Data were collected on TBUT, a measure of how long it takes...

Data were collected on TBUT, a measure of how long it takes for tears to form. This is a commonly used measure to assess dry-eye patients, with a smaller number indicating more severe disease. One issue is how reproducible this measure is. For this purpose, replicate values of this measure were obtained from the right eye of 14 dry-eye patients 5 minutes after instillation of a placebo drop. The data for the first 7 patients are given in Table 12.45 . Assume overall that the In (TBUT) is approximately normally distributed. The sd [In, (TBUT)] over the 14 observations) is 0.459. What is the coefficient of variation for TBUT as estimated from these data?

Data were collected on TBUT, a measure of how long it takes for tears to form. This is a commonly used measure to assess dry-eye patients, with a smaller number indicating more severe disease. One issue is how reproducible this measure is. For this purpose, replicate values of this measure were obtained from the right eye of 14 dry-eye patients 5 minutes after instillation of a placebo drop. The data for the first 7 patients are given in Table 12.45 .
Assume overall that the In (TBUT) is approximately normally distributed. The sd [In, (TBUT)] over the 14 observations) is 0.459.
What is the coefficient of variation for TBUT as estimated from these data?

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Key Concepts

Log-Normal Distribution

A log-normal distribution arises when the logarithm of a variable is normally distributed. In such cases, while the transformed data meet the assumptions of normality, the original data are skewed. There are specific formulas to convert parameters from the log scale back to the original scale, including the calculation of the coefficient of variation. For a log-normally distributed variable, the CV can be computed using the relationship CV = sqrt(exp(?²) - 1), where ? is the standard deviation of the logarithmically transformed variable.

Coefficient of Variation

The coefficient of variation (CV) is a standardized measure of dispersion of a probability distribution, defined as the ratio of the standard deviation to the mean. It is useful for comparing the relative variability of different data sets, regardless of their units or scales. In contexts where the variable is strictly positive, such as measurements of tear film breakup time, CV provides a dimensionless measure that indicates variability relative to the magnitude of the mean.

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