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

Published at November 22, 2024 ·  7 min read

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 Q and W, with standard errors respectively equal to \(\sigma_Q\) and \(\sigma_W\), we can build a linear combination as follows:

\[ Z = aQ + bW + c\]

where \(a\), \(b\) and \(c\) are three coefficients. The standard error for this combination can be obtained as:

Plotting weather data with ggplot()

Published at June 6, 2024 ·  7 min read

Very often, we agronomists have to deal with weather data, e.g., to evaluate and explain the behaviour of genotypes in different environments. We are very much used to representing temperature and rainfall data in one single graph with two y-axis, which gives a good immediate insight on the weather pattern at a certain location. Unfortunately, I had to discover that doing such graphs with ggplot() is not a straightforward task.

Here is why I don't care about the Levene's test

Published at March 15, 2024 ·  5 min read

During my stat courses, I never give my students any information about the Levene’s test (Levene and Howard, 1960), or other similar tests for homoscedasticity, unless I am specifically prompted to do so. It is not that I intend to underrate the tremendous importance of checking for the basic assumptions of linear model! On the contrary, I always show my students several methods for the graphical inspection of model residuals, but I do not share the same aching desire for a P-value, that most of my colleagues seem to possess.

Pairwise comparisons in nonlinear regression

Published at February 23, 2024 ·  8 min read

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 appropriate use of this very useful technique and, for those who are interested, some colleagues and I have given a bunch of (hopefully) useful suggestions in a paper, a few years ago (follow this link here).

According to the emails I often receive, there might be some interest in making pairwise comparisons in linear/nonlinear regression models. In particular, whenever we have grouped data and we have fitted the same model to each group, we might like to compare the groups, to state whether the regression lines/curves are significantly different from each other. To this aim, we could consider two approaches: