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Is it possible to detect ourliers within univariate reaction time data using the Hoeffding Inequality described below? enter image description here

Let's say We have following reaction time data.

// some observed reaction times
double dataPoints[] = {0.464, 0.443, 0.424, 0.386, 0.367, 0.382, 0.455, 0.410, 0.411, 0.424, 0.338, 0.355, 0.342, 0.324,
        0.354, 0.322, 0.364, 0.375, 1.085, 0.575, 0.597, 0.464, 0.414, 0.408, 1.156, 0.819, 1.156, 1.024, 1.152, 1.103,
        0.431, 0.378, 0.358, 0.382, 0.354, 0.435, 0.386, 0.361, 0.397, 0.362, 0.334, 0.357, 0.344, 0.362, 0.317, 0.331,
        0.199, 0.351, 0.284, 0.343, 0.354, 0.336, 0.280, 0.312, 0.778, 0.723, 0.755, 0.774, 0.759, 0.762, 0.490, 0.400,
        0.364, 0.439, 0.441, 0.673};

UPDATE 1

The Hoeffding inequality can be used to provide tight bounds when strict upper and lower limits exist on tracked values. This bounds could be used to detect outliers, isn't it?

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Hoeffding's inequality equivalently states that when the variables are bounded, the sample average converges exponentially quickly to the actual mean.

Outlier detection is generally about identifying things as being in low probability areas - Hoeffding's inequality is not sufficient here as it only deals with the average.

Markov's and Chebyshev's inequality could be used for outlier detection, although the assumptions are very weak - thus, the bounds may not be that useful when comparing to more accurate models of the actual data.

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  • $\begingroup$ The Hoeffding inequality can be used to provide tight bounds when strict upper and lower limits exist on tracked values. This bounds could be used to detect outliers, isn't it? $\endgroup$ – lidox Jun 9 '17 at 13:45
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    $\begingroup$ The variables must be bound by those values - that wouldn't be outlier detection but a data cleanliness issue. If you KNOW that your data must be in the range $[l,u]$ and you see a data point outside that range, then obviously it's not valid - Hoeffding inequality requires the bounds, so it doesn't provide anything extra beyond having the bounds in terms of that kind of detection. $\endgroup$ – MotiN Jun 9 '17 at 17:57

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