## Monday, April 11, 2016

### Because Most Things Change... (Continuous Variables)

Since I was a little girl, I have had one thing clear: most things change. I have grown older, taller, and gained more weight.  This is because none of these characteristics are constant. When thinking of numerical values, we hardly ever see them as a variable amount that describes a measurement. Notice the importance of the word “variable” when used as an adjective, given it is a number that may be assigned more than one value. For example, the last time I weighed myself, the value on the scale was different than the previous time (although I wish it wasn’t). This is because weight is a variable measurement. Among other variables we may have height, age, time, distance, and temperature. However, it is not as simple as deciding if something is constant or variable.

A variable can be either continuous or discrete. As opposed to the discrete variable, the continuous variable can assume an infinite number of real values. So from the variables described above, time, height, distance, age, and temperature would be continuous. Harvey Motulsky explains in his book Intuitive Biostatistics that one way to summarize continuous values is to calculate the mean, median, mode, geometrical mean, or harmonic mean. On the other hand, if it can only take a finite number of real values, it is discrete. Thus, examples of something that cannot be divided, as Dr. Murphy stated in class, could be a person or a pregnancy. The type of variables we have will determine the type of graph and type of statistical analysis we will perform.

In Harvey Motulsky’s Intuitive Biostatistics, he states that when graphing continuous variables, we should consider creating a graph that shows the scatter of the data. He suggests for us to either show every value on a scatter plot or show the distribution of values with a box-and-whiskers plot or a frequency distribution histogram. The fact that he emphasizes on the way we should graph the data is an indicator of the importance of differentiating between these two types of variables. The main importance is to know which statistical analysis you will use for your data. In Michael Cheatam’s A Practical Guide to Biostatistics, he states that the t distribution is frequently used to evaluate hypotheses regarding the means of continuous variables, assuming the data is normally distributed. However, the most commonly used nonparametric methods for non-normally distributed data are the sign test, the Wilcoxon signed-ranks test, and the Mann-Whitney U test.

It is because of the difference in the way the data is presented and the analysis being made to the variables that it is crucial to understand what a continuous variable is. It amazes me how something so simple in definition can be so crucial for correctly exposing your data to others in a way that it actually conveys what the crude data was showing.