Manolis,
It sounds to me like you want to justify the choice of a measure of
central tendency. I doubt that deciding Guassian or not is of interest.
So I will give the simplest of answers.
1. The mean and median are the most accepted and understandable measures
of central tendency.
2. When distributions are too skewed, the mean is not good for
representing the whole population because it gives to much weight to
large values. Think of family income. The mean gives a distorted view
of income because the top 1% pulls the mean far to the right. Thus, the
US census reports median family income.
3. You really want to know how much skewness is "too skewed." I'm afraid
there is no justifiable rule of thumb for this, but I could be wrong.
4. Sometimes you must use the mean. In population surveys, the total is
often of paramount interest. In such cases the mean is forced on you
because total=N*mean.
Dennis Boos
On 2/25/2020 6:35 AM, American Statistical Association wrote:
> 2 new threads, 6 replies and 1 library entry from 7 authors in the "ASA
> Connect" community ... Hi ASA Connect, The newest episode of the show is
> now out. Shane Burns presents the visual data platforms that monitor the
> health of dairy cows...
> Please note that using your email client's "Reply" option will send your
> response to all members of the discussion group. To send a private
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> *Feb 24, 2020*
>
>
> Discussions
>
> started 6 hours ago, Glen Colopy
> <https://community.amstat.org/network/members/profile?UserKey=7f331d59-fe82-4d90-837c-5178ce3939c1>
> (0 replies)
>
> *Machine Learning for Animal Vital-Sign Time-Series - New Episode on Pod
> of Asclepius
> <https://community.amstat.org/communities/community-home/digestviewer/viewthread?MessageKey=904a01db-2beb-4e0c-9c86-bfd39d36c9ec&CommunityKey=6b2d607a-e31f-4f19-8357-020a8631b999&tab=digestviewer#bm904a01db-2beb-4e0c-9c86-bfd39d36c9ec>*
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>
> 1. Hi ASA Connect, The newest episode of the... <#m0> Glen Colopy
>
> started 17 hours ago, Xiaofei Wang
> <https://community.amstat.org/network/members/profile?UserKey=c16da042-647c-4b2e-ab95-8936e8da011d>
> (0 replies)
>
> *Duke-Industry Statistics Symposium (DISS2020)
> <https://community.amstat.org/communities/community-home/digestviewer/viewthread?MessageKey=317e4382-6b2c-4db2-b0a5-27b07d5d9286&CommunityKey=6b2d607a-e31f-4f19-8357-020a8631b999&tab=digestviewer#bm317e4382-6b2c-4db2-b0a5-27b07d5d9286>*
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>
> 2. Dear Colleagues, We are happy to announce... <#m1> post has
> attachment Xiaofei Wang
>
> started 2 days ago, Manolis Antonoyiannakis
> <https://community.amstat.org/network/members/profile?UserKey=b9ec4383-7888-47ed-aa7e-961c9799726c>
> (8 replies)
>
> *skewness
> <https://community.amstat.org/communities/community-home/digestviewer/viewthread?MessageKey=0672d1d8-b499-4a6d-863f-64acd51d3ae4&CommunityKey=6b2d607a-e31f-4f19-8357-020a8631b999&tab=digestviewer#bm0672d1d8-b499-4a6d-863f-64acd51d3ae4>*
> external link to thread view
> <https://community.amstat.org/communities/community-home/digestviewer/viewthread?MessageKey=0672d1d8-b499-4a6d-863f-64acd51d3ae4&CommunityKey=6b2d607a-e31f-4f19-8357-020a8631b999&tab=digestviewer#bm0672d1d8-b499-4a6d-863f-64acd51d3ae4>
>
> 3. Hi Manolis, It all depends on what you are... <#m2> Frank Harrell
> 4. To me, the best protection against bias due to... <#m3> Michael Mout
> 5. Why would anyone default to the normal... <#m4> Andrew Ekstrom
> 6. Manolis - You asked "Perhaps p=0.001? I... <#m5> James Knaub
> 7. Dear James, Andrew, Michael, and Frank, ... <#m6> Manolis
> Antonoyiannakis
> 8. Perhaps use medians instead of means and discuss... <#m7> Andrew
> Ekstrom
>
>
>
> top <#toca> next <#m1>
>
> 1. Machine Learning for Animal Vital-Sign Time-Series - New Episode on
> Pod of Asclepius
> <https://community.amstat.org/communities/community-home/digestviewer/viewthread?MessageKey=904a01db-2beb-4e0c-9c86-bfd39d36c9ec&CommunityKey=6b2d607a-e31f-4f19-8357-020a8631b999&tab=digestviewer#bm904a01db-2beb-4e0c-9c86-bfd39d36c9ec>
>
> Reply to Group Online
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>
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> Glen Colopy
> <https://community.amstat.org/network/members/profile?UserKey=7f331d59-fe82-4d90-837c-5178ce3939c1>
>
> Feb 24, 2020 11:40 PM
> Glen Colopy
> <https://community.amstat.org/network/members/profile?UserKey=7f331d59-fe82-4d90-837c-5178ce3939c1>
>
>
> ??Hi ASA Connect,
>
> The newest episode of the show is now out.*Shane Burns presents the
> visual data platforms that monitor the health of dairy cows and bees.*
> From wearables to stationary sensors, animals' health is being
> monitored via rich multivariate time series, which leads to plenty of
> opportunities for analysis and optimization.
