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Median test (also Mood’s median-test, Westenberg-Mood median test or Brown-Mood median test) is a special case of Pearson's chi-squared test. It is a nonparametric test that tests the null hypothesis that the medians of the populations from which two or more samples are drawn are identical. The data in each sample are assigned to two groups ...
Calculating the median in data sets of odd (above) and even (below) observations. The median of a set of numbers is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution.
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.
Statistics defined to be a function on a sample, without dependency on a parameter. An example is Order statistics, which are based on ordinal ranking of observations. The discussion following is taken from Kendall's Advanced Theory of Statistics. [3] Statistical hypotheses concern the behavior of observable random variables....
The sample mean is thus more efficient than the sample median in this example. However, there may be measures by which the median performs better. For example, the median is far more robust to outliers, so that if the Gaussian model is questionable or approximate, there may advantages to using the median (see Robust statistics).
where I is the indicator function, Q is the sample median of the X i, and u i = x i − Q 9 ⋅ M A D . {\displaystyle u_{i}={\frac {x_{i}-Q}{9\cdot {\rm {MAD}}}}.} Its square root is a robust estimator of scale, since data points are downweighted as their distance from the median increases, with points more than 9 MAD units from the median ...
All classical statistical physics is based on the concentration of measure phenomena: The fundamental idea (‘theorem’) about equivalence of ensembles in thermodynamic limit (Gibbs, 1902 [4] and Einstein, 1902-1904 [5] [6] [7]) is exactly the thin shell concentration theorem.
The appropriate statistic depends on the level of measurement. For nominal variables, a frequency table and a listing of the mode(s) is sufficient. For ordinal variables the median can be calculated as a measure of central tendency and the range (and variations of it) as a measure of dispersion.