p-values were calculated using a one-way anova test, assuming equal variance (homoscedasticity) in the 2 groups. If the groups are of similar size, this is typically a valid assumption, since one-way anova is not very sensitive to heteroscedasticity. FDR adjusted p-values were calculated using the Benjamini–Hochberg procedure.

In a (2D) scatterplot, each sample is represented by a dot that is placed on a coordinate system. The placement is determined by the value of 2 variables. For example, each dot could be the representation of a person and the 2 variables could be the BMI and the body fat percentage of these subjects. The BMI would determine the placement of the sample on (for example) the x-axis and the bodyfat percentage would determine the placement on the other axis. It is easy to see that points that are located close to each other represent samples that are similar (in terms of BMI and body fat %). A very useful property of scatterplots is that they can easily reveal trends such as outliers or clusters of similar samples. A typical BMI/body fat % scatterplot for example, reveals 2 clusters that correspond to the male and female population.

Let’s say we want to expand our BMI/body fat % study and also study the relation with age. Now there are 3 variables per sample/subject. One option to visualise this data would be to introduce an 3rd z-axis to our scatterplot for a 3D visualisation. Another option would be to create multiple 2D scatterplots for each possible combination of our variables: BMI vs body fat, BMI vs age and body fat vs age. But what if there are more than 3 variables? The first option is no longer possible and due to the increasing number of possible combinations the second option quickly becomes impractical.

This is a typical problem in omics experiments. In lipidomics, typically hundreds to thousands of variables (lipid species) are measured in each sample. With so many variables, how could you plot the samples in a scatter plot? Dimensionality reduction techniques such as principal component analysis (PCA) or t-SNE offer a solution to this problem (‘dimensions’ in this context refers to the measurement parameters). These techniques reduce the thousands of measurements variables to two new variables that allow each data point to be plotted on a x- and y-axis.

This is sometimes misunderstood as ‘these techniques somehow select two measurement parameters out of the many and put these on a scatter plot’. In reality they construct entirely new parameters that take into account all the measurement parameters. PCA creates these new parameters by generating a linear combination of the measurement parameters and it favours parameters that show high variance. t-SNE on the other hand is a non-linear algorithm that can perform different transformations in different regions of the data. t-SNE tries only to map local relationships accurately while global distances (e.g. distances between different clusters) are not preserved (i.e. it is not suitable for outlier detection).While both techniques aim to get a faithful representation of high dimensional data in a 2D plane, neither technique is perfect.