>
> *Why should data scientists and statisticians watch this episode?*
>
> * It's a great visual presentation, where Shane shows you the data
> behind animal health decision making.
> * The analytics involved runs the gamut of technical fields, including
> multivariate time series modelling, optimization, and statistical
> control.
> * Shane highlights how these machine learning applications have a
> great benefit to the animals health along with a strong business case.
> * Its got critters! And did I mention the cool visuals?
>
> *Watch it on???*
>
> *YouTube*:
www.youtube.com/watch?v=8uPu-vHahdc> <https://www.youtube.com/watch?v=8uPu-vHahdc>
>
> *Podbean*: podofasclepius.podbean.com/e/...
> <https://podofasclepius.podbean.com/e/s01-ep04-with-shane-burns-data-platforms-to-monitor-animal-health/>
>
> Also available on: Stitcher?????????? Podchaser?????????? Tune In Radio?????????? Apple
> iTunes ?????????????????? Google Play
>
> You can catch up on all of Season 0 here
> <https://www.podofasclepius.com/season-0?ss_source=lkdinads&ss_campaign_name=ASAConnect>.
> Or what's coming up in Season 1 here
> <https://www.podofasclepius.com/season-1?ss_source=lkdinads&ss_campaign_name=ASAConnect>.
>
>
> Pod of Asclepius is sponsored by the ASA's Statistical Learning and Data
> Science Section, Medical Device and Diagnostics Section, and North
> Carolina Chapter.
>
>
> Enjoy!
>
>
>
> ------------------------------
> Glen Wright Colopy
> DPhil Oxon
> Data Scientist at Cenduit LLC, Durham, NC
> ------------------------------
>
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> 2. Duke-Industry Statistics Symposium (DISS2020)
> <https://community.amstat.org/communities/community-home/digestviewer/viewthread?MessageKey=317e4382-6b2c-4db2-b0a5-27b07d5d9286&CommunityKey=6b2d607a-e31f-4f19-8357-020a8631b999&tab=digestviewer#bm317e4382-6b2c-4db2-b0a5-27b07d5d9286>
>
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> Xiaofei Wang
> <https://community.amstat.org/network/members/profile?UserKey=c16da042-647c-4b2e-ab95-8936e8da011d>
>
> Feb 24, 2020 12:44 PM | attachment view attached
> <https://community.amstat.org/viewdocument/duke-industry-statistics-symposium?CommunityKey=6b2d607a-e31f-4f19-8357-020a8631b999&tab=librarydocuments&MessageKey=317e4382-6b2c-4db2-b0a5-27b07d5d9286>
>
> Xiaofei Wang
> <https://community.amstat.org/network/members/profile?UserKey=c16da042-647c-4b2e-ab95-8936e8da011d>
>
>
> Dear Colleagues,
>
> We are happy to announce the 2020 Duke-Industry Statistics Symposium
> (DISS2020), which is to be held on April 1-3, 2020. The direct link for
> registration to the symposium and the short courses is
> sites.duke.edu/diss/register <https://sites.duke.edu/diss/register/>.
