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The mean and the standard deviation of a set of data are descriptive statistics usually reported together. In a certain sense, the standard deviation is a "natural" measure of statistical dispersion if the center of the data is measured about the mean. This is because the standard deviation from the mean is smaller than from any other point.
For example, suppose that scale scores are found to have a mean of 23.5, a standard deviation of 4.2, and to be approximately normally distributed. Then sten scores for this scale can be calculated using the formula, () +. It is also usually necessary to truncate such scores, particularly if the scores are skewed.
Bias in standard deviation for autocorrelated data. The figure shows the ratio of the estimated standard deviation to its known value (which can be calculated analytically for this digital filter), for several settings of α as a function of sample size n. Changing α alters the variance reduction ratio of the filter, which is known to be
The standard deviation is more amenable to algebraic manipulation than the expected absolute deviation, and, together with variance and its generalization covariance, is used frequently in theoretical statistics; however the expected absolute deviation tends to be more robust as it is less sensitive to outliers arising from measurement ...
In statistics, deviance is a goodness-of-fit statistic for a statistical model; it is often used for statistical hypothesis testing.It is a generalization of the idea of using the sum of squares of residuals (SSR) in ordinary least squares to cases where model-fitting is achieved by maximum likelihood.
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
The JND formula has an objective interpretation (implied at the start of this entry) as the disparity between levels of the presented stimulus that is detected on 50% of occasions by a particular observed response, [3] rather than what is subjectively "noticed" or as a difference in magnitudes of consciously experienced 'sensations'.
Important examples include the sample variance and sample standard deviation. Without Bessel's correction (that is, when using the sample size instead of the degrees of freedom), these are both negatively biased but consistent estimators. With the correction, the corrected sample variance is unbiased, while the corrected sample standard ...