variation ratio

(noun)

the proportion of cases not in the mode

Related Terms

  • qualitative data

Examples of variation ratio in the following topics:

  • Measures of Variability of Qualitative and Ranked Data

    • The variation ratio is a simple measure of statistical dispersion in nominal distributions.
    • Just as with the range or standard deviation, the larger the variation ratio, the more differentiated or dispersed the data are; and the smaller the variation ratio, the more concentrated and similar the data are.
    • This group is more dispersed in terms of gender than a group which is 95% female and has a variation ratio of only 0.05.
    • Similarly, a group which is 25% Catholic (where Catholic is the modal religious preference) has a variation ratio of 0.75.
    • This group is much more dispersed, religiously, than a group which is 85% Catholic and has a variation ratio of only 0.15.
  • Overview of How to Assess Stand-Alone Risk

    • Another statistical measure that can be used to assess stand-alone risk is the coefficient of variation.
    • In probability theory and statistics, the coefficient of variation is a normalized measure of dispersion of a probability distribution.
    • It is also known as unitized risk or the variation coefficient.
    • A lower coefficient of variation indicates a higher expected return with less risk.
    • The coefficient of variation, an example of which is plotted in this graph, can be used to measure the ratio of volatility to expected return.
  • Mean Squares and the F-Ratio

    • There are two sets of degrees of freedom for the $F$-ratio: one for the numerator and one for the denominator.
    • To calculate the $F$-ratio, two estimates of the variance are made:
    • The variance is also called variation due to treatment or explained variation.
    • The variance is also called the variation due to error or unexplained variation.
    • Then, the F-ratio will be larger than one.
  • The F-Distribution and the F Ratio

    • The F statistic is a ratio (a fraction).
    • To calculate the F ratio, two estimates of the variance are made.
    • The variance is also called variation due to treatment or explained variation.
    • Then the F-ratio will be larger than 1.
    • If the groups are the same size, the calculations simplify somewhat and the F ratio can be written as: F-Ratio Formula when the groups are the same size
  • Direct Variation

    • When two variables change proportionally to each other, they are said to be in direct variation.
    • No matter how many toothbrushes purchased, the ratio will always remain: $2 per toothbrush.
    • Direct variation is easily illustrated using a linear graph.
    • Graph of direct variation with the linear equation y=0.8x.
    • The line y=kx is an example of direct variation between variables x and y.
  • Comparisons Within an Industry

    • When comparing past and present financial information, one will want to look for variations such as higher or lower earnings.
    • Ratios of risk such as the current ratio, the interest coverage, and the equity percentage have no theoretical benchmarks.
    • Ratios must be compared with other firms in the same industry to see if they are in line .
    • Ratio analyses can be used to compare between companies within the same industry.
    • For example, comparing the ratios of BP and Exxon Mobil would be appropriate, whereas comparing the ratios of BP and General Mills would be inappropriate.
  • Test of Two Variances

    • For instance, college administrators would like two college professors grading exams to have the same variation in their grading.
    • In order for a lid to fit a container, the variation in the lid and the container should be the same.
    • Since we are interested in comparing the two sample variances, we use the F ratio
    • NOTE: The F ratio could also be $\frac{(s_1)^2}{(s_2)^2}$.
    • Two college instructors are interested in whether or not there is any variation in the way they grade math exams.
  • Risk Adjusting the Discount Rate

    • Individuals and firms use methods for adjusting discount rates for risk, include adding risk premiums, Sharpe Ratios, rNPV, and Monte Carlo evaluation.
    • Risk will also increase due to the amount of variation in the possible outcomes.
    • The Sharpe Ratio is a measure of risk premium per unit of deviation in an investment asset.
    • The Sharpe Ratio is defined as: where Ra is the asset return, Rb is the return on a benchmark asset, such as the risk free rate of return or an index such as the S & P 500.
    • The Sharpe ratio characterizes how well the return of an asset compensates the investor for the risk taken.
  • Total Debt to Total Assets

    • The debt ratio is expressed as Total debt / Total assets.
    • Financial ratios are categorized according to the financial aspect of the business which the ratio measures.
    • Debt ratios measure the firm's ability to repay long-term debt.
    • The higher the ratio, the greater risk will be associated with the firm's operation.
    • Like all financial ratios, a company's debt ratio should be compared with their industry average or other competing firms.
  • Comparing Two Population Variances

    • In order for a lid to fit a container, the variation in the lid and the container should be the same.
    • Since we are interested in comparing the two sample variances, we use the $F$ ratio:
    • If the null hypothesis is $\sigma_1^2 = \sigma_2^2$, then the $F$ ratio becomes:
    • Note that the $F$ ratio could also be $\frac { { s }_{ 2 }^{ 2 } }{ { s }_{ 1 }^{ 2 } }$.
    • Two college instructors are interested in whether or not there is any variation in the way they grade math exams.
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