The statement made by Lord Kelvin is suggesting that any qualitative knowledge that cannot be quantified is not sufficient as knowledge should have both qualitative and quantitative aspects.
This applies to medicine and biology quite well. Whilst doing experiments in school, we make a link between an independent variable and a dependent variable. We then measure the dependent variable using apparatus such as a stopclock, measuring cylinder or water baths. This way, we obtain quantitative data to prove our hypothesis. Without the results, we would not be able to provide sufficient evidence for the link that we made between the independent variable and the dependent variable.
A good example of this is the yeast experiment to measure the rate of respiration. We use a stopclock to measure the time taken for methylene blue to change colour. We can then use the times to calculate the rate of respiration.
In medical treatments, the use of blood reports is important for the identification of certain conditions. We need to quantify the RBC count, platelets count etc. to be able to recognise which condition a patient is suffering from.
However, we are still unable to quantify many results in medicine. This mainly applies for psychiatric disorders such as depressive disorders, neurodevelopmental disorders and personality disorders.