Survival analysis and germination data: an overlooked connection

Published at July 2, 2019 ·  16 min read

Stabilising transformations: how do I present my results?

Published at June 15, 2019 ·  5 min read

ANOVA is routinely used in applied biology for data analyses, although, in some instances, the basic assumptions of normality and homoscedasticity of residuals do not hold. In those instances, most biologists would be inclined to adopt some sort of stabilising transformations (logarithm, square root, arcsin square root…), prior to ANOVA. Yes, there might be more advanced and elegant solutions, but stabilising transformations are suggested in most traditional biometry books, they are very straightforward to apply and they do not require any specific statistical software. I do not think that this traditional technique should be underrated.

Genotype experiments: fitting a stability variance model with R

Published at June 6, 2019 ·  8 min read

Yield stability is a fundamental aspect for the selection of crop genotypes. The definition of stability is rather complex (see, for example, Annichiarico, 2002); in simple terms, the yield is stable when it does not change much from one environment to the other. It is an important trait, that helps farmers to maintain a good income in most years.

Agronomists and plant breeders are continuosly concerned with the assessment of genotype stability; this is accomplished by planning genotype experiments, where a number of genotypes is compared on randomised complete block designs, with three to five replicates. These experiments are repeated in several years and/or several locations, in order to measure how the environment influences yield level and the ranking of genotypes.

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

Published at May 25, 2019 ·  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:

Dealing with correlation in designed field experiments: part II (asreml)

Published at May 10, 2019 ·  16 min read

With field experiments, studying the correlation between the observed traits may not be an easy task. Indeed, in these experiments, subjects are not independent, but they are grouped by treatment factors (e.g., genotypes or weed control methods) or by blocking factors (e.g., blocks, plots, main-plots). I have dealt with this problem in a previous post and I gave a solution based on traditional methods of data analyses.

In a recent paper, Piepho (2018) proposed a more advanced solution based on mixed models. He presented four examplary datasets and gave SAS code to analyse them, based on PROC MIXED. I was very interested in those examples, but I do not use SAS. Therefore, I tried to ‘transport’ the models in R, which turned out to be a difficult task. After struggling for awhile with several mixed model packages, I came to an acceptable solution, which I would like to share.

Dealing with correlation in designed field experiments: part I

Published at April 30, 2019 ·  7 min read

When we have recorded two traits in different subjects, we can be interested in describing their joint variability, by using the Pearson’s correlation coefficient. That’s ok, altough we have to respect some basic assumptions (e.g. linearity) that have been detailed elsewhere (see here). Problems may arise when we need to test the hypothesis that the correlation coefficient is equal to 0. In this case, we need to make sure that all the couples of observations are taken on independent subjects.

Some everyday data tasks: a few hints with R

Published at March 27, 2019 ·  9 min read

We all work with data frames and it is important that we know how we can reshape them, as necessary to meet our needs. I think that there are, at least, four routine tasks that we need to be able to accomplish:

1. subsetting
2. sorting
3. casting
4. melting

Obviously, there is a wide array of possibilities; I’ll just mention a few, which I regularly use.

Going back to the basics: the correlation coefficient

Published at February 7, 2019 ·  7 min read

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 Pearson correlation coefficient:

$$\rho _{X,Y} =\textrm{corr} (X,Y) = \frac {\textrm{cov}(X,Y) }{ \sigma_X \sigma_Y } = \frac{ \sum_{1 = 1}^n [(X - \mu_X)(Y - \mu_Y)] }{ \sigma_X \sigma_Y }$$

Other measures of correlation can be thought of, such as the Spearman $\rho$ rank correlation coefficient or Kendall $\tau$ rank correlation coefficient.

My first experience with blogdown

Published at November 15, 2018 ·  1 min read

This is my first day at work with blogdown. I must admit it is pretty overwhelming at the beginning …

I thought that it might be useful to write down a few notes, to summarise my steps ahead, during the learning process. I do not work with blogdown everyday and I tend to forget things quite easily. Therefore, these notes may help me recap how far I have come. And they might also help other beginners, to speed up their initial steps with such a powerful blogging platform.

Sample variance and population variance: which of the two?

Published at November 9, 2018 ·  7 min read

Teaching experimental methodology in agriculture related master courses poses some peculiar problems. One of these is to explain the difference between sample variance and population variance. For the students it is usually easy to grasp the idea that, being the mean the ‘center’ of the dataset, it is relevant to measure the average distance to the mean for all individuals in the dataset. Of course, we need to take the sum of squared distances, otherwise negative and positive residuals cancel each other out.