Tuesday, April 12, 2016

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 CT 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.

1 comment:

  1. Excitation of a fluorophore occurs over a range of wavelengths, within which is a peak wavelength where maximum excitation is achieved. Bleed-through is when you excite a system of multiple fluorophores at a certain wavelength appropriate for the target fluorophore, but a non-target fluorophore emission is also detected. This occurs when two conditions are met: (1) the fluorophores are improperly matched such that the excitatory wavelength efficiently excites one fluorophore – as intended – but also inefficiently excites another because the excitatory wavelength falls somewhere in that fluorophore’s excitatory range; and (2) the emission filter on your detector allows a range of wavelengths into the detector that includes the possible emission from both fluorophores. A solution is to use properly-matched fluorophores, which means that the ranges of excitation wavelengths for each overlap minimally. Another solution is to just replace the filter with one that only allows for detection of the emission of the fluorophore of interest. It is not that excitation “can” be thought of as a range of wavelengths; rather, it must be. Knowing this would keep one from worrying about bleed-through only because then they would understand this phenomenon and prepare for it in advance. Please correct me if I have misunderstood something.