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NBA Player Heights

  • 1.  NBA Player Heights

    Posted 04-29-2000 13:08
    Just for the heck of it, I went to the NBA player site and obtained the
    height of all 410 NBA players. I put them in a spreadsheet and took at
    look at some basic stats:

    Mode 6' 9"
    Average Height 6' 8"
    Median Height 6' 7"

    Range 5' 3" to 7' 7"

    The spreadsheet can be found at http://home.att.net/~nickols/nba.xls if
    anyone wants to do any additional crunching. A bar chart is included. It
    is skewed toward the 6' 9" side of things but you can also see the good old
    bell curve in there.

    Enjoy...

    --

    Fred Nickols
    The Distance Consulting Company
    "Assistance at A Distance"
    http://home.att.net/~nickols/distance.htm
    nickols@worldnet.att.net
    (609) 490-0095


  • 2.  NBA Player Heights

    Posted 04-29-2000 13:40
    On 29 Apr 00, at 13:07, Fred Nickols wrote:

    > Just for the heck of it, I went to the NBA player site and obtained the
    > height of all 410 NBA players. I put them in a spreadsheet and took at
    > look at some basic stats:
    >
    > Mode 6' 9"
    > Average Height 6' 8"
    > Median Height 6' 7"
    >
    > Range 5' 3" to 7' 7"
    >
    > The spreadsheet can be found at http://home.att.net/~nickols/nba.xls if
    > anyone wants to do any additional crunching. A bar chart is included. It
    > is skewed toward the 6' 9" side of things but you can also see the good
    > old bell curve in there.

    Uhh, could you tell me who exactly is 5 ft. 3 and who is 7 ft. 7?

    Also the good ole bell curve is not a statistical term. Is it normal or
    not?


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  • 3.  NBA Player Heights

    Posted 04-29-2000 21:22
    On 29 Apr 00, at 13:07, Fred Nickols wrote:

    > Just for the heck of it, I went to the NBA player site and obtained the
    > height of all 410 NBA players. I put them in a spreadsheet and took at
    > look at some basic stats:
    >
    > Mode 6' 9"
    > Average Height 6' 8"
    > Median Height 6' 7"
    >
    > Range 5' 3" to 7' 7"
    >
    > The spreadsheet can be found at http://home.att.net/~nickols/nba.xls if
    > anyone wants to do any additional crunching. A bar chart is included. It
    > is skewed toward the 6' 9" side of things but you can also see the good
    > old bell curve in there.

    Ok, actually you don't determine whether a distribution is normal
    by looking at it you do it with numbers. So, let's assume that we
    haven't ruled out the possibility it isn't normal.

    (here's a bonus question. Can you have a distribution with the
    same median and mean and have it not be a normal distribution?

    Ok, if you answer that right you get to go to the next round of data
    testing.

    Calculate the standard deviation. Then determine what percentage
    of people in the group fall + or - one standard deviation to the
    mean. Compare that with the characteristics of a normal
    distribution.

    Do the same for two SD's and three SD's from the mean.

    For those of you who can't figure out what this is about, we are
    actually going through what can be an excellent teaching tool if you
    ever have to teach about data and normal distributions.

    If it conforms to those characteristics, we probably have a normal
    distribution. If it doesn't, it ain't. We could also do other tests for
    skewness.


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  • 4.  NBA Player Heights

    Posted 04-30-2000 07:02
    Here's an update on the NBA stats...

    My original data entry was based on a tallying of NBA player heights. I
    didn't enter each height as an individual data point but instead entered
    the frequency counts. I think that's why Excel gave me a different answer
    for median the first time. In any event, I went back and entered all 410
    player heights as discrete data points and the median changed
    slightly. Here are the new stats, plus the standard deviations.

    Average or Mean 6' 8" (Actually, 79.1878 inches)

    Median 6' 8"

    Range 5' 3" to 7' 7"

    Mode 6' 9"

    SD(S) 3.805 (SD for the 410 as a sample)

    SD(P) 3.801 (SD for the 410 as the entire population)

    Going one SD either side picks up 77% of the players; going two SDs either
    side picks up 97% and three SDs either side picks up 99%.

