporal, spatial, or spatiotemporal pro-
file, or how that profile interacts with other treatments or
covariates.
Historically, the most common alternatives for analyzing
repeated measures data were either to use multivariate analy-
sis of variance (MANOVA) or to treat the repeated measures
(referred to as the within-subject factor) as being analo-
gous to the sub-plots in a split-plot or split-block experiment
(for a completely randomized design or randomized com-
plete block design, respectively) (Steel et al., 1997). The
former is often conservative and, correspondingly, has lim-
ited statistical power. It can also be very inefficient because a
missing observation from any timepoint or location renders
the rest of the data from that subject unusable. Regarding
the latter approach, the split-plot (or split-block) analogy is
an imperfect one: neither time nor location are treatments
being randomly assigned to experimental units the way a
sub-plot factor is in an actual split-plot experiment. This
approach implicitly treats observations as being equally cor-
related regardless of their degree of separation in space or
time (which is not typically a realistic assumption) and cor-
respondingly has a tendency to underestimate the degree of
correlation among the residuals, ultimately resulting in overly
narrow confidence intervals and increased type I error rate
(Littell et al., 2000; Stroup, 2013a).
With the advent, beginning in the 1990s, of software for fit-
ting mixed models, it has been possible for researchers to relax
the linear model assumptions of independence and homo-
geneity of variance, to directly model the correlation in the
residuals of repeated measures data, and to thereby avoid the
shortcomings of the two earlier modeling approaches. The use
of mixed models for the analysis of repeated measures data has
thus since become commonplace across a wide variety of dis-
ciplines (Molenberghs & Verbeke, 2000). At the same time,
numerous other methods have been developed or deployed for
modeling serially correlated data, mostly within the general
frameworks of time-series analysis and spatial (or spatiotem-
poral) statistics, but to date these methods have seen fairly
limited adoption in the fields of agronomy and crop science.
These methods include, among others, various autocovariate
and autoregressive models (Dormann et al., 2007), gener-
alized additive models, and dynamic (state-space) models
(Wikle et al., 2019).
Finally, when seeking—in a mixed modeling framework—
to identify a parsimonious model for the dependence among
repeated measures, it will in many instances be plausible
to assume that the degree of correlation among residuals is
purely a function of the distance (in time or space), which sep-
arates the two observations. In others, however, the direction
or dimension of separation as well as the distance deter-
mine the degree of correlation. These patterns are known
as anisotropic correlation structures, and are the norm when
the dimensions in question, such as time and depth, are not
directly comparable in the way that, for example, latitude
and longitude are. Many ways of modeling anisotropic cor-
relation structures have been developed (see Montero et al.
[2015] for an in-depth treatment of the topic), but among
the simplest ways is to take the Kronecker product of two
isotropic correlation structures (Piepho et al., 2004), but this
functionality is not consistently implemented in statistical
software; it is available for a variety of correlation structures
in SAS PROC MIXED (SAS/STAT 15.2; SAS Institute) and
for power correlation structures in PROC GLIMMIX, is avail-
able in AS-REML (VSN International Ltd.), and to a limited

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FIGURE 1 A hypothetical example of how the modifiable areal unit problem could introduce challenges to the interpretation of minirhizotron
(MR) data.
degree in the R package sommer. It is not available in any
of the other, more commonly employed mixed modeling R
packages: nlme, lme4, or glmmTMB.
1.2.3 Data aggregation and the modifiable
areal unit problem
The MAUP, a term first coined by the geographers Stan Open-
shaw and Peter Taylor (1979), is an issue which arises when
spatial data are aggregated prior to their analysis, but in the
absence of an a priori basis for defining the size and/or loca-
tion of the resulting aggregations or “areal units” (Jelinski &
Wu, 1996). In the Zurweller study, for example, the authors
chose to aggregate their minirhizotron measurements taken
from 1.95 cm images into 20-cm depth classes before ana-
lyzing them. The essentially arbitrary size (or placement) of
the areal units, however, can give rise to similarly arbitrary
estimates and spurious inferences: a different choice of depth
class size can produce very different, even contradictory, con-
clusions from the same minirhizotron data. The sizing of the
aggregates—termed the “scale problem”—is more relevant to
minirhizotron studies than their location—known as the “zon-
ing problem”—since depth classes are usually delineated to
be contiguous and beginning at the soil surface. The zoning
problem can enter into minirhizotron studies if the topmost
depth class begins not at the soil surface but after some arbi-
trary depth below it or if non-contiguous depth classes were
employed.
Consider the following hypothetical example (Figure 1),
in which total root lengths (mm), originally measured from
images capturing 1 cm of vertical depth and 1 cm width of
the soil profile from three replicate minirhizotrons (MR 1–3),
are to be aggregated into either two depth classes of 6 cm each
or three depth classes of 4 cm each.
If two depth classes are employed, the mean root length
intensity (total root length [mm], divided by the total area
[cm2]) in the upper depth class is larger than that of the
lower depth class (7.21 and 7.11 mm/cm2, respectively),
although the p-value for the corresponding test exceeds 0.40.
But when three depth classes are employed, the upper depth
class becomes the smallest of the three (6.08, 8.75, and
6.65 mm/cm2), and all three pairwise comparisons have
p-values below 0.05.