> Group discount for registration fee is available and please contact
>
xiaofei.wang@duke.edu for more details.
>
> The Duke-Industry Statistics Symposium is organized by the Department of
> Biostatistics and Bioinformatics, Duke University School of Medicine and
> co-sponsored by Amgen, ASA-NC Chapter, Boehringer-Ingelheim, Eli Lilly,
> ICSA, IQVIA, Janssen, Journal of Biopharmaceutical Statistics, Merck,
> PAREXEL, PPD, SAS, UCB and ViiV. The symposium was established seven
> years ago to discuss challenging issues and recent advances related to
> the clinical development of drugs, biologics and devices and to promote
> research and collaboration among statisticians from industry, academia,
> and regulatory agencies.
>
> The theme for this year will be "Emerging Clinical Initiatives in
> Pharmaceutical Development: Methodology and Regulatory Perspectives."
> DISS2020 will be held at the Durham Hilton in Durham, NC, about one mile
> from Duke University campus. The first day will be devoted to four short
> courses. The 2nd day will begin with a keynote speech by Dr. ShaAvhr??e
> Buckman-Garner is the Director of the Office of Translational Sciences
> (OTS), Center for Drug Evaluation and Research (CDER), U.S. Food and
> Drug Administration. Fifteen parallel sessions will be followed as well
> as a poster session. On the morning of the 3rd day, Dr. David Page,
> Chair for the Department of Biostatistics & Bioinformatics with Duke
> University School of Medicine will give a keynote speech on Machine
> Learning from Electronic Health Records followed by another ten parallel
> scientific sessions.
>
> Attached is a draft program book for the symposium, which summarizes the
> schedule of the two and half day event. Please feel free to forward the
> flyer along this announcement to your colleagues or whoever may have
> interest in the event. For updated information about program schedule,
> talk abstracts, registration and travel, please visit
> sites.duke.edu/diss. <https://sites.duke.edu/diss.>
>
> We are excited about this great event and look forward to seeing you on
> April 1-3 in Durham, North Carolina.
>
> Sincerely yours,
>
> The Organizing Committee of DISS2020
>
>
>
> ------------------------------
> Xiaofei Wang
> Duke University Medical Center
> ------------------------------
>
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> top <#toca> previous <#m1> next <#m3>
>
> 3. Re: skewness
> <https://community.amstat.org/communities/community-home/digestviewer/viewthread?MessageKey=0672d1d8-b499-4a6d-863f-64acd51d3ae4&CommunityKey=6b2d607a-e31f-4f19-8357-020a8631b999&tab=digestviewer#bm0672d1d8-b499-4a6d-863f-64acd51d3ae4>
>
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>
>
> Frank Harrell
> <https://community.amstat.org/network/members/profile?UserKey=103eea7a-1d00-4c3f-a7ec-882e53d3b401>
>
> Feb 24, 2020 7:46 AM
> Frank Harrell
> <https://community.amstat.org/network/members/profile?UserKey=103eea7a-1d00-4c3f-a7ec-882e53d3b401>
>
>
> Hi Manolis,
>
> It all depends on what you are doing with the distributions.?? Without
> knowing any context I would say that it is not productive to make a
> dichotomous decision re: normality.?? Since you know the distributions
> and do not need to estimate them from data, I would just use the
> parametric distributions as they stand.?? If needing to estimating
> distributions from data, pick a 4-parameter distribution function that
> includes Gaussian as a special case and use that throughout.?? One
> example of a multipurpose distribution is Tukey's generalized lambda
> distribution.
>
> ------------------------------
> Frank Harrell
> Department of Biostatistics
> Vanderbilt University School of Medicine
> ------------------------------
>
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> -------------------------------------------
> Original Message:
> Sent: 02-23-2020 22:10
> From: Manolis Antonoyiannakis
> Subject: skewness
>
> Dear Frank,
>
> Thank you so much for your response and for the reference to your course
> which is interesting. To clarify, I have thousands of distributions and
> I know the skewness of each one. Strictly speaking, almost none of these
> is a Gaussian, but is it reasonable to approximate them by a Gaussian by
> allowing some level of skewness???I am trying to figure out what level of
> skewness is acceptable in order to??decide whether these distributions
> can be represented by their means or whether the mean fails as a measure
> of central tendency.
