TP R n°1
Normal distribution, random sampling, and dataframe manipulation.

For the R practical exercises, you can record your code samples in R scripts, if you want, but you should better write them down in Rmarkdown or Quarto documents. You may want to use an integrated development environment (IDE) such as Rstudio, Positron, or Visual Studio Code with R extensions. Otherwise, any text editor with R code syntax highlighting is sufficient, if you manage the command line.

1. R includes a large number of builtin functions that make working on statistical analysis rather easy.

   The function rnorm allows us to perform a random sampling of the normal law.

   This function accepts two main arguments, the mean and the standard deviation of the normal distribution.

   Use the rnorm function to make 100 samples of a variable \(X \sim \mathcal{N}(\mu, \sigma^2)\), where the mean \(\mu = 159.5\) and standard deviation \(\sigma = 10\).

   Store this sample values into a vector.

2. Using the hist functions, represent your sampling with the histogram value.

3. Add the density plot of the normal distribution using the following code snippets:

   x <- seq(140, 180)
   plot(x, dnorm(x, mean = mean , sd = sd), type = "l",
        ylim = c(0, 0.1), ylab = "", lwd = 2, col = "red")
   

4. Do you think your histogram does correctly fit the theoretical distribution?

5. Using the plot and dnorm functions, represent on the same plot two Gaussian (normal) distribution \(N_1 \sim \mathcal{N}(\mu = 0, \sigma = 1)\) the reduced and centered normal law, and \(\mathcal{N}(\mu = 19, \sigma = 4)\) variables.

   You can use the function lines instead of plots for the second curve, to add a curve to the plot.

   You can use the seq function argument length.out to increase the resolution.

6. What happens to the density curve of a normal law when \(\sigma\) increases?

For this R exercise, we will let the normal law aside for a moment, to practice a little bit with data analysis on a csv table dataset.

We will use a dataset from GISSOL, the French geo information system on the organisms of the soil: https://www.gissol.fr/

1. Download the data archive from https://entrepot.recherche.data.gouv.fr/dataset.xhtml?persistentId=doi:10.57745/1Z90HV

2. Unzip the archive in folder ./data

   You should have the following files:

   ls data
   

      dataverse_files.zip
      MANIFEST.TXT
      rmqs1_ratio_18s_16s.ct_values.tsv
      rmqs1_ratio_18s_16s.tsv
   

3. Load the tab-separated values file in a rmqs1_ratio_18s_16s.tsv in a data.frame.

4. Let’s have a look at the content of this table.

   We can use the R function head to see the first rows of the table.

   We have data sampled from the RMQS (« Réseau de Mesure de la Qualité des Sols », “measure network on soil quality”, in english) program. RMQS is a program that aims to follow the health of French soil. It is running since 2000. The dataset contains, for each sample site, the density of 16S rRNA and 18S rRNA measured with RT qPCR on soil samples. The ratio of 16S and 18S can be used as a proxy of the ratio of Bacteria and Fungi content in soils.

   Cropfield soils have a higher Bacteria over Fungi ratio than Forest soils.

   With the R function colnames check what are the columns of the dataframe:

5. Count how many different sites are referenced in the dataframe.

   You can use the function unique, to remove duplicate in a vector, to avoid counting the same site twice.

6. Is there any sample site referenced more than one time in the table?

7. What are the identifiers of those sites?

   To answer this question, you can use the table function which outputs a table of count of each items of a vector.

   The function which can also be helpful. The which function return the index of the TRUE values in a vector. For instance:

   vector <- 1:10
   even <- function(x) {
     return(sapply(x, function(item) item %% 2 == 0))
   }
   which(even(vector))
   

      2
      4
      6
      8
      10
   

   If you prefer a more direct demonstration of how the which function works:

   which(c(TRUE, FALSE, FALSE, TRUE))
   

      1
      4
   

8. Now we want to check whether the soil habitat type can have an impact on the 16S over 18S ratio (i.e., the fungus over bacteria ratio).

   To do so, download the dataset https://entrepot.recherche.data.gouv.fr/dataset.xhtml?persistentId=doi:10.57745/JK5WCD. Then, load the rmqs1_16S_microbial_habitat.tsv table in a dataframe.

9. List the different habitat categories.

10. The description of the different habitat codes meaning is available in the file rmqs1_16S_microbial_habitat.metadata.tab from the same dataset.

    We want to answer the following question: “do aciding agricultural plains contain more bacteria than fungi, compared to neutral soils of deciduous forests?”.

    Identify what is the microbial habitat code for both habitats.

11. Merge the 16S ratio dataframe with the microbial habitate dataframe on the site identifier column with the function merge.
12. Extract two 16S/18S ratio vectors: one for the “Acidic soils of agricultural plains” sites and the other for “Neutral soils in deciduous forests”.
13. Perform a test to try to answer the question.
    1. Formulate your test hypotheses
    2. Set a level \(\alpha\) for your test
    3. Do you know the variance of the distribution of your samples?
    4. What test statistics would you use?
    5. Run your test with R on the vectors you got in the previous question.
    6. What is the conclusion of your test?