Fixing the bridge between biologists and statisticians

Multi-trait models for correlation analyses in designed experiments

A solution with R and ‘sommer’
R
correlation
R-bloggers
Imagine a field experiment comparing several treatments in a randomised complete block design. In each plot, we usually record several traits of interest, and we may want to…
Oct 21, 2026
Andrea Onofri

Can we trust the correlation coefficient in designed field experiments?

Spoiler: no, we cannot…
R
correlation
R-bloggers
One of the fundamental aims of field experiments is to explorare the relationships between several experimental traits, which have been recorded/measured altogheter for all…
Oct 16, 2026
Andrea Onofri

A Trip from Covariance to Correlation and Back

R
correlation
R-bloggers
When we have a multi-trait table of data, we might be interested in investigating variability structure and the reciprocal relationships (whether causal or non-causal) among…
Oct 15, 2026
Andrea Onofri

Going back to the basics: the correlation coefficient

R
correlation
R-bloggers
In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data. It is often measured by the…
Oct 9, 2026
Andrea Onofri

Back-transformations with emmeans()

R
linear_models
emmeans
R-bloggers
I am one of those old guys who still uses variance-stabilising transformations when data do not conform to the basic assumptions of ANOVA. Indeed, apart from counts and…
Sep 28, 2026
Andrea Onofri

Book cover

General code to fit ANOVA models with JAGS and ‘rjags’

R
JAGS
bayesian_stat
R-bloggers
There is a quote I really love from Marc Kéry’s book, “Introduction to WinBUGS for Ecologists” (2010, p. 11):
Sep 16, 2026
Andrea Onofri

Book cover

Analysing seed germination and emergence data with R (a tutorial)

R
Time_to_event_models
Seed_germination
drcte
drcSeedGerm
R-bloggers
Germination and emergence assays are pretty straightforward to set up: you grab a sample of seeds, put them in a container under controlled environmental conditions…
Sep 7, 2026
Andrea Onofri

From ‘’for()’’ loops to the ‘’split-apply-combine’’ paradigm for column-wise tasks in R

R
data management
tidyverse
dplyr
R-bloggers
Today, I want to discuss performing column-wise tasks on relatively large datasets. These tasks are particularly common in agricultural and biological research, where we…
Aug 27, 2026
Andrea Onofri

Book cover

Some everyday data tasks: a few hints with R (for dinosaurs)

R
R-bloggers
data management
dplyr
tidyr
tidyverse
It is important to know how to reshape a dataframe for data analysis. Personally, I also value being able to perform the most important reshaping tasks (and other common…
Aug 14, 2026
Andrea Onofri

Dual scaled y-axis with ggplot()

R
R-bloggers
ggplot
I have often found myself needing to plot a single graph with two y-axes having different scales. For example, this might be useful for representing temperature and rainfall…
Aug 11, 2026
Andrea Onofri

Some useful equations for biological processes

nonlinear_regression
R-bloggers
drm
nls
statforbiology
Biological phenomena are often studied by examining how a numerical variable, usually called the response (e.g., the weight or height of an organism), is affected by another…
Jul 24, 2026
Andrea Onofri

A collection of self-starters for nonlinear regression in R

R
nonlinear_regression
R-bloggers
nls
drm
statforbiology
Usually, the first step in every nonlinear regression analysis is to select the function \(f\) that best describes the phenomenon under study. The next step is to fit this…
Jul 21, 2026
Andrea Onofri

Finally migrating to Quarto

An introduction with R
news
A few months ago, my blogdown-based blogs started giving me a few headaches, after more than seven years of remarkably reliable service. After doing some research on the web…
Jul 20, 2026
Andrea Onofri
 

Migration from Blogdown to Quarto

R
quarto
More than twenty-five years ago, I had the idea that having a website would be a good way to store my teaching and research materials, keep them organised, retrieve them…
Jul 15, 2026
Andrea Onofri

Testing for interactions in nonlinear regression

R
mixed_models
nlme
nonlinear_regression
R-bloggers
Factorial experiments are very common in agriculture and they are usually laid down to test for the significance of interactions between experimental factors. For example…
Feb 14, 2026
Andrea Onofri

Book cover

Correcting for multiplicity in the ‘emmeans’ package

R
MCP
multiple_comparisons
emmeans
R-bloggers
In my recent book (see below), on page 166 and earlier, I made the point that, with pairwise comparisons and, more generally, whenever simultaneous statistical tests are…
Jan 21, 2026
Andrea Onofri

How do we combine errors, in biology? The delta method

R
general
R-bloggers
In a recent post I have shown that we can build linear combinations of model parameters (see here ). For example, if we have two parameter estimates, say \(X\) and \(Z\)…
Dec 12, 2025
Andrea Onofri

Book cover

Fitting an Environmental Variance mixed model to genotype experiments

R
mixed_models
multi_environment_studies
lme
sommer
R-bloggers
Yield stability is a key aspect in the selection of crop genotypes. Its definition is not entirely straightforward (see, for example, Annichiarico, 2002), but, in simple…
Dec 4, 2025
Andrea Onofri

