Compute the Pearson correlation coefficient for pairwise samples, with its p-value.

The Pearson correlation coefficient measures the linear relationship between two datasets. The calculation of the p-value relies on the assumption that each dataset is normally distributed. The p-value returned is a two-sided p-value. Like other correlation coefficients, this ones vary between -1 and +1 with 0 implying no correlation. Correlations of -1 or +1 imply an exact linear relationship. Positive correlations imply that as x increases, so does y. Negative correlations imply that as x increases, y decreases.

• Input: a table containing the sample measurements, with the name of the samples.
• Output: a table listing the correlation coefficient, and its associated p-value for each pairwise comparison testing.
• Config Parameters:
  • preselected_column_names: List of columns to pre-select for pairwise comparisons. By default a maximum pre-defined number of columns are selected (see configuration).
  • reference_column: If given, this reference column is compared against all the other columns.
  • row_tag_key: If give, this parameter is used for group-wise comparisons along row tags (see example below). This parameter is ignored of a reference_column is given.
  • adjust_pvalue:
    • method: The correction method for p-value adjustment in multiple testing.
    • alpha: The FWER, family-wise error rate. Default is 0.05.

Example 1: Direct column comparisons

Let's say you have the following table.

This task performs pairwise comparison of almost all the columns of the table (the first 500 columns are pre-selected by default).

• A will be compared with B and with C, respectively
• B will be compared with C

To only compare a given column with all the others, set the name of the reference_column (a.k.a Reference column). Suppose that B is used as reference column,only the following comaprisons will be done:

• B versus A
• B versus C

It is also possible to perform comparison on a well-defined subset of the table by pre-selecting the columns of interest. Parameter preselected_column_names (a.k.a. Selected columns names) allows pre-selecting a subset of columns for analysis.

Example 2: Advanced comparisons along row tags using row_tag_key parameter

In general, the table rows represent real-world observations (e.g. measured samples) and columns correspond to descriptors (a.k.a features or variables). Theses rows (samples) may therefore be related to metadata information given by row tags as follows:

Actually, the column row_tags does not really exist in the table. It is just to show here the tags of the rows Here, the first row correspond to 10-years old male individuals. In this this case, we may be interested in only comparing each columns along row metadata tags. For instance, to compare Males (M) versus Females (F) of each columns separately, you can use the advance parameter row_tag_key=Gender.

For more details on the Pearson correlation coefficient, see https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pearsonr.html.