Discrete or continous? Well why not both?

On the surface, it seems obvious what the differences are between discrete and continuous variables. It is as their names imply; a discrete variable is defined as a “variable that arises upon random chance and possessing only countable variables” (Biostat Lecture 3), while a continuous variable is defined as “variable that can take on any value between two specified numbers” (Biostat lecture 3). These two types of variables can easily be applied to many of the experiments I conduct around the lab. The number of Drosophila that have developed brain tumors can easily be considered a discrete variable, while the C_T values obtained in my qPCR can be easily thought of as continuous variables. However, on closer inspection, these variables are not so obviously defined. Eloquently expressed in Velleman and Wilkinson’s article “Nominal, Ordinal, Interval, andRatio Typologies are Misleading”, argues that often these categories introduced by S.S. Stevens, such as nominal, ordinal, interval, and ratio, can be restrictive, and more importantly, by asserting the scale type “independent of the questions asked of the data” it in turn, limits what can be asked of the data generated in an experiment. This close-minded thinking may have detrimental effects on hypothesis-driven research and limits what subsequent experiments should be run as a direct result of the data generated in the pilot experiment. Furthermore, Motulsky introduces an interesting concept in Intuitive Biostatistics that variables can be much more ambiguous than they originally seem. One such example is that of color. The perception of color can be thought of as nominal variable with discrete outputs such as blue, red, or yellow. However, the concept of color as a nominal variable becomes much more ambiguous once you consider monochromatic color as a wavelength where it can be considered a ratio variable. Something that seems so obviously to be a categorical variable can be seen as a continuous variable as well. This idea of wavelength of color is extremely important in microscopy work. In many of the fluorphores used in microscopy, they express their excitation as a single wavelength say 647 nm. On the surface, it is possible to consider this value as a discrete variable since it is advertised to be excited at this single wavelength. However, in actuality, photo bleed through may occur where you observe detection of fluorescence in other fluorescent channels as well, indicating a possible range of excitation. This is a real world application of the idea of the pitfalls of thinking so concretely of the idea of what type of variable it should be and instead allowing for an open-mind. By understanding the idea that excitation can be thought of as a range of wavelengths, I can play out microscopy experiments that includes multiple fluorophores without worry of photo-bleed through.