>
> Any advice would be appreciated.
>
> Thanks and regards,
> Manolis
>
> ------------------------------
> Manolis Antonoyiannakis
> Associate Editor & Bibliostatistics Analyst
> The American Physical Society
>
>
>
>
> top <#toca> previous <#m2> next <#m4>
>
> 4. Re: skewness
> <https://community.amstat.org/communities/community-home/digestviewer/viewthread?MessageKey=225cfe53-85be-4879-a242-a60db9874a9f&CommunityKey=6b2d607a-e31f-4f19-8357-020a8631b999&tab=digestviewer#bm225cfe53-85be-4879-a242-a60db9874a9f>
>
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> Michael Mout
> <https://community.amstat.org/network/members/profile?UserKey=deb55b91-8898-4b29-8188-ecc9d9840446>
>
> Feb 24, 2020 1:21 PM
> Michael Mout
> <https://community.amstat.org/network/members/profile?UserKey=deb55b91-8898-4b29-8188-ecc9d9840446>
>
>
> To me, the best protection against bias due to distribution is to have
> enough sample to create a hold out or find a separate independent sample
> against which to test the results of whatever test is being conducted.
>
> ------------------------------
> Michael Mout
> MIKS
> ------------------------------
>
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> -------------------------------------------
> Original Message:
> Sent: 02-23-2020 07:16
> From: Frank Harrell
> Subject: skewness
>
> If you knew the true skewness then you would already know whether a
> distribution is Gaussian.?? If you have to estimate the skewness then you
> have to account for the fuzziness in the estimate in making your
> decision.?? Since everything can break down in the case of skewness
> (e.g., the standard deviation is no longer an appropriate measure of
> dispersion so the central limit theorem ceases being your friend) this
> is an important issue.?? But a deeper question is what are you doing
> downstream that depends on this??? Why not use nonparametric methods, or
> semiparametric ordinal response models such as the proportional odds
> model??? I discuss this in hbiostat.org/bbr <http://hbiostat.org/bbr> .
>
> When using parametric methods, the most coherent approach, and one that
> for the first time provides honest uncertainty intervals (accurate
> confidence interval coverage or accurate lengths of credible intervals)
> is a Bayesian approach that embeds Gaussian as a special case but
> smoothly transitions to a non-Gaussian model as data clarity permit.
> When one allows the kurtosis to change (but not skewness) see the
> Bayesian one- and two-sample t-test examples in the BBR course notes.
>
> ------------------------------
> Frank Harrell
> Department of Biostatistics
> Vanderbilt University School of Medicine
>
>
>
>
> top <#toca> previous <#m3> next <#m5>
>
> 5. Re: skewness
> <https://community.amstat.org/communities/community-home/digestviewer/viewthread?MessageKey=f2229fb2-bc57-45c5-ba0b-fd419e23cdbb&CommunityKey=6b2d607a-e31f-4f19-8357-020a8631b999&tab=digestviewer#bmf2229fb2-bc57-45c5-ba0b-fd419e23cdbb>
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> Andrew Ekstrom
> <https://community.amstat.org/network/members/profile?UserKey=b265d2b6-f0d7-4b78-9068-9662e69e8cfc>
>
> Feb 24, 2020 1:41 PM
> Andrew Ekstrom
> <https://community.amstat.org/network/members/profile?UserKey=b265d2b6-f0d7-4b78-9068-9662e69e8cfc>
>
>
> Why would anyone default to the normal distribution? As a
> chemist/physicist/engineer, I have yet to find a single instance where a
> normal distribution was correct. Or even close to correct. It's great
> for statistical theory and some applications
>
> Use a function that tells you the most likely distribution for the data.
> If you then have several possible distributions and one of those is what
> theory suggests, then go with that. Otherwise, listen to your data. And
> deal with it
>
> I can't think of a place where using the wrong distribution is a good thing.