Since the MAUP, by definition, only arises when there is
no a priori basis for preferring one scale or arrangement of
areal units over another, the simplest way to avoid it is to
find and use areal units with a meaningful physical, biolog-
ical, or pedological basis whenever possible. When this is not
possible, two avenues have been pursued within the statisti-
cal literature, namely, identifying algorithms which will scale
and arrange areal units optimally or near optimally according
to some criteria (e.g., Osnes, 1999) or methods for sensitivity
analysis which can help identify how robust some estimate or
inference is, given the data at hand, to alternative definitions
of the areal units being analyzed (see, for example, Duque
et al., 2018; Re et al., 2020). The final, albeit trivial, way to
avoid the MAUP is to completely aggregate the data: as with
the issue of repeated measures, reducing the data to a single
summary statistic prior to analysis avoids the modeling com-
plications at the cost of not being able to investigate the spatial
distribution of the roots.
1.2.4 The probability distribution of root
measures and the question of transformation
Minirhizotron measurements of root length (or root length
density) are not normally distributed: such values are obvi-
ously strictly non-negative, but often feature a relatively large

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number of zeros, including both those which arise from sam-
pling variation (i.e., from regions where roots are present but,
by chance, not observed in a particular minirhizotron on a
particular sampling date) as well as true absences (i.e., from
regions of the soil profile where the root system has not yet
penetrated by the time of sampling). Yet, high-length obser-
vations are made with enough regularity to produce data with
heavy right skew. Finally, the variance has a tendency to
increase or decrease in concordance with the mean: observa-
tions taken from areas, times, or treatments with high average
root length are more variable than those taken from areas
with low average root count, which tend to all be consistently
low. Given the linear model assumptions that the residuals
are normally distributed1and with homogeneous variance, the
question then becomes whether and how to address the clear
violations of these assumptions.
Before proceeding further, however, it is worth noting that
these two assumptions—commonly known as the assump-
tions of normality and homoscedasticity, respectively—are
too closely related but distinct concerns. For example, many
distributions have a variance which is wholly or partially a
function of the mean, including the Poisson and negative bino-
mial distributions (which model data in the form of counts per
unit of time or space), the binomial distribution (which mod-
els data in the form of counts of “successes” out of some total
number of trials), the beta distributions (which models con-
tinuous proportions or percentages), and the exponential and
gamma distributions (which model time-to-event data, among
others), and so on. Thus, in these cases the non-normality of
the data also necessarily implies heteroscedasticity. In other
cases, however, data may exhibit heteroscedasticity while
still being normal (as when the data from untreated con-
trols exhibit substantially greater variability in their response
than the treated subjects) or may exhibit deviations from
normality in the form of excess skew (asymmetry) or kur-
tosis (“peaky-ness,” informally) while still having constant
variance.
First, consider the implications if, in the context of the Zur-
weller et al. study, the non-normality and heteroscedasticity in
the data had simply been ignored. Estimated treatment means
would remain unbiased, but confidence intervals could easily
extend beyond the limits of what is physically or biologically
possible (e.g., negative total root length or root mortality in
excess of 100%), leading to truncated confidence intervals
and uncertain type I error control (Stroup, 2015). At the same
time, modest sample sizes combined with unequal replica-
1The residuals being normally distributed is equivalent to saying that the data
are normally distributed conditional upon the fixed (and random) effects,with
the conditionality aspect usually left implicit and unstated in discussion of
modeling assumptions. This convention has been a source of some confusion
among researchers (Kozak & Piepho, 2018), so here we wish to state explic-
itly that all subsequent references to data having a particular distribution, we
are referring to the conditional, not the marginal, distribution of the data.
tion, variance, or skewness among treatment groups can badly
affect the efficiency of t-tests (Kaufman, 2013; Miller, 1997),
increasing the risk that existing differences in total root length
among, for example, cultivars, irrigation treatments, or stages
in the growing season, would have remained obscured.
Rank-based nonparametric methods are sometimes used as
an alternative analytical approach when the assumptions of
the linear model are violated, although they are perhaps less
widely employed in the fields of agronomy and crop science
than in some other disciplines. These methods can be more
efficient than the linear model when the assumptions of nor-
mality are not met but will always be less efficient than a
parametric analysis whose distributional assumptions are met
(Miller, 1997). In other words, if there is a distribution other
than the normal that characterizes the minirhizotron data, non-
parametric methods may be an improvement over the linear
model but not over a generalized linear model (see below). It
should also be noted that nonparametric methods have their
own assumptions, which likewise should be assessed during
model development and evaluation, and which may not hold
in all instances (Hart, 2001; Verma & Abdel-Salam, 2019).
