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In order for the absolute deviation to be an unbiased estimator, the expected value (average) of all the sample absolute deviations must equal the population absolute deviation. However, it does not. For the population 1,2,3 both the population absolute deviation about the median and the population absolute deviation about the mean are 2/3.
The median absolute deviation is a measure of statistical dispersion. Moreover, the MAD is a robust statistic, being more resilient to outliers in a data set than the standard deviation. In the standard deviation, the distances from the mean are squared, so large deviations are weighted more heavily, and thus outliers can heavily influence it ...
A simple Monte Carlo spreadsheet calculation would reveal typical values for the standard deviation (around 105 to 115% of σ). Or, one could subtract the mean of each triplet from the values, and examine the distribution of 300 values. The mean is identically zero, but the standard deviation should be somewhat smaller (around 75 to 85% of σ).
SSMD is the ratio of mean to the standard deviation of the difference between two groups. When the data is preprocessed using log-transformation as we normally do in HTS experiments, SSMD is the mean of log fold change divided by the standard deviation of log fold change with respect to a negative reference.
The absolute value of the deviation indicates the size or magnitude of the difference. In a given sample, there are as many deviations as sample points. Summary statistics can be derived from a set of deviations, such as the standard deviation and the mean absolute deviation, measures of dispersion, and the mean signed deviation, a measure of ...
Each cell may contain either numeric or text data, or the results of formulas that automatically calculate and display a value based on the contents of other cells. The term spreadsheet may also refer to one such electronic document. [5] [6] [7] Spreadsheet users can adjust any stored value and observe the effects on calculated values.