# Outlier detection using Hoeffding Inequality

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

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?

• 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. – MotiN Jun 9 '17 at 17:57