Signs of the Ratio Method

In statistics, the parameter known as population variance is essential to statistical analyses. In short, this parameter states how large the variation is among individuals in the population. Statisticians use many ways to estimate this population variance, and often provide estimates in their statistical reports. But it is not always immediately obvious which method the statisticians used in their estimation of population variance. The ratio method of estimating population variance has some signs associated with it, so you can analyze a report to find whether this method was used.
  1. The Use of Auxiliary Information

    • The ratio method relies on auxiliary information about the population distribution to find a more precise estimate for the population variance. Thus, statisticians using the ratio method are likely to include this auxiliary data in their reports. Some common forms of population distribution information used as auxiliary data are distribution parameters such as population kurtosis. An example of a study that you could expect to see the ratio method used is one in which the statisticians state that certain auxiliary data is integral to understanding the population distribution.

    Mean Squared Error Calculation

    • The mean squared error calculation of the estimate found through the ratio method will rely on approximation methods instead of the standard mean squared error calculation methods. Therefore, you should look for signs of Taylor series approximations for mean squared error, which often come in the form of a vector multiplied by a correlation matrix and then multiplied by the same vector’s transpose.

    Unbiased

    • The ratio method produces an unbiased estimator of the population variance. That is, this estimator will not consistently overestimate nor underestimate the population variance. If a statistical report has emphasized that the estimate for population variance is unbiased, it is possible that the statisticians used the ratio method to arrive at their estimator.

    Precision and Efficiency

    • The ratio method is high in precision -- its precision is equal to that of other traditional methods. Where the ratio method really shines, though, is that it is more efficient than other methods. Therefore, you may expect statisticians to use this estimator when precision and efficiency are important factors in their studies. Examples of these types of situations are when statisticians perform multiple analyses in one study, perform an analysis on multiple sets of populations or need to conserve computing power.

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