Multiple outlier stats test suggestion

[jlizzamora]

Hello,

I was wondering if you could suggest a statistical test to detect more than one outlier from a data set with n=7 . I thought of using Dixon’s Q test or Grubb’s Test but they seem to be for single outliers.


Thank you,

Juana

[scooke]

Dear Juana,

I appreciate the desire to identify multiple outliers with one test, but the reason the tests used target individual values is that the "rejection" criteria depend on its relationship to the statistics of the whole data set.  IF you identify an "outlier" and remove it from your 'legitimate' data set, the statistics of that set change as well.  The change may or may not move other data points into the 'outlier' region.  You cannot determine that until you have the 'new' data set to work with, so you can't identify multiple outliers with a single test - it will require sequential tests of each suspect data point.

In practical terms, you are applying this to a relatively small data set.  As an analytical chemist, if I find that even 2 out of 7-8 data points may be 'outliers' I would prefer to find out why, and rerun my tests with greater confidence.  Reducing my 'valid' data set to only 5-6 data points also reduces my confidence in any "statistical" analyses that I may want to do with them.

I prefer the Grubb's test because it includes the standard deviation of the sample as an indicator of the central tendency, which I think is better than a simple arithmetic (linear approximation) ratio of the raw values.

In ALL cases, you should never simply 'remove' data from your records!  An explanation of the reason for removal (including these tests) of a data point and a retention of the total raw data and calculations should always be retained for the most ethical reporting of any data and results.  You may then proceed to your statistical analyses of the 'valid' data remaining.

Best regards,

Steven Cooke

Process Systems Consulting

[Stangog]

Thank you Steven! I have also learned from your brilliant explanation.

Cheers,

Saki

[mayaaa]

Hey everyone! I wanted to jump into the discussion about outlier detection techniques and share some thoughts on this topic. Firstly, it's great to see the interest in exploring different statistical tests for identifying outliers in a dataset. Understanding and handling outliers is crucial for accurate data analysis.

Juana, you mentioned Dixon's Q test and Grubb's Test, which are indeed commonly used for detecting single outliers. However, as Steven Cooke rightly pointed out, these tests focus on individual values because the presence of an outlier can affect the overall statistics of the dataset. Therefore, detecting multiple outliers with a single test can be challenging.

In your case, with a dataset of n=7, it's important to consider the implications of removing multiple data points. This could significantly impact the reliability and validity of your statistical analysis.

I agree with Steven's suggestion of investigating the reasons behind potential outliers and running the tests again for greater confidence. Maintaining the integrity of your data and providing a transparent explanation for any removals is essential for ethical reporting. Perhaps you should explore other testing methods in this article: Explore 4 Top Usability Testing Techniques in User-Centric Design

Let's keep exploring different techniques and discussing best practices in outlier detection. It's through sharing our knowledge and experiences that we can enhance our understanding of this important aspect of data analysis.

[JakariZaka]

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