Loser level

Loser level (central red point)

A loser level (はずれち British: outlier) is the value that greatly came off from other values in statistics.

It is different from the abnormal value due to measurement error, record errors conceptually, but may not distinguish the practical use top.

Table of contents

Official approval

The official approval statistic which fell below a deviation in impartiality standard deviation about the specimen which I wanted to examine whether it was a loser level

${\displaystyle \tau _{1}={\frac {x_{1}-\mu }{\sigma}}}$ 

I demand を (x₁ averages specimen value, μ as for σ standard deviation) and examine it whether this value (when I do a two-tail test this modulus) is bigger than a meaningful point.

By the simple method, I assume 2 or 3 a meaningful point. In other words, I assume it a loser level outside μ ± 2–3σ.

Smirnoff gloves official approval

I assume normal distribution more precisely and use the Smirnoff gloves (Smirnov-Grubbs) official approval. The number of the specimens n, a level of significance of the indispensability α, α/ n *100 percentile of the t distribution of flexibility n -2 as t,

${\displaystyle \tau ={\frac {(n-1)t}{\sqrt {n(n-2)+nt^{2}}}}}$ 

I assume it を meaningful point. I use this expression recursively. In other words, if I examine only 1 specimen which came off most, and it is judged with a loser level it, I examine the specimen which I came off using a specimen of the n-one which excluded it second and repeat it until a loser level is not detected as follows.

Thompson official approval

By the Thompson (Thompson) official approval,

${\displaystyle t={\frac {\tau {\sqrt {n-2}}}{\sqrt {n-1-\tau ^{2}}}}}$ 

I use を. It is reverse to the Smirnoff gloves official approval and, on account of the calculating formula, often finds level of significance α ₁ from official approval statistic τ ₁ of the specimen value via t₁. If n is big enough, it becomes the result same as Smirnoff gloves official approval.

Allied item

• Huber loss

Outside link

Wiki media Commons has the category in conjunction with the loser level.

• Meaningful point of the Smirnoff gloves official approval

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This article is taken from the Japanese Wikipedia Loser level

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