Re: Mean vs Median

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> Hello Stenio,
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> Thanks for your comments. Please see my comments inline.
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> From: [email protected]
> [mailto:[email protected] <[email protected]>]
> On Behalf Of Stenio Fernandes
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> Sent: Tuesday, November 3, 2015 5:45 PM
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> To: GEORGESCU LIVIU MARIUS <[email protected]>
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> Cc: [email protected]; [email protected]
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> Subject: Re: [bmwg] Mean vs Median
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> my two cents on this... see inline comments
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> this is my first interaction with the wg... so, bear
> with me if i'm a bit wordy :-)
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> stenio
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> Thanks for joining the discussion.
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> On Tu
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> e, Nov 3, 2015 at 3:57 AM, GEORGESCU LIVIU MARIUS <[email protected](https://mail.google.com/mail/?view=cm&fs=1&tf=1&[email protected])> wrote:
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> Hello BMWG,
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> Following some of the discussion we had in IETF93 about
> using either mean or median as a summarizing function for the results of
> multiple test iterations, I added the following section in http://tools.ietf.org/html/draft-ietf-bmwg-ipv6-tran-tech-benchmarking-00 
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> .
>  10. Summarizing function
> and repeatability 
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>  To ensure the stability of the benchmarking scores obtained using
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>  the tests presented in Sections 6(http://tools.ietf.org/html/draft-ietf-bmwg-ipv6-tran-tech-benchmarking-00#section-6)-9(http://tools.ietf.org/html/draft-ietf-bmwg-ipv6-tran-tech-benchmarking-00#section-9), multiple test iterations are
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>  recommended. Following the recommendations of RFC2544(http://tools.ietf.org/html/rfc2544), the average
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>  was chosen to be the summarizing function for the reported values.
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>  While median can be an alternative summarizing function, a rationale
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>  for using one or the other is needed.
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> average is a colloquial term. although, in this context,
> there might be nothing wrong with that, imho precise terms are preferred.
> measures of central tendency could be used as the general term, where mean and
> median fit in. 
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> Average seems to be a term accepted and used by industry, and
> not just a “colloquial” term. We could quibble about definitions and what
> we need to follow just as well. I prefer to go with RFC2544.
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>  The median can be useful for summarizing especially when outliers
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>  are not a desired quantity. However, in the overall performance of a
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>  network device the outliers can represent a malfunction or
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>  misconfiguration in the DUT, which should be taken into account.
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>  The average is a more inclusive summarizing function. Moreover, as
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>  underlined in [DeNijs(http://tools.ietf.org/html/draft-ietf-bmwg-ipv6-tran-tech-benchmarking-00#ref-DeNijs)], the average is less exposed to statistical
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>  uncertainty. These reasons make it the RECOMMENDED summarizing
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>  function for the results of different test iterations, unless stated
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>  otherwise.
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> i'm having a hard time to understand this paragraph... i)
> "inclusive" is very vague; ii) "less exposed to uncertainty"
> is confusing. the mean is just a measure of centrality, whereas measures of
> dispersions (e.g., sd, variance) can be used to assess the degree of
> uncertainty around that measure (think of confidence intervals).
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> i know this is not the objective of the document, but the
> recommendation could be very simple. for example, stating that one should
> assess statistical significance of results would be enough, and then
> pointing out to a strong reference. le boudec's book seems appropriate
> here (cf. chap 2).
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> Just assessing statistical significance would be great. I would
> recommend the study of this book: “Jain, Raj. The art of computer systems
> performance analysis. John Wiley & Sons, 2008.”
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> I wonder if text like this in an RFC would see the print.
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> I am sure this would be perfect for certain types of academic
> papers. I would rather have a clearer recommendation.
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>  To express the repeatability of the benchmarking tests through a
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>  number, the Margin of error (MoE) can be used. Of course, other
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>  functions, such as standard error could be employed as well. The
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>  advantage the MoE has is expressing an associated confidence
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>  interval by using the alpha parameter.
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>  The recommended formula for calculating the MoE is presented in 
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> Section 6.3.1.
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> if the document will not give detailed approaches for
> summarizing performance data (and i think it shouldn't), it should provied the
> simplest recommendation as possible. otherwise, in order to be scientifically
> correct, lots of assumptions must be made and provided, like iid, which might
> not hold true for all cases.
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> In order to be scientifically correct, the most important
> part would be to assess the probability distribution of the data. I am trying
> to find a solution where that wouldn’t be necessary. Of course it would
> not hold for all cases, but the goal is to find a pareto-optimal solution where
> the summarized result would be representative enough for the test sample and
> simple enough to obtain. Or at least that’s how I see things.
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> Marius
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>

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