>
> ------------------------------
> Andrew Ekstrom
>
> Statistician, Chemist, HPC Abuser;-)
> ------------------------------
>
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> -------------------------------------------
> Original Message:
> Sent: 02-22-2020 17:52
> From: Manolis Antonoyiannakis
> Subject: skewness
>
> Hi,
>
> What is the acceptable level of skewness to decide whether a
> distribution is close enough to being a Gaussian? I have heard of a rule
> such as |skewness| < 2 but I can't find a reference.
>
> Alternatively, is it better/safer to resort to normality tests such as
> the Shapiro-Wilk test or D' Agostino's K^2 test? And if so, what is a
> safe value of these statistics to use as cutoff for deciding departure
> from normality? Perhaps p=0.001? I guess p=0.05 is way too high.
>
> Thank you,
>
> Manolis
>
> ------------------------------
> ---------------------------------------------------
> Manolis Antonoyiannakis
>
> Bibliostatistics Analyst, The American Physical Society
> Adjunct Associate Research Scientist, Applied Physics and Applied
> Mathematics, Columbia University
>
www.bibliostatistics.org <http://www.bibliostatistics.org>
> ---------------------------------------------------
> ------------------------------
>
>
>
>
> top <#toca> previous <#m4> next <#m6>
>
> 6. Re: skewness
> <https://community.amstat.org/communities/community-home/digestviewer/viewthread?MessageKey=e950f700-eb06-47ce-8c9f-a8d4798f0db0&CommunityKey=6b2d607a-e31f-4f19-8357-020a8631b999&tab=digestviewer#bme950f700-eb06-47ce-8c9f-a8d4798f0db0>
>
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>
> James Knaub
> <https://community.amstat.org/network/members/profile?UserKey=f6e453c2-1310-4c37-855f-060d7e73569d>
>
> Feb 24, 2020 3:40 PM
> James Knaub
> <https://community.amstat.org/network/members/profile?UserKey=f6e453c2-1310-4c37-855f-060d7e73569d>
>
>
> Manolis -
>
> You asked "Perhaps p=0.001? I guess p=0.05 is way too high."
>
> Well that depends on the effect size that matters, and your sample size.
>
> Perhaps you want to keep two measures: means and medians.?? ??You might
> see if that suits your purpose(s).
>
> Cheers.?? ???
>
>
>
>
> ------------------------------
> James Knaub
> Retired Lead Mathematical Statistician
> ------------------------------
>
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> -------------------------------------------
> Original Message:
> Sent: 02-22-2020 17:52
> From: Manolis Antonoyiannakis
> Subject: skewness
>
> Hi,
>
> What is the acceptable level of skewness to decide whether a
> distribution is close enough to being a Gaussian? I have heard of a rule
> such as |skewness| < 2 but I can't find a reference.
>
> Alternatively, is it better/safer to resort to normality tests such as
> the Shapiro-Wilk test or D' Agostino's K^2 test? And if so, what is a
> safe value of these statistics to use as cutoff for deciding departure
> from normality? Perhaps p=0.001? I guess p=0.05 is way too high.
>
> Thank you,
>
> Manolis
>
> ------------------------------
> ---------------------------------------------------
> Manolis Antonoyiannakis
>
> Bibliostatistics Analyst, The American Physical Society
> Adjunct Associate Research Scientist, Applied Physics and Applied
> Mathematics, Columbia University
>
www.bibliostatistics.org <http://www.bibliostatistics.org>
> ---------------------------------------------------
> ------------------------------
>
>
>
>
> top <#toca> previous <#m5> next <#m7>
>
> 7. Re: skewness
> <https://community.amstat.org/communities/community-home/digestviewer/viewthread?MessageKey=964ff9c5-3d94-4616-b8db-83f6bb212437&CommunityKey=6b2d607a-e31f-4f19-8357-020a8631b999&tab=digestviewer#bm964ff9c5-3d94-4616-b8db-83f6bb212437>
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> Manolis Antonoyiannakis
> <https://community.amstat.org/network/members/profile?UserKey=b9ec4383-7888-47ed-aa7e-961c9799726c>
>
> Feb 24, 2020 5:02 PM
> Manolis Antonoyiannakis
> <https://community.amstat.org/network/members/profile?UserKey=b9ec4383-7888-47ed-aa7e-961c9799726c>
>
>
> Dear James, Andrew, Michael, and Frank,
>
> Thank you for your comments. To provide more context, I am dealing with
> citation distributions of research journals.
