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.

Know Your Data

Defining the type of data you will produce is a key step in designing an experiment. While categorizing data as discrete or continuous is one of the most straightforward concepts in statistics, things are not always as simple as they seem. Giving thought to typical data produced in my lab revealed that discrete data is not always discrete and continuous data is not always continuous. It is therefore important to understand your data in the form used for statistical testing and draw appropriate conclusions.

Discrete data may include whole numbers (5 pups in a litter) or categorical assignments (pregnant vs not pregnant) while continuous data is described as being scalar and able to take on a range of values when measured (e.g. height, weight, , time etc.). Data may start out as discrete or continuous, but categorization or manipulation of the data can quickly change its properties. For instance, binning of continuous data, such as weight of mice into underweight, normal, and overweight produces discrete data from the same measures. A major focus of my lab is the study of conditions and factors which influence gene reassortment of influenza viruses. To measure reassortment levels, we employ a two-virus system in which the original virus, designated “wild-type” (Wt), and a “variant” (Var) virus differ only by engineered silent mutations. These markers allow differentiation of segments by high resolution melt analysis, with mutations conferring different melt temperatures for segments of the Wt or Var origin. Genotypes which contain all segments from either the Wt or Var virus are categorized as “parental” while a virus isolate containing any combination of Wt and Var gene segments are “reassortant.” 

The reassortment level arising from a coinfection is determined by calculating percent reassortment as follows:

Much like the transformation of continuous data by binning into groups, discrete genotypes are transformed into a value for % reassortment and then treated as continuous data. Despite not being true continuous data discussed here, the percent value is routinely treated as such for meaningful statistical comparisons between groups.Though the underlying data is discrete, it intuitively makes sense to treat the values this way as we are describing the features of a population instead of individual data. For instance, calculating the percent of your mice which are pregnant, say 75% does not mean that mice are 75% pregnant, it means that 75% of your sample population is pregnant. Being able to accurately define the type of data you are using for analysis enables one to choose statistical tests and appropriately describe results.