Use of Coefficient of Variation in Assessing Variability of Quantitative Assays

As a dimensionless quantity, the coefficient of variation offers two main advantages. In fluid dynamics, the CV, also referred to as Percent RMS, %RMS, %RMS Uniformity, or Velocity RMS, is a useful determination of flow uniformity for industrial processes. The term is used widely in the design of pollution control equipment, such as electrostatic precipitators (ESPs),15 selective catalytic reduction (SCR), scrubbers, and similar devices. The Institute of Clean Air Companies (ICAC) references RMS deviation of velocity in the design of fabric filters (ICAC document F-7).16 The guiding principal is that many of these pollution control devices require “uniform flow” entering and through the control zone.

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However, cautions should be taken when calculating and interpreting CVs when the distribution comprises both positive and negative numbers. Because the zero point has a clear definition in this case, both mathematically and biologically, the CV may be meaningful, but its value may be extreme coefficient of variation meaning or even undefined (i.e., +∞) when the mean is close or equal to 0 (e.g., see Pélabon and Hansen 2008). The log‐transformation of the data changes the meaning of the zero point and the calculation of the CV loses its meaning.

1. If the number of observed pairs equals or exceeds the table value, the null hypothesis that the CV is at most the indicated value is rejected.
2. The second application is as a quality control tool through which the laboratory may determine if the current assay variability exceeds what has been established from past performance.
3. The CV is never exactly known and must be estimated from appropriate validation studies.
4. The coefficient of variation (CV) is the ratio of the standard deviation to the mean.
5. This is still the case even if the comparable means are completely different from each other.
6. And because it’s independent of the unit in which the measurement was taken, it can be used to compare data sets with different units or widely different means.
7. Such an approach was used by Wellstein et al. (2013) to test the relationship between intraspecific variation in plant traits and the variation of environmental parameters such as light, soil moisture, temperature, pH, and soil nutrients.

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1. Because the zero point has a clear definition in this case, both mathematically and biologically, the CV may be meaningful, but its value may be extreme or even undefined (i.e., +∞) when the mean is close or equal to 0 (e.g., see Pélabon and Hansen 2008).
2. Analysis would be undertaken based on the 15-year historical information that the investor used to initially make their decision.
3. However, the transformation of the data involved in these calculations are often performed with little attention given to the meaning of the numbers.
4. The term is used widely in the design of pollution control equipment, such as electrostatic precipitators (ESPs),15 selective catalytic reduction (SCR), scrubbers, and similar devices.
5. You also need to learn how to use other statistical techniques, such as hypothesis testing, confidence intervals, and correlation.
6. Only the Kelvin scale can be used to compute a valid coefficient of variability.

Here, we show that despite apparent similarities, evolvability and phenotypic plasticity have different properties that prevent the use of CVs for comparing phenotypic plasticity across traits and environments. Statistical analyses in ecology and evolution often involve the calculation of summary statistics to facilitate interpretation. However, the transformation of the data involved in these calculations are often performed with little attention given to the meaning of the numbers. In some cases, this compromises the meaning of the analyses and undermines the conclusions of the studies.

The coefficient of variation can be useful when comparing data sets with different units or widely different means. The coefficient of variation formula can be performed in Excel by first using the standard deviation function for a data set. Since the coefficient of variation is the standard deviation divided by the mean, divide the cell containing the standard deviation by the cell containing the mean. In this article we have outlined some ways to use the precision of an assay, as measured by the CV, after the precision has been established from validation studies. Equation A4, the nomogram, and the critical-value table are simple tools that extend the understanding of the CV and increase its usefulness in study design, laboratory procedures, and interpretation of diagnostic results.

From here, you just need to divide the standard deviation by the mean to determine the coefficient of variation. There are a few advantages that come with using the coefficient of variation. Essentially, this allows a coefficient of variation to be compared against another. Other measures for example, such as root mean squared residuals and standard deviations, cannot be compared in a similar way.

Laboratory measures of intra-assay and inter-assay CVs

Besides his extensive derivative trading expertise, Adam is an expert in economics and behavioral finance. Adam received his master’s in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology. He is a CFA charterholder as well as holding FINRA Series 7, 55 & 63 licenses. He currently researches and teaches economic sociology and the social studies of finance at the Hebrew University in Jerusalem.

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Furthermore, if the variable has a mean of 1 on the original scale, it will have a mean of 0 in the difference scale and this will prevent the calculation of the CV. After you’re able to find out the data variance, you simply take the square root of the value to determine the standard variation. A high standard deviation often shows, in the case of regular data distributions, that individual numerical values are far away from the mean. The article explains what variance means, how to calculate it, how to use the formula and the main differences between variance and standard deviation.

Particular properties of the variables CV and k must be kept in mind when applying equation A4. In clinical research the variable k is a fixed quantity, set by the investigator based on knowledge of the biological relevance of differences between measurements. The choice of k may also be made to optimize the sensitivity and specificity of diagnostic tests by employing k as a cutoff. In other settings k could be selected not to make clinical judgements but to monitor laboratory performance.

The coefficient of variation (CV) is a statistical measure of the dispersion of data points in a data series around the mean. The coefficient of variation represents the ratio of the standard deviation to the mean, and it is a useful statistic for comparing the degree of variation from one data series to another, even if the means are drastically different from one another. Essentially, it accounts for the relative variability in data sets to determine the size of a standard deviation compared to its mean.

Here, a natural choice of k would be one that maximizes differences between CV in the range of interest. 1 shows that the p(k) curve for a k of 4 is essentially zero in the range of CVs less than 40%; thus monitoring the frequency of fourfold differences among replicate measurements would not readily differentiate between CVs below 40%. On the other hand, a k of 1.5 or 2 visually separates CVs between 10 and 90% very well. CVs expected to fall below 10% would require an assignment of k closer to 1.0. Apart from the issue of differentiating the CV, there is flexibility in the selection of k. However, it would be desirable for the sake of comparability among laboratories to have laboratories in specific research areas conform to some consensus, if possible, on the choice of k.