The approach actually taken by Zurweller et al. to address
the issues of non-normality and heteroscedasticity was to
apply a variance stabilizing transformation, specifically a
square-root transformation. The use of such transformations
prior to the analysis of skewed and/or heteroscedastic data is
very common and, to the extent that it succeeds in eliminat-
ing skew and heteroscedasticity, can improve the efficiency
of tests performed. Their use, however, also introduces a
number of complications which are perhaps underappreciated
by many researchers. First, it can be difficult to interpret
effects when they are reported on the transformed scale:
how might one understand, for example, the practical agri-
cultural importance of a seed treatment which increases
the arcsine-square-root-transformed germination rate from
1.11 to 1.252? How much greater is a log-transformed root
length intensity (cm cm−2) of 2.802 compared with one of
0.5003? Importantly, such point estimates and their stan-
dard errors and confidence intervals also cannot simply be
back-transformed while retaining their original interpretation
when the transformation used is nonlinear. A bias correction
factor, of which there are several, must be applied to correct
point estimates during back-transformation if they are to
be reported as a mean on the original scale (Piepho, 2009;
Smith, 1993), while the delta rule is needed to generate
approximate standard errors and confidence intervals (Bow-
ley, 2015). Finally, the use of a transformation on data from a
non-normal distribution such as the binomial or Poisson may
not only fail to eliminate bias in the estimates or standard
errors, it can sometimes make them worse (Stroup, 2015).
280% and 90% germination, respectively.
3Approximately an order of magnitude.

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The angular transformation (as the arcsine-square-root
transformation is sometimes known), for example, can fail
to produce homoscedastic data (even while rendering the
variance independent of the mean) and introduce spurious
differences among treatments when it is applied to binomial
counts taken from differing numbers of trials (Kasuya, 2004).
A more modern approach to these issues is to employ linear
mixed models (LMMs), generalized linear models (GLMs),
or generalized linear mixed models (GLMMs). The former
enable researchers to directly model patterns in the variance
(of normally distributed data) as a function of covariates
within the data, or even as a function of the linear predictor
(Pinheiro & Bates, 2009, pp. 206–225). One might, for exam-
ple, model minirhizotron measurements of root length density
having a residual variance as being equal to |μ|2ϴ, where μis
the estimated treatment mean and ϴis an estimated dispersion
parameter. This approach requires that degrees of freedom
for testing treatment effects be approximated, and there will
no longer be a single least significant difference applicable
to all comparisons, among other minor inconveniences, but
the approach otherwise generally ensures statistical power
and efficiency are maintained (Piepho, 2009). GLMs and
GLMMs (the latter differing from the former by the inclu-
sion of random effects) are appropriate when theoretical or
practical considerations make it reasonable to assume that the
data come from a distribution in the exponential family other
than the normal, and are the most efficient available option
when those assumptions are true, among other advantages.
An in-depth treatment of GLMMs are beyond the scope of
this work, but interested readers are referred to the works of
Stroup (2015) and Gbur et al. (2012).
Finally, we consider some of the ways available to model
data with a high proportion of zeros. Tobin (1958) defined a
likelihood function for censored (normal) variables, for which
negative values manifest as zero (or the value at some other
censoring point). This is similar to hurdle models (Cragg,
1971) in which the occurrence of an event (e.g., the observa-
tion of a root segment) is assumed to be Bernoulli distributed
while the magnitude of the event (e.g., the length of the root
segment) is defined by some positive continuous distribution,
such as the lognormal, gamma, or chi-square distribution. The
Tweedie distribution (with power parameter between 1 and
2) characterizes events which occur with Poisson-distributed
frequency and gamma-distributed magnitude (Foster & Brav-
ington, 2013). Finally, zero-inflated models (Lambert, 1992)
are employed to describe data assumed to contain a mixture
of zeros from different sources (distributions). For exam-
ple, one might assume counts of root segments to follow a
zero-inflated Poisson or zero-inflated negative binomial dis-
tribution, since only zeros can be observed at depths below
the rooting zone while some zeros are still observed within
the rooting zone simply due to sampling variability. The
chief obstacle to the use of these approaches is that they can
require larger sample sizes than are typical of most agronomic
experiments.
Having now considered, from a statistical perspective,
some of the features of minirhizotron data, how those issues
have historically been addressed, and some of the implications
of those different modeling choices (see the Supplementary
Information for a brief summary of these issues in check-
list form), we now turn to consider the analytical methods
being employed in the field of agronomy for the analysis of
minirhizotron data and the agronomic implications of those
choices.
2MATERIALS AND METHODS
2.1 Literature search
This is not a systematic review in the sense of, for exam-
ple, Higgins et al. (2019), in that it does not seek to be an
exhaustive search of all the relevant literature, including non-
peer-reviewed and unpublished works. Like such systematic
reviews, however, it does seek to comprehensively examine
peer-reviewed studies within a well-defined scope and using
predefined search and inclusion criteria. The nature of the
inquiry precludes any meta-analysis, and we are only con-
cerned with the methodological and analytical choices made
by the authors of articles published in journals with the high-
est editorial and peer-review standards, so there is little to be
gained from a search of the grey literature or searches among
databases, which included non-indexed journals (e.g., Google
Scholar or lens.org).
A search was performed within the Web of Science’s “Sci-
ence Citation Index Expanded” (SCIE) for original research
articles in the domains of agriculture, plant science, soil sci-
ence, horticulture, and ecology, which were published within
the 20 years preceding June 1, 2023, and which contain the
word “minirhizotron” or “mini-rhizotron” (or the plural form
of either spelling) in their abstract. This search returned 315
results. Of these studies, 163 were removed: 113 because they
were studies of non-cultivated plants (including 12 focused
on mycorrhizal fungi, 16 on crop parasites such as Striga
(Lour.), and the rest from natural ecosystems) (Table S1),
24 were removed because the study did not employ minirhi-
zotrons (Table S2), either at all or as here defined, and 26
were removed because they were not field studies (e.g., lab-
oratory studies, mesocosm studies, or review articles) (Table
S3). Finally, two studies were removed because no statistical
analysis was performed on the minirhizotron data collected
(Table S4). Of the 150 articles retained, 30 were related to the
development of methodological, data processing, or analyti-
cal methods for minirhizotron studies (Table S5), while the
remaining 120 were minirhizotron field studies of crop root
systems (Table S6).

