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I have a data set that includes the different response times of a user that is visiting a web application. For example, a visitor enters www.test.com in the browser and navigates through this domain watching child pages like www.test.com/news, www.test.com/overview, www.test.com/overview/current, etc. If a user watches a web site, it is called a user action.

Let's say a user has performed 5 user actions with the response times 200ms, 500ms, 350ms, 1200ms, 154ms. Now I want to find the outliers that express either fast page loads or slow page loads. Is that somehow possible?

Thanks

EDIT: I want to detect outliers because I want to determine the user experience depending on the response time. Let's say I have three ux-states, namely happy, ok and unhappy. All user actions are ok except the outliers. They are either unhappy if the response time is too high or happy if the response time is very low.

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Why do you want to detect outliers? The reason might guide the criterion you use to determine whether a page is an outlier or not. –  Patrick Coulombe Jul 13 at 17:25
    
Please have a look at my edit. –  enne87 Jul 14 at 7:33

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up vote 3 down vote accepted

It depends on how you want to define outlier, since there isn't one particular definition of this concept. One of the more common ways to define this, though, is to consider the region $$ [ \pi_{.25} - 1.5 \times \mathrm{IQR}\,, \; \pi_{.75} + 1.5 \times \mathrm{IQR} ] $$ where $\pi_{.25}$ and $\pi_{.75}$ are the 25th and 75th percentiles, respectively, and $\mathrm{IQR}$ is the interquartile range, i.e. $\pi_{.75} - \pi_{.25}$. Of course, this region may be too wide or too narrow for a dataset of only 5 observations, but that is really just an inherent problem of trying to define an outlier from a small sample - having only 5 observations it's hard to get a feel for what the true distribution is that you are sampling from with such little information.

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Sounds good, thank you :) –  enne87 Jul 13 at 17:49
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You cant really define an outlier by such an arbitrary criterion. You should first tell us why you want to classify some observations as outliers---what are you going to do with them? Why do you need it? –  kjetil b halvorsen Jul 13 at 19:52
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I'm note sure this will necessarily be an ideal choice for what will likely be a very skewed distribution –  Glen_b Jul 13 at 21:19
    
Please see my edit. –  enne87 Jul 14 at 7:33

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