    >On 29 Apr 00, at 13:07, Fred Nickols wrote:
    >
    > > Just for the heck of it, I went to the NBA player site and obtained the
    > > height of all 410 NBA players. I put them in a spreadsheet and took at
    > > look at some basic stats:
    > >
    > > Mode 6' 9"
    > > Average Height 6' 8"
    > > Median Height 6' 7"
    > >
    > > Range 5' 3" to 7' 7"
    > >
    > > The spreadsheet can be found at http://home.att.net/~nickols/nba.xls if
    > > anyone wants to do any additional crunching. A bar chart is included. It
    > > is skewed toward the 6' 9" side of things but you can also see the good
    > > old bell curve in there.
    >
    >Ok, actually you don't determine whether a distribution is normal
    >by looking at it you do it with numbers. So, let's assume that we
    >haven't ruled out the possibility it isn't normal.
    >
    >(here's a bonus question. Can you have a distribution with the
    >same median and mean and have it not be a normal distribution?
    >
    >Ok, if you answer that right you get to go to the next round of data
    >testing.
    >
    >Calculate the standard deviation. Then determine what percentage
    >of people in the group fall + or - one standard deviation to the
    >mean. Compare that with the characteristics of a normal
    >distribution.
    >
    >Do the same for two SD's and three SD's from the mean.
    >
    >For those of you who can't figure out what this is about, we are
    >actually going through what can be an excellent teaching tool if you
    >ever have to teach about data and normal distributions.
    >
    >If it conforms to those characteristics, we probably have a normal
    >distribution. If it doesn't, it ain't. We could also do other tests for
    >skewness.
    >
    >
    >Visit the work911.com supersite at http://www.work911.com
    >for work related articles, or to find almost anything including
    >book reviews and suggestions, discussion lists and more.

    Fred Nickols
    The Distance Consulting Company
    "Assistance at A Distance"
    http://home.att.net/~nickols/distance.htm
    nickols@worldnet.att.net
    (609) 490-0095


  • 5.  NBA Player Heights

    Posted 05-01-2000 09:11
    >Just for the heck of it, I went to the NBA player site and obtained the
    >height of all 410 NBA players. I put them in a spreadsheet and took at
    >look at some basic stats:
    >
    > Mode 6' 9"
    > Average Height 6' 8"
    > Median Height 6' 7"
    >
    > Range 5' 3" to 7' 7"
    >
    >The spreadsheet can be found at http://home.att.net/~nickols/nba.xls if
    >anyone wants to do any additional crunching. A bar chart is included. It
    >is skewed toward the 6' 9" side of things but you can also see the good old
    >bell curve in there.
    >
    >Enjoy...
    >
    >--
    >
    >Fred Nickols
    >The Distance Consulting Company
    >"Assistance at A Distance"
    >http://home.att.net/~nickols/distance.htm
    >nickols@worldnet.att.net
    >(609) 490-0095
    >

    1. As stated earlier in this discussion, the term "bell-shaped curve" is not
    a well-defined concept. Many distributions are unimodal with a well defined
    mode, and hence roughly bell-shaped. Not all such distributions are normal.
    In "real life" the central limit theorem ensures that most random
    populations are roughly normal (hence the name "normal"). Where the
    assumptions of the central limit theorem do not hold, it is unlikely that
    the resultant distribution will be normal.

    2. Given a normal population, selecting only members above a cutoff
    will result in a non-normal distribution that may look roughly "bell-shaped"
    but is not at all normal. Since height is only a (strong) correlate of the
    actual NBA selection criteria, the resultant distribution, just
    "eye-balled," looks like a skewed, non-normal distribution.

    3. The NBA data have been "histogrammed." If Mr. Nickols has the raw data
    available, Excel provides one-click skewness and kurtosis (but can we do
    this in light of the Amazon patent, or do we have to make it more
    complicated?). Based on other tests already done it appears that the data
    are very roughly a "good old bell curve" but not at all normal.

    4. The normality of the distribution of personnel in an organization is not
    particularly relevant. A distribution with any variance at all, however
    miniscule, can be mapped to a normal distribution. In statistics, the
    standard table of random numbers is uniform, and all other distributions are
    generated by mapping them from the uniform distribution. Thus, ratings based
    on a measure with any variance whatsoever can be mapped to fit a normal
    distribution. There is no need to assume the underlying population is normal
    for the mapping function to "work."

    5. The question then becomes whether mapping personnel ratings,
    compensation, etc., into a given distribution is the