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The 120 field studies employing minirhizotrons to study
crop root growth and distribution were then carefully
reviewed and key details were extracted and recorded in
a spreadsheet. Specific attention was given to the studies’
methodologies, including data collection, collation, aggrega-
tion, analysis, and reporting. Following a careful examination
of the types of the sampling procedures, data processing
methods, and statistical analyses reported in the reviewed
articles, each article was subsequently coded in terms of
(i) the type and frequency of minirhizotron sampling (e.g.,
at regular intervals or at specific physiological stages of
plant development), (ii) the type and scale of spatial data
aggregation (e.g., uniformly sized depth classes or accord-
ing to the soil horizons), (iii) the modeling approach,
including both general features (e.g., fixed or mixed mod-
eling approach) as well as specifics (e.g., factors treated as
repeated or random effects), and (iv) distributional assump-
tions employed in fitting the model (including whether they
were verified and what approach was taken if they were
not).
3 RESULTS
Before proceeding with the results, it is necessary to acknowl-
edge that many of the papers reviewed do not provide enough
detail regarding the methods they employed for their analy-
sis to confidently characterize some of the modeling choices
which are of interest to this study. Some of the details can,
in some instances, be reasonably inferred from the results
presented in these studies, but not in all cases. Thus, for exam-
ple, some studies in which the choice of depth class appear
arbitrary could have been determined based on, for exam-
ple, the depth of the plowed layer or some other function
of management decisions, or based on the arrangement or
spacing of other research instruments, but those facts were
simply not made explicit in the methods. Similarly, among
those studies which are described as having not discussed the
distributional assumptions of their model, there may be some
whose authors did carefully verify that the residuals were
normally distributed and would have taken some corrective
action had the assumption been violated, but simply did not
report doing so. In fact, 71 out of 120 studies, or nearly 60%,
made no mention whatsoever of whether or how they veri-
fied model assumptions or assessed model fit. Moreover, of
the 42 studies which describe fitting a mixed model, 10%, or
nearly 25%, failed to describe which terms were fixed and/or
which were random or omitted other crucial details. This is
an important caveat to bear in mind when interpreting the
results presented here, but the lack of detail in the description
of statistical methods is also an important finding in its own
right.
3.1 Study locations, durations, and
sampling frequencies
The 120 articles represented research conducted across 19
countries, although most of the experiments were performed
in the United States (30.0%), Denmark (19.2%), or China
(12.5%). The experiments included more than 57 distinct
crops, including forages, wheat (Triticum aestivum L.), bar-
ley (Hordeum vulgare L.), and maize (Zea mays L.) among
the most commonly studied. The studies ranged in duration
from one to nine cropping seasons, although a majority were
either one (32.5%) or two (40.8%) cropping seasons in dura-
tion. Minirhizotrons were most commonly installed either at
a 45˚ from horizontal (54 studies, or 43.2%) or 60˚ from hori-
zontal (43 studies, or 34.4%). Minirhizotrons were installed at
angles between 0˚ and 45˚ in 14 studies, between 45˚ and 60˚
in four studies, and between 60˚ and 90˚ in three studies; three
additional studies did not report the angle of minirhizotron
installation. Forty-two of the 120 studies (35%) conducted
sampling at irregular intervals, an additional 67 conducted
sampling at (approximately) regular intervals, whereas 11
conducted sampling only one to three times in the whole of the
study. Of those that conducted sampling at irregular intervals,
21 (17.5% of all studies, 50% of those with irregular sampling)
explicitly timed the sampling dates to correspond with spe-
cific stages in the crop’s physiological development, whereas
the remaining 21 did not give any justification for the choice of
sampling dates. Of those that sampled at regular intervals, the
most common practice was to do so fortnightly (32 studies),
monthly (14 studies) or weekly (seven studies).
3.2 Modeling repeated measures
Not all of the minirhizotron studies involved doubly repeated
measures: 20 studies aggregated or subset their data prior to
analysis such that all of the analyses involved only repeated
measures in time, while 14 others involved only repeated mea-
sures in space. Of the former, 15 recognized the repeated
measures aspect of their studies and made some effort to
account for it: three using a fixed-effects model, eight using
MANOVA, and four using mixed models. Among those stud-
ies with repeated measures in space, more than half did not
recognize or otherwise failed to account for the repeated mea-
sures aspect of their data, while one employed MANOVA and
two more fit mixed models.
Eighty analyses involved doubly-repeated measures, but at
least 41 of these (including 30 using fixed-effects models and
11 using mixed-effects models) did not describe taking this
into consideration during the analysis (Table 1). Ten stud-
ies employed MANOVA, although only two appear to have
recognized that both time and space were repeated measures.