Book cover

Fitting a ‘Stability Variance’ mixed model to genotype experiments

R
mixed_models
multi_environment_studies
lme
sommer
R-bloggers
Yield stability is a fundamental aspect of the selection of crop genotypes. Its definition is rather complex (see, for example, Annichiarico, 2002), but, in simple terms, it…
Dec 2, 2025
Andrea Onofri

Book cover

Getting the Absolute/Relative Growth Rate from growth curves

R
nonlinear_regression
nls
drm
statforbiology
R-bloggers
Yesterday, a colleague of mine pointed me to the article “How to fit nonlinear plant growth models and calculate growth rates: an update for ecologists” (Paine et al.…
Nov 27, 2025
Andrea Onofri

Why are derivatives important in life? A case-study with nonlinear regression

R
nonlinear_regression
nls
drm
statforbiology
R-bloggers
In general, undergraduate students in biology/ecology courses tend to consider the derivatives as a very abstract entity, with no real usefulness in the everyday life. In my…
Nov 26, 2025
Andrea Onofri

Book cover

Field Research methods in Agriculture

An introduction with R
news
Hi everybody, I have exciting news!
Nov 25, 2025
Andrea Onofri

Book cover

How do we combine errors? The linear case

R
linear_models
R-bloggers
In our research work, we usually fit models to experimental data. Our aim is to estimate some biologically relevant parameters, together with their standard errors. Very…
Nov 22, 2024
Andrea Onofri

Book cover

Pairwise comparisons between curves in nonlinear regression

R
nonlinear_regression
nls
statforbiology
drm
R-bloggers
Pairwise comparisons are one of the most debated topic in agricultural research: they are very often used and, sometimes, abused, in literature. I have nothing against the…
Feb 23, 2024
Andrea Onofri

Book cover

Repeated measures and subsampling with perennial crops

R
mixed_models
repeated_measures
subsampling
R-bloggers
In a recent post, I have talked about repeated measures, for a case where measurements were taken repeatedly in the same plots across years see here. Previously, in another…
Dec 4, 2023
Andrea Onofri

Designed experiments with replicates: Principal components or Canonical Variates?

R
multivariate_stat
CVA
biplot
R-bloggers
A few days ago, a colleague of mine wanted to hear my opinion about what multivariate method would be the best for a randomised field experiment with replicates. We had a…
Nov 2, 2023
Andrea Onofri

GGE analyses for multi-environment studies

R
GGE_analysis
multi_environment_studies
PCA
biplot
R-bloggers
In a recent post we have seen that we can use Principal Component Analyses (PCA) to elucidate the ‘genotype by environment’ relationship (see this post). Whenever the…
May 31, 2023
Andrea Onofri

AMMI analyses for multi-environment studies

R
AMMI_analysis
multi_environment_studies
PCA
biplot
R-bloggers
Again into a subject that is rather important for most agronomists, i.e. the selection of crop varieties. All farmers are perfectly aware that crop performances are affected…
May 26, 2023
Andrea Onofri

Book cover

Repeated measures with perennial crops

R
mixed_models
repeated_measures
R-bloggers
In this post, I want to discuss a concept that is often mistaken by some of my collegues. With all crops, we are used to repeating experiments across years to obtain…
Mar 30, 2023
Andrea Onofri

Book cover

Subsampling in field experiments

R
mixed_models
subsampling
R-bloggers
Subsampling is very common in field experiments in agriculture. It happens when we collect several random samples from each plot and we submit them to some sort of…
Mar 29, 2023
Andrea Onofri

Book cover

Multi-environment split-plot experiments

R
mixed_models
split_plot
R-bloggers
Have you made a split-plot field experiment? Have you repeated such an experiment in two (or more) years/locations? Have you run into troubles, because the reviewer told you…
Sep 13, 2022
Andrea Onofri

Book cover

Meta-analysis for a single study. Is it possible?

R
meta_analysis
multi_environment_studies
lme
nlme
metafor
mixed_models
R-bloggers
We all know that the word meta-analysis encompasses a body of statistical techniques to combine quantitative evidence from several independent studies. However, I have…
Jul 21, 2022
Andrea Onofri

Biplots are everywhere: where do they come from?

R
multivariate_stat
PCA
biplot
R-bloggers
Principal Component Analysis (PCA) is perhaps the most widespread multivariate technique in biology and it is used to summarise the results of experiments in a wide range of…
Nov 24, 2021
Andrea Onofri

Principal Component Analysis: a brief intro for biologists

R
multivariate_stat
PCA
biplot
R-bloggers
In this post I am revisiting the concept of Principal Component Analysis (PCA). You might say that there is no need for that, as the Internet is full with posts relating to…
Nov 23, 2021
Andrea Onofri

Book cover

The R-squared and nonlinear regression: a difficult marriage?

