## Monday, 10 June 2013

### R: Measure of Relative Variability

The measure of relative variability is the coefficient of variation (CV). Unlike measures of absolute variability, the CV is unitless when it comes to comparisons between the dispersions of two distributions of different units of measurement. In R, CV is obtained using the cv function of the raster package.

Example 1. Below are the mean and standard deviation of the number of hours spent by Jacob every time he study the Stochastic Process with the corresponding scores he got out of the 100 items. Basing from this data, should one say that the number of hours he spent in studying is more variable than his exam scores, or the other way around?

 Variable Mean Standard Deviation Study Hours 25 2.6 Scores 69 5.3

To determine this, we use the function below

And thus,

Interpretation: It is very clear from the computed CV that, the study hours is more variable than the exam scores, even though the standard deviation of the scores is higher than the hours spent.

Example 2. Consider the heights (in centimetres) of 11 AB English junior students at MSU-TCTO: 151, 160, 162, 155, 154, 168, 153, 158, 157, 150, and 167. And also their corresponding weights (in kilograms): 61, 69, 73, 65, 64, 78, 63, 68, 67, 60, and 77. Compute and interpret the coefficient of variation.

Using the cv function of the raster package, we have

Interpretation: The weights of the students are more variable than their heights as confirmed by the computed CV.

### Reference

Asaad, Abubakar S. (2011). Simplified Biostatistics. Manila: Rex Book Store, Inc.