How to Interpret the Coefficient of Variation in Data Analysis

Outside of finance, it is commonly applied to audit the precision of a particular process and arrive at a perfect balance. The coefficient of variation formula or calculation can be used to determine the deviation between the historical mean price and the current price performance of a stock, commodity, or bond, relative to other assets. The coefficient of variation shows the extent of variability of data in a sample in relation to the mean of the population. There are some requirements that must be met in order for the CV to be interpreted in the ways we have described. Even if the mean of a variable is not zero, but the variable contains both positive and negative values and the mean is close to zero, then the CV can be misleading.

To compare this variation, one can calculate the CV of the traits for each genotype in each experiment (CVs are reported with the color of the corresponding genotype). The CV of the two genotypes can be meaningfully compared within each experiment because the range of environmental variation over which CVs are estimated is similar. However, any comparison of CVs among experiments (i.e., among environmental gradients) is meaningless because °C cannot be compared with % humidity. The coefficient of variation may not have any meaning for data on an interval scale.2 For example, most temperature scales (e.g., Celsius, Fahrenheit etc.) are interval scales with arbitrary zeros, so the computed coefficient of variation would be different depending on the scale used. On the other hand, Kelvin temperature has a meaningful zero, the complete absence of thermal energy, and thus is a ratio scale.

If, for example, the data sets are temperature readings from two different sensors (a Celsius sensor and a Fahrenheit sensor) and you want to know which sensor is better by picking the one with the least variance, then you will be misled if you use CV. The problem here is that you have divided by a relative value rather than an absolute. The coefficient of variation is a simple way to compare the degree of variation from one data series to another. It can be applied to pretty much anything, including the process of picking suitable investments.

Formula for Coefficient of Variation

In plain language, it is meaningful to say that 20 Kelvin is twice as hot as 10 Kelvin, but only in this scale with a true absolute zero. While a standard deviation (SD) can be measured in Kelvin, Celsius, or Fahrenheit, the value computed is only applicable to that scale. Only the Kelvin scale can be used to compute a valid coefficient of variability.

Statistics Formula

The statistical measurement shows the variability of data when comparing data sets when it comes to the mean of the population. In the financial industry, the coefficient of variation provides investors with extra information, such as investment risks or even investment options. It can commonly be referred to as relative standard deviation, but it uses variability in data sets to show the standard deviation to its mean. The coefficient of variation helps when you want to compare a data series with another to determine the degree of variation. This is still the case even if the comparable means are completely different from each other.

Use of Coefficient of Variation in Assessing Variability of Quantitative Assays

In this article we develop a simple procedure to determine the probability that an assay will accurately coefficient of variation meaning discern whether two samples have the same analyte concentration or not based on a knowledge of the assay variability as measured by the coefficient of variation (CV). At best, such practice introduces variation in the CVs that decreases the statistical power of any comparisons between groups of traits (e.g., Acasuso‐Rivero et al. 2019). Although the conclusions of these studies may turn out to be correct, they remain questionable as long as the possible effects of a nonproportional increase of the standard deviation with the mean on the CVs have not been considered.

(iii) Since the CV is estimated and has a distribution of its own, it may be prudent in some applications to employ not the point estimate but rather a more conservative estimate such as an upper percentile of the observed distribution of the CV. The CV expresses variation of an entity on a proportional scale that is easily interpretable when comparing variation among entities. If this remains the only goal for computing CVs, the only restriction for this computation concerns the scale on which entities are measured (Table 1, Box 1).

As well, the investor is able to assume that each ETF has roughly the same returns compared to their long-term averages. Let’s say that a risk-averse investor is looking into an exchange-traded fund (ETF) as an investment. An ETF is essentially several securities that are able to track a market index broadly. On the other hand, a lower standard deviation shows that the values are likely to be grouped around the mean.

This would ultimately provide the investor with actionable information to be able to compare the data sets. From here, they can make a more informed decision about which investment would be the best moving forward. Yet, when it comes to the coefficient of variation, standard deviation considers the distribution of the values related to its mean. The good news is that calculating the coefficient of variation can be a fairly simple process as long as you have the relevant information. If the expected return is zero or a negative number, it might mean the calculations are misleading or inaccurate.

If your data have very different means, the CV may not be a good measure of relative variability. The CV is not a perfect measure of variability, and it has some limitations that you need to be aware of. One limitation is that the CV is only meaningful for data that are positive and have a meaningful zero point. For example, you cannot use the CV to compare the variability of temperatures in Celsius or Fahrenheit, because they are not based on a true zero point and can have negative values. Another limitation is that the CV can be misleading for data that are skewed or have outliers.

1. In contrast, the standard deviation converts variance into “standardized,” easy-to-interpret units that are the same as the units used in your data.
2. Here, a natural choice of k would be one that maximizes differences between CV in the range of interest.
3. It is a parameter or statistic used to convey the variability of your data in relation to its mean.
4. However, comparing such measures would be meaningless for phenotypic variation estimated in experiments where the magnitude of the variation of the environmental factor is fixed by the experimental design and generally chosen to generate detectable changes in the phenotypic traits.
5. Comparing their coefficients of variation might prove useful to some physiological investigations of homeostasis.

It is often used to compare the degree of variation between different datasets, especially when the units of measurement differ or the means of the datasets are significantly different. Before you use the CV to compare or interpret your data, you need to check some assumptions to make sure it is appropriate and reliable. One assumption is that your data are normally distributed, or at least approximately symmetric.

1. Although the conclusions of these studies may turn out to be correct, they remain questionable as long as the possible effects of a nonproportional increase of the standard deviation with the mean on the CVs have not been considered.
2. Ultimately, this makes it easier to identify the midpoint of any research or data.
3. However, cautions should be taken when calculating and interpreting CVs when the distribution comprises both positive and negative numbers.
4. Using the example above, a notable flaw would be if the expected return in the denominator is negative or zero.
5. In many laboratories, the variability of the ELISA and other methods of chemical assay that produce continuous-type values is summarized not by the standard deviation (SD) but by the CV, which is defined as the SD divided by the mean, with the result often reported as a percentage.
6. Such studies will typically provide a range of estimates of intra-assay, interassay, and combined variability on serum samples which cover the working range of analyte concentrations.

This may also be accomplished by a simple F test that compares the variance of log-transformed replicates with the assumed variance, which is calculated by equation A3 from the assumed CV. However, the proposed method of counting twofold disparate pairs and referring the result to Table 2 translates the process into language familiar to vaccine and immunology research and therefore may convey a better understanding of the magnitude of the departure from expectation. In many laboratories, the variability of the ELISA and other methods of chemical assay that produce continuous-type values is summarized not by the standard deviation (SD) but by the CV, which is defined as the SD divided by the mean, with the result often reported as a percentage. The main appeal of the CV is that the SDs of such assays generally increase or decrease proportionally as the mean increases or decreases, so that division by the mean removes it as a factor in the variability. The CV is therefore a standardization of the SD that allows comparison of variability estimates regardless of the magnitude of analyte concentration, at least throughout most of the working range of the assay. The coefficient of variation (CV) is an important measurement unit and concept to help predict variables.