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TABLE 1 Models used in the analysis of doubly repeated
minirhizotron data among 80 field studies focused on cultivated species
that were published between 2013 and 2023 in journals indexed in the
Science Citation Index Expanded collection.
Model type
Repeated factor
or random effect
No. of
studies
Fixed-effects models Nonea30
Time 2
Depth 2
Depth/time 1
MANOVAbTime 7
Depth 1
Time and depth 2
Mixed-effects models Nonec11
MRd3
Time 2
Time/depth 1
Depth 3
Depth/time 1
Correlated
residuals|time
6
Correlated
residuals|depth
2
Correlated
residuals|both
1
Other analyses/not
applicable
5
Abbreviation: MANOVA, multivariate analysis of variance; MR, minirhizotron.
aThis category includes those analyses which reported using “ANOVA”, “analysis
of variance”, “PROC GLM,” or other similarly vague or generic descriptors of
how the analysis was performed, and which did not comment on or report taking
action to account for the repeated measures nature of the data.
bIn addition to those who report using MANOVA explicitly, this category also
includes those which reported employing SAS’s PROC GLM with a repeated fac-
tor, which may then perform a multivariate analysis depending on the results of a
test of sphericity (Wolfinger & Chang, 1995).
cThis category includes mixed-effects models which included random terms unre-
lated to the repeated measures aspects of the study, such as block, or in the case of
studies with a split-plot restriction on randomization, block and mainplot.
dThis category includes studies which included a random effect corresponding to
the minirhizotron only, whereas in other mixed-effects models the minirhizotron
term is implied (i.e., random effect for time implies a term for minirhiztrons and
timepoints nested in minirhizotron).
Among the nine studies that explicitly modeled correlation in
the residuals, six did so only for measures repeated in time,
while only a single study included correlation structures for
both spatial and temporal dependence. Finally, among those
mixed model analyses modeled on a “split-plot-in-time” (or
space) analysis, there was a wide variety of ways that the
random effects were reported as having been specified.
Twenty-two studies included survival analysis, either alone
or in addition to others, typically modeling root lifespan
using the Cox Proportional Hazards model and Kaplan–Meier
curves.
In a number of cases, the researchers chose to perform sep-
arate analyses on each date, depth class, or date ×depth class
combination included in their study. The specific reason for
these decisions is not always clear, but in at least one case,
it may have been at least partly motivated by the fact that
it was perceived to obviate the need to account for repeated
measures. It may also have been related to the statistical folk
“wisdom”—widely believed in the field of agronomy but not
endorsed by any statistical text that the authors are aware
of—that the presence of a statistically significant interaction
between one of the treatment factors and either location or
year necessitates refitting separate models for each year or
location4
3.3 Type and scale of spatial data
aggregation
In total, 24 of the studies reviewed here aggregated their data
over the whole of the observed soil profile, thereby eliminat-
ing the possibility of examining the spatial or spatiotemporal
differences in root system distribution, but also eliminating
concerns associated with the MAUP (Table 2). At the other
extreme, 15 studies did not aggregate their data at all, instead
analyzing their data using depth classes equal to the size deter-
mined by the minirhizotron camera and the angle of insertion.
This was most often the case for those studies employing the
CI-600 camera (CID Bio-Sciences), which produces images
of approximately 20 cm in length. These studies thus used
depth classes of 20, 14.1, or 10 cm when minirhizotrons were
installed at 0˚, 45˚, and 60˚ from horizontal, respectively. In
only three studies did researchers with a camera that produced
images of circa 1 cm in height opt not to aggregate their data.
One of these studies was also the only one reviewed here in
which depth was treated as a continuous covariate, rather than
as discrete classes.
Among the 79 studies that did aggregate their data into
more than one depth class, only two chose to treat the pedolog-
ically identified soil horizons as natural units for aggregation,
15 used irregularly sized depth classes, and 61 used uniform
but essentially arbitrary depth class sizes (Table 2).
4Where a linear mixed model includes the appropriate treatment-by-
environment interaction terms as well as environment-specific variance
parameters (including residual variance, block variance, and possibly oth-
ers), the fixed effects estimates will exactly correspond to those produced
by a separate analysis of the data from each environment. But when variance
parameters can be assumed to be homogeneous among all or even some of the
environments, the combined analysis can produce more precise estimates of
the fixed effects than would be achieved by the separate analyses. For discus-
sion of where it may be advantageous to perform a two-stage analysis which
initially fits separate models for each environment, see Damesa et al. (2017).

10 of 16 RILEY ET AL.
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TABLE 2 Type and scale of spatial aggregation employed in
minirhizotron field studies focused on cultivated species which were
published between 2013 and 2023 in journals indexed in the Science
Citation Index Expanded collection.
Aggregation type Depth class size
No. of
studies
Complete Various 24
None ∼1cm 3
10 cm 5
14.1 cm 4
20 cm 3
Total 15
Soil profile based Various 3
Irregular/unequally sized Various 15
Uniform 10 cm 18
15 cm 6
20 cm 11
25 cm 9
50 cm 4
Other 13
Total 61
Not applicablea3
aThis includes two studies where minirhizotrons were installed horizontally into
the side of excavated trenches.
Several studies reported that their choice as to the scale of
aggregation was so that minirhizotron measurements would
correspond with measurements being collected by other sen-
sors, but in most instances there was no discussion of or
justification for the choice of depth class size or location (in
11 studies, the specification of the depth classes included an
offset, such that the top of the first depth class started, e.g., 3,
5, or 10 cm below the soil surface).