R
nonlinear_regression
nls
statforbiology
drm
R-bloggers
Making sure that a fitted model gives a good description of the observed data is a fundamental step of every nonlinear regression analysis. To this aim we can (and should)…
Mar 25, 2021
Andrea Onofri

Book cover

Multienvironment diallel models

R
multi_environment_studies
lmDiallel
diallel_models
R-bloggers
In recent times, a few colleagues at my Department and I have devoted some research effort to data management for diallel mating experiments, which we have summarised in a…
Mar 5, 2021
Andrea Onofri, Niccolò Terzaroli and Luigi Russi

Book cover

The Gardner-Eberhart diallel model

R
multi_environment_studies
lmDiallel
diallel_models
R-bloggers
In this post we are going to talk about the Gardner-Eberarth models, which are particularly suitable to describe heterotic effects, in diallel mating experiments. The…
Feb 22, 2021
Andrea Onofri, Niccolò Terzaroli and Luigi Russi

Book cover

Split-plot designs: the transition to mixed models for a dinosaur

R
mixed_models
Those who long ago took courses in ‘analysis of variance’ or ‘experimental design’ … would have learned methods … based on observed and expected mean squares and methods of…
Feb 11, 2021
Andrea Onofri

Book cover

Pairwise comparisons in nonlinear regression

R
nonlinear_regression
nls
statforbiology
R-bloggers
Pairwise comparisons are one of the most debated topic in agricultural research: they are very often used and, sometimes, abused, in literature. I have nothing against the…
Jan 19, 2021
Andrea Onofri

Book cover

The Griffing’s diallel models (1956)

R
multi_environment_studies
lmDiallel
diallel_models
R-bloggers
Diallel mating designs are often used by plant breeders to compare the possible crosses between a set of genotypes. In spite of such widespread usage, the process of data…
Jan 12, 2021
Andrea Onofri, Niccolò Terzaroli and Luigi Russi

Accounting for the experimental design in linear/nonlinear regression analyses

R
mixed_models
nonlinear_regression
nlme
R-bloggers
In this post, I am going to talk about an issue that is often overlooked by agronomists and biologists. The point is that field experiments are very often laid down in…
Dec 4, 2020
Andrea Onofri

Book cover

The Hayman’s diallel model (type 1)

R
multi_environment_studies
lmDiallel
diallel_models
R-bloggers
Let’s imagine we have a genotype experiment with the three parental lines A, B and C with their selfs A\(\times\)A, B\(\times\)B and C\(\times\)C, their crosses A\(\times\)B…
Nov 26, 2020
Andrea Onofri, Niccolò Terzaroli and Luigi Russi

Book cover

lmDiallel: a new R package to fit diallel models. Introduction

R
multi_environment_studies
lmDiallel
diallel_models
R-bloggers
Together with some colleagues from the plant breeding group, we have just published a new paper, where we presented a bunch of R functions to analyse the data from diallel…
Nov 11, 2020
Andrea Onofri, Niccolò Terzaroli and Luigi Russi

QQ-plots and Box-Whisker plots: where do they come from?

R
descriptive statistics
R-bloggers
This post is ‘only’ for the most curious students…
Oct 15, 2020
Andrea Onofri

Building ANOVA-models for long-term experiments in agriculture

R
long_term_experiments
multi_environment_studies
lme
mixed_models
R-bloggers
This is the follow-up of a manuscript that we (some colleagues and I) have published in 2016 in the European Journal of Agronomy (Onofri et al., 2016). I thought that it…
Aug 20, 2020
Andrea Onofri

A joint regression model for genotype experiments

R
AMMI_analysis
multi_environment_studies
lme
mixed_models
R-bloggers
Joint Regression is a very old, but, nonetheless, useful technique. It is widely known that the yield of a genotype in different environments depends on environmental…
Jun 5, 2020
Andrea Onofri

Self-starting routines for nonlinear regression models

R
nonlinear_regression
R-bloggers
nls
drm
statforbiology
In R, the drc package represents one of the main solutions for nonlinear regression and dose-response analyses (Ritz et al., 2015). It comes with a lot of nonlinear models…
Feb 14, 2020
Andrea Onofri

Linear/Nonlinear combinations of model parameters

R
nonlinear_regression
delta_method
error_propagation
nls
statforbiology
gnlht
R-bloggers
Nonlinear regression plays an important role in my research and teaching activities. While I often use the ‘drm()’ function in the ‘drc’ package for my research work, I tend…
Jan 9, 2020
Andrea Onofri

Book cover

A multi-environment ‘split-plot’ with heteroscedastic errors

R
mixed_models
split_plot
R-bloggers
In this post I am going to deal with a repeated split-plot experiment with heteroscedastic errors. Ready for this trip?
Sep 13, 2019
Andrea Onofri
 

My learning path with blogdown

R
This is my first day at work with blogdown. I must admit it is pretty overwhelming at the beginning …
Nov 15, 2018
Andrea Onofri

The Variance Puzzle: Why Doesn’t R Divide by ‘n’?

descriptive statistics
R-bloggers
Teaching Experimental Methodology in master’s courses related to agriculture poses some peculiar challenges. One of them is explaining the difference between population…
Nov 9, 2018
Andrea Onofri

Book cover

Is R dangerous? Side effects of free software for biologists

R
R-bloggers
When I started my career in biology (almost forty years ago), only the luckiest of us had access to advanced statistical software. Licences were very expensive, and it was…
Jun 8, 2014
Andrea Onofri
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