>
> While almost all of these distributions have high enough skewness that
> in my understanding renders the use of means invalid, these means are
> widely used... in the form of the Journal Impact Factor! I am writing a
> paper where I am making the case that with such levels of skewness (eg
> 88% of journals have skewness > 1.5) the use of means (i.e., Impact
> Factors) makes no sense. I just wanted to know if there is a consensus
> in this community about some threshold level of skewness above which the
> use of means is frowned upon.
>
> To sum up:??The distributions I am using are by and large non-normal, but
> all those people out there who use and reference Impact Factors are
> implicitly stating that use of means for these distributions is OK. And
> this is what I am trying to counter.
>
> Thanks again,
> Manolis
>
>
> ------------------------------
> Manolis Antonoyiannakis
> Associate Editor & Bibliostatistics Analyst
> The American Physical Society
> ------------------------------
>
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> -------------------------------------------
> Original Message:
> Sent: 02-24-2020 13:40
> From: Andrew Ekstrom
> Subject: skewness
>
> Why would anyone default to the normal distribution? As a
> chemist/physicist/engineer, I have yet to find a single instance where a
> normal distribution was correct. Or even close to correct. It's great
> for statistical theory and some applications
>
> Use a function that tells you the most likely distribution for the data.
> If you then have several possible distributions and one of those is what
> theory suggests, then go with that. Otherwise, listen to your data. And
> deal with it
>
> I can't think of a place where using the wrong distribution is a good thing.
>
> ------------------------------
> Andrew Ekstrom
>
> Statistician, Chemist, HPC Abuser;-)
>
>
>
>
> top <#toca> previous <#m6>
>
> 8. Re: skewness
> <https://community.amstat.org/communities/community-home/digestviewer/viewthread?MessageKey=7db63609-629e-49e0-a54f-33c299ee98a4&CommunityKey=6b2d607a-e31f-4f19-8357-020a8631b999&tab=digestviewer#bm7db63609-629e-49e0-a54f-33c299ee98a4>
>
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> <https://community.amstat.org/network/members/profile?UserKey=b265d2b6-f0d7-4b78-9068-9662e69e8cfc>
>
> Feb 24, 2020 9:17 PM
> Andrew Ekstrom
> <https://community.amstat.org/network/members/profile?UserKey=b265d2b6-f0d7-4b78-9068-9662e69e8cfc>
>
>
> Perhaps use medians instead of means and discuss how using means is
> highly flawed in the situation.
>
> ------------------------------
> Andrew Ekstrom
>
> Statistician, Chemist, HPC Abuser;-)
> ------------------------------
>
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> -------------------------------------------
> Original Message:
> Sent: 02-24-2020 17:01
> From: Manolis Antonoyiannakis
> Subject: skewness
>
> Dear James, Andrew, Michael, and Frank,
>
> Thank you for your comments. To provide more context, I am dealing with
> citation distributions of research journals.
>
> While almost all of these distributions have high enough skewness that
> in my understanding renders the use of means invalid, these means are
> widely used... in the form of the Journal Impact Factor! I am writing a
> paper where I am making the case that with such levels of skewness (eg
> 88% of journals have skewness > 1.5) the use of means (i.e., Impact
> Factors) makes no sense. I just wanted to know if there is a consensus
> in this community about some threshold level of skewness above which the
> use of means is frowned upon.
>
> To sum up:??The distributions I am using are by and large non-normal, but
> all those people out there who use and reference Impact Factors are
> implicitly stating that use of means for these distributions is OK. And
> this is what I am trying to counter.
>
> Thanks again,
> Manolis
>
>
> ------------------------------
> Manolis Antonoyiannakis
> Associate Editor & Bibliostatistics Analyst
> The American Physical Society
>
>
>
>
> You are subscribed to "ASA Connect" as
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>
>
--
Dennis Boos, Assoc. Head email:
dennis_boos@ncsu.eduDepartment of Statistics Phone: 919-515-1918
NC State University Fax: 919-515-1169
Raleigh, NC 27695-8203
http://www4.stat.ncsu.edu/~boosAim for kindness, tolerance, and humility.
The rest of life will then fall into place.