3.4 Distributional assumptions and
transformations
Seventy-one studies did not report checking the normality of
the residuals or modeling the data as coming from a distribu-
tion other than the normal. As noted previously, this does not
mean that such steps were not taken during the analysis, only
that they were not reported. In 11 of these cases, however, at
least one of the response variables was a count or proportion.
In one article which included analyses of both aboveground
and belowground measures of crop health and performance,
the methods describe modeling one count variable (the num-
ber of infected plants) as being distributed following the
negative binomial distribution, but a different count variable
(number of roots) was implicitly treated as being normally
distributed. Six studies reported verifying the assumption that
the residuals were normally distributed, either using graphical
techniques or via one of several formal tests, and another six
fit GLMMs with distributions more appropriate to the data-
generating process in question. Thirty-four studies reported
employing one or more type of transformation. The most com-
monly reported were the log (22 studies), square root (nine),
and fourth root (four) transformations, but also reported were
Tukey’s (1957) ladder of powers transformation (which is
similar to the Box and Cox (1964) transformation), arcsine-
square root, and others (note that studies are double counted
here if they report using more than one type of transforma-
tion). Six of the studies that employed a log transformation
on their data noted adding a constant either to all values or
to zero values prior to applying the transformation, while one
study employing the square root transformation noted that the
chosen transformation would need to accommodate zeros.
Of the 34 studies that employed a transformation, 10
stated explicitly that it was in order to “stabilize the vari-
ance” or “obtain homogeneity of variance” (including two
studies that based the decision on a formal test), while
seven additional studies had vaguer explanations about meet-
ing “distributional assumptions” or “model assumptions.”
The remaining 17 either referred only to “normalizing” or
“removing skew” from the data, or else provided no expla-
nation for the use of the transformation at all. Only a single
study described explicitly modeling heteroscedasticity in the
data.
4 DISCUSSION
The studies reviewed here are highly diverse in the crops
and rotations they examined, the experimental treatments
they employed, the metrics used, the geographical location
they were performed, the specific comparisons tested, and
in various other aspects. As such, the findings are most
usefully interpreted with regard to root systems research
broadly, or even more generally to the field of agronomy as a
whole.
Of these findings, four key issues, discussed in detail below,
regarding the analysis and reporting of minirhizotron stud-
ies stand out: (1) Statistical methods are not being adequately
described, (2) lack of independence among repeated measures
are being ignored, (3) analyses remain over-reliant on the use
of variance-stabilizing transformations, and (4) the MAUP
remains unacknowledged. It should also be noted, more as an
opportunity than a concern, that while most researchers opt
to treat depth and time as categorical variables in their analy-
sis of minirhizotron data (performing an analysis of variance
[ANOVA]-like, rather than regression type, analysis), there
exist tools that may better leverage the quantitative nature of

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this data, including in particular generalized additive mod-
els (Wood, 2017), and the tensor product splines for residual
modeling described by Verbyla et al. (2018).
4.1 Descriptions of the statistical methods
employed in minirhizotron studies are
frequently inadequate
Only when a study fully describes the methods it employed,
including its analytical methods, is it possible to make an
informed assessment of the strength of the evidence pre-
sented in support of its findings. In the framing of Lang
and Altman (2015, p. 6), the statistical methods of a study
should be described “with enough detail to enable a knowl-
edgeable reader with access to the original data to verify
the reported results.” Hofner et al. (2016, p. 416) go fur-
ther, calling for reproducible research, which they define as
“a publication [...] accompanied by all relevant material to
reproduce the results and findings of a scientific work.” Nel-
son and Rawlings (1983, p. 105) identified “failing to report
in the materials and methods section of the research report
the experimental design and statistical procedures used” as
one of their Ten Common Misuses of Statistics in Agronomic
Research and Reporting. Yet 40 years later, this review finds
that too many researchers continue to publish descriptions
of their analyses which are overly general, ambiguous, or
incomplete. Although it is impossible to determine from this
review whether this issue is more or less prevalent than in
the past, it remains a serious concern. The 2019 report on
reproducibility and replicability in science published by the
National Academies of Science, Engineering and Medicine
credits incomplete reporting as a contributor to low replicabil-
ity (NAS, 2019). Indeed, when reviewers and editors permit
manuscripts to be published that provide little or no detail
as to how the analysis was performed, and when researchers
cite and include in reviews the resulting articles, the disci-
pline chooses in effect to exempt statistical methodology from
peer review. The resulting uncertainty around how analyses
are performed also hinders efforts, such as this one, to char-
acterize current statistical practice and to identify areas for
potential improvement.
The increasing adoption of Open Science principles by
research institutions, funding agencies, publishers, and many
in the broader research community means that there is increas-
ing acceptance of the need to make available to the public the
data employed in an analysis (CGIAR, 2013;OSTP,2013).
If this were to be extended to the code employed in the anal-
ysis, it would go a long way toward addressing the issue of
inadequate reporting, although efforts in that direction appear
somewhat less well developed at present than they are for open
data (Culina et al., 2020). Additionally, a number of checklists
and other guidance on how to describe one’s statistical meth-
ods have been published (Davis & Kay, 2023; Kramer et al.,
2019; Parker et al., 2018), and journals could work to make
these materials more visible to both authors and reviewers.
