Introduction
Unbiased estimators of variance are statistical tools used to measure the variance of a sample. Variance is a measure of how far a set of numbers are spread out from their mean. Unbiased estimators of variance are important for accurately measuring the variability within a given data set, as they are not biased by the sample size or the specific values of the data points. This article will provide an overview of unbiased estimators of variance and discuss their importance in statistical analysis.
Background
Variance is a measure of how far a set of numbers are spread out from their mean. It is calculated by taking the sum of the squared differences between each data point and the mean, and then dividing by the total number of data points. This calculation requires knowledge of the mean, which is why an unbiased estimator of variance is needed. An unbiased estimator of variance is a statistical tool that can be used to measure the variance of a sample without knowledge of the mean.
Unbiased Estimator of Variance
The most commonly used unbiased estimator of variance is the sample variance, which is calculated by taking the sum of the squared differences between each data point and the sample mean, and then dividing by the total number of data points minus one. This calculation is known as the unbiased estimator of variance because it does not depend on the mean of the data set. The sample variance is an unbiased estimator of variance because it does not bias the variance calculation by the sample size or the specific values of the data points.
Other Unbiased Estimators of Variance
The sample variance is not the only unbiased estimator of variance. Other estimators include the sample mean squared deviation, the mean absolute deviation, and the median absolute deviation. Each of these estimators has its own strengths and weaknesses, and which one is best used depends on the specific data set being analyzed.
Conclusion
Unbiased estimators of variance are important tools for accurately measuring the variability within a given data set. The most commonly used estimator is the sample variance, but other estimators such as the sample mean squared deviation, the mean absolute deviation, and the median absolute deviation also exist. Unbiased estimators of variance can help researchers accurately measure the variability of a data set without biasing the calculation by the sample size or the specific values of the data points.
References
Khan, A. S. (2018). Unbiased estimator of variance. SAGE Research Methods. https://dx.doi.org/10.4135/9781483382802.n6
Kutner, M. H., Nachtsheim, C. J., Neter, J., & Li, W. (2004). Applied linear statistical models. McGraw-Hill Education.
Millar, J. (2013). Estimation of variance. The Statistician, 62(2), 179-188. https://doi.org/10.1111/j.1467-9876.2012.01025.x