Unbiased estimation of standard deviation

About: Unbiased estimation of standard deviation is a research topic. Over the lifetime, 425 publications have been published within this topic receiving 11885 citations.

Estimation of Average Concentration in the Presence of Nondetectable Values

Abstract: In the attempt to estimate the average concentration of a particular contaminant during some period of time, a certain proportion of the collected samples is often reported to be below the limit of detection. The statistical terminology for these results is known as censored data, i.e., nonzero values which cannot be measured but are known to be below some threshold. Samples taken over time are assumed to follow a lognormal distribution. Given this assumption, several techniques are presented for estimation of the average concentration from data containing nondetectable values. The techniques proposed include three methods of estimation with a left-censored lognormal distribution: a maximum likelihood statistical method and two methods involving the limit of detection. Each method is evaluated using computer simulation with respect to the bias associated with estimation of the mean and standard deviation. The maximum likelihood method was shown to produce unbiased estimates of both the mean and s...

Standard deviations and standard errors.

Abstract: The terms “standard error” and “standard deviation” are often confused.1 The contrast between these two terms reflects the important distinction between data description and inference, one that all researchers should appreciate. The standard deviation (often SD) is a measure of variability. When we calculate the standard deviation of a sample, we are using it as an estimate of the variability of the population from which the sample was drawn. For data with a normal distribution,2 about 95% of individuals will have values within 2 standard deviations of the mean, the other 5% being equally scattered above and below these limits. Contrary to popular misconception, the standard deviation is a valid measure of variability regardless of the distribution. About 95% of observations of any distribution usually fall within the 2 standard …

The distribution of range in samples from a normal population, expressed in terms of an independent estimate of standard deviation

Abstract: STARTING from the contribution of Tippett (1925), a considerable amount of computational work has been carried out in recent years with the object of making possible the use of range, i.e. the distance between the highest and lowest observation, when dealing with samples from a normal population. Thus Tippett's tables of the mean range expressed in terms of the population standard deviation, o', for sample sizes n = 2 to 1000 have been republished in Tables for Statisticians and Biometricians, Part II, Table XXII (K. Pearson, 1931). Later E. S. Pearson (1932) gave a table containing the standard deviation of range, and also the approximate upper and lower 10, 5, 1 and 0 5 % probability levels for sample sizes n = 2 to 100, again in terms of o as unit. In doing this he used empirical Pearson-type curves with correct moments, and checked his results against some experimental sampling distributions. If a number of small samples are available, it has been shown that a rapid estimate of omay be obtained from the mean value of the range, which is only slightly less accurate than the estimate obtained from the sums of squares. Again, owing to the high correlation between range and standard deviation in a sample of size 10 or less, it was pointed out by Pearson & Haines (1935) that range may be usefully substituted for standard deviation in control charts used to study changes in the variation of quality in industry. In all these cases, however, the basic sampling distribution used has been that of the ratio of range to O. Not very long ago " Student " (the late Mr W. S. Gosset) suggested to Prof. E. S. Pearson that it might be useful to know more about the sampling distribution of the ratio q = w/s,

Measurement error proportional to the mean.

Abstract: We often need to know the error with which measurements are made—for example, so that we can decide whether the change in a clinical observation represents a real change in a patient's condition. We have discussed previously the within-subject standard deviation as a practical index of measurement error.1 We said that this approach should be used when the measurement error was not related to the magnitude of the measurement and recommended that we plot the subject standard deviation against the subject mean to check this. Table 1 shows some duplicate salivary cotinine measurements taken from a larger study. Figure 1 shows absolute subject difference against subject mean, which is equivalent to a standard deviation versus mean plot when we have only two measurements per subject.1 If we are to use the within-subject standard deviation as an index of measurement error we need the subject standard deviation to be …