Alternatively, journals in the fields of agronomy and crop sci-
ence could adopt the approach, employed by some medical
journals, of employing dedicated statistical reviewers (Gore
et al., 1992), although Kramer et al. (2016) seem to suggest
this solution is impracticable. Beyond helping to enforce suf-
ficient reporting, this approach would naturally also directly
help to correct some of the other statistical concerns raised by
this review.
4.2 The repeated measures aspect of
minirhizotron studies is often ignored
An overwhelming majority of the minirhizotron studies
reviewed here involved repeated measures, either in time,
space, or both, yet nearly half do not describe incorporat-
ing appropriate random effects, modeling residual correlation,
employing multivariate methods, or taking any other action
to account for this fact. To the extent that these analyses
involved pseudoreplication (as opposed to simply failing to
fully or accurately describe their analytical methods), then
these studies can be expected to exhibit an elevated fre-
quency of spurious findings, and to present estimates having
artificially high degrees of precision (Hulbert, 1984).
The frequency with which the repeated measures aspect
of minirhizotron studies was unrecognized (or ignored) by
both authors and reviewers suggests that there may be room
for improvement both in the statistical training provided to
graduate students (and researchers) in agronomy as well as
the norms and procedures employed in peer-review. A num-
ber of authors have previously suggested that the statistics
training provided to agronomists (Stroup, 1997), ecologists
(Touchon & McCoy, 2016), and biologists (Boyles et al.,
2008) may be in need of updating and revision. The find-
ings reported here certainly seem to suggest that agronomists
would still benefit from greater exposure to, and training in
LMM and GMM, especially but not exclusively as it per-
tains to the analysis of repeated measures data. Kramer et al.
(2016), however, argue that better statistical training for grad-
uate students by itself is insufficient, and researchers should
accommodate themselves to being life-long learners of statis-
tics, which is and will remain an evolving field in its own right.
This issue becomes doubly consequential, as those authors
note, when reviewers with inadequate or outdated statistical
training either defer to an author’s statistical methods without
adequate scrutiny or, worse still, give incorrect or misleading
feedback on authors’ analytical methods. As discussed pre-
viously, there may be opportunities for checklists, rubrics, or
more formal guidance from journals to help minimize such
occurrences.

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In fact, some journals and societies have attempted to
address this specific issue, alongside the broader efforts at
promoting open data and open code. Already by 2004, for
example, the Canadian Journal of Plant Science, the Canadian
Journal of Animal Science, and the Canadian Journal of Soil
Science were declining to publish “papers reporting the use
of the SAS GLM procedure to analyze datasets that include
random effects or repeated measurements on the same exper-
imental unit where the data show heterogeneous variances
and/or unequal within-subject time-dependent correlations.”
In contrast, the ASA-CSSA-SSSA Publications Handbook
and Style Manual (2023, pp. 4–01) takes the more ambigu-
ous position that “data observed at different points in space
and/or time on the same experimental material are often cor-
related. Many methods of statistical analysis are available for
examining such data [...]. For those that manifest tempo-
ral or spatial dependence, methods derived from regionalized
variable analysis and applied time series may be selected.”
This is somewhat surprising, given that the ASA-CSSA-SSSA
has elsewhere published guidance on the analysis of repeated
measures data that much more clearly and emphatically advo-
cate a mixed modeling approach to the analysis of repeated
measures data (Gezan & Carvalho, 2016).
4.3 Reliance on transformations remains
widespread in minirhizotron research
A large majority of the studies employing linear models in
their data analysis fail to describe whether the assumptions
of normality or homoscedasticity were assessed, and even
among those who report applying a transformation to their
data prior to analysis, most of these fail to report how these
assumptions were assessed. These facts speak further of the
aforementioned need for researchers to more fully document
the statistical methods employed in their analysis.
Forty-two percent of those studies that included an analysis
of root counts or proportions reported employing a GLMM.
This suggests that there is still considerable room for improve-
ment with regard to the efficiency of the methods with which
we, as a discipline, choose to analyze our data.
Moreover, there were no instances in which non-normality
and/or heteroscedasticity in measures of root length inten-
sity or other continuous metrics were addressed except by
a transformation. That the resulting estimates and standard
errors were often reported on the transformed scale suggests
that, although transformation bias is of minimal concern,
researchers may be giving insufficient attention to esti-
mates, and their interpretation, relative to test statistics and
p-values: statistical significance taking precedence over bio-
logical importance (McShane & Gelman, 2022). In two-thirds
of these cases, the measurements were log transformed, and
in a few cases a small constant was added either to all values
or to zero values prior to transformation. Adding a constant
to only the zero values will produce biased estimates, while
adding a constant to all values can negatively affect estimates
and inferences if the specific value employed is not chosen
with care (Berry, 1987). Moreover, employing maximum like-
lihood to select a value for the constant is problematic because
the likelihood will be unbounded for certain values (Voorn,
1981). Some proposed alternative approaches include using
Bayesian estimation (Hill, 1963) and selecting a value that
minimizes the sum of the skew and kurtosis in the residuals
(Berry, 1987).
4.4 The MAUP pervades minirhizotron
research but remains unacknowledged and
unaddressed by researchers
A large majority of the minirhizotron studies reviewed here
divided the soil profile into depth classes (explicitly, by aggre-
gating the data, or implicitly, by defaulting to the size of
the image produced by the minirhizotron camera) in order
to examine some aspect of the spatial distribution of crop
roots. And of these, nearly all used arbitrary depth class sizes,
determined without reference to the crops’ root anatomy or
physiology, any pedagogical factors, a consensus, or accepted
standard among researchers in the field, which this review
clearly shows does not exist. This implies that nearly all
minirhizotron studies considered here were subject to the
MAUP, yet the authors are not aware of any explicit treat-
ment or discussion of the implications it may have for crop
root systems research in the peer-reviewed literature.
It should also be noted that this issue is not specific to
analyses that treat depth classes as a categorical variable
(i.e., ANOVA-like analyses, by far the most typical in agro-
nomic studies employing minirhizotrons), but also potentially
impacts the estimates produced from fitting nonlinear mod-
els which treat depth as a continuous covariate. These models
include simple, purely empirical models such as the expo-
nential model of Gerwitz and Page (1974), as well as much
more sophisticated, mechanistic models such as that of Dupuy
et al. (2010). Although the use of such models avoids concerns
surrounding the interpretability or meaningfulness of pair-
wise comparisons among or between arbitrarily sized depth
classes, these models must still be fitted to data in which
measurements of root length are taken over some discretized
interval, the size of which may still potentially not only impact
parameter estimates but also the relative fitness of different
models.
Given the pervasiveness of this conceptual challenge
and the lack of a clear solution (absent some biologically
or pedagogically meaningful division of the soil profile),
it seems advisable for minirhizotron researchers to pursue
sensitivity analyses, since it is irrelevant that the depth class

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size is arbitrarily chosen if the results can be shown to be
robust to that decision. Additional research is also needed
to more fully understand the statistical implications that the
choice of depth class size has on analyses of minirhizotron
data and whether and how these may be conditioned by
other characteristic features of minirhizotron data, such as
non-normality and spatiotemporal correlation.
5CONCLUSION
Minirhizotrons play an important role in crop root systems
research and will likely remain for the foreseeable future
among the most cost-effective means of measuring both root
system distribution in the soil profile how such distributions
evolve over time. Depending on the specific objectives and
protocols of the study, however, minirhizotrons can generate
data that possess characteristics with important implications
for how their statistical analysis should proceed. Specifi-
cally, minirhizotron measures of root length and root length
intensity frequently constitute doubly repeated measures in
space and time, are often non-normal (including possessing
potentially high proportions of zeros, besides exhibiting con-
siderable skew), and being subject to the MAUP, wherein
estimates are sensitive to the arbitrary division of the soil
profile into depth classes prior to analysis.
Ignoring these features of minirhizotron data during the
analysis can negatively affect one’s analysis, with conse-
quences ranging from estimates and inferences, which are
difficult to interpret, to reducing statistical power and the effi-
ciency of one’s analysis, to greatly increasing the risk of type
I errors and the frequency of spurious findings. Naturally, a
variety of methods have been developed in the past to help
address each of these issues, but this review finds that many
crop root systems researchers working with minirhizotrons
appear to be either unaware of these issues or unfamiliar with
modern statistical methods capable of accommodating them.
Of the 120 field studies of crop species published in SCIE-
indexed journals in the last 20 years that were reviewed here,
a large proportion of analyses involving repeated measures
reported no effort to account for that fact. Even among those
who employed mixed models in their analysis, some strug-
gled to specify a model appropriate for their experimental
design. Moreover, most of the studies employing a linear
model in their analysis did not report assessing the assump-
tions of homoscedasticity and normality. Among those who
detected violations of these assumptions, a log or other trans-
formation was by far the most common remedy adopted, with
only a small minority employing GLMMs. Finally, the MAUP
remains pervasive in minirhizotron data, as most researchers
examining the spatial distribution of crop root systems employ
arbitrary depth class sizes, for which no consensus or standard
exists in the field.
The field of agronomy would stand to benefit considerably
if its journals established clear guidance for both statistical
practice and reporting. Such guidance could, though need not
necessarily, be based on the growing Open Science move-
ment and corresponding calls to mandate making data and
code readily available for scrutiny. Editors and reviewers, for
the sake of the discipline, must give greater attention to the
choice of analytical methods and the detail with which they
are described.
AUTHOR CONTRIBUTIONS
Simon Riley: Conceptualization; formal analysis; investi-
gation; methodology; visualization; writing—original draft.
Edzard van Santen: Conceptualization; methodology; super-
vision; writing—review and editing.
CONFLICT OF INTEREST STATEMENT
The authors declare no conflicts of interest.
ORCID
Simon Riley https://orcid.org/0000-0002-4833-2026
Edzard van Santen https://orcid.org/0000-0001-5969-8931
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SUPPORTING INFORMATION
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Supporting Information section at the end of this article.
How to cite this article: Riley, S., & van Santen, E.
(2025). Statistical considerations in the analysis of
minirhizotron data and a review of current practice in
agronomic research. Vadose Zone Journal,24,
e20395. https://doi.org/10.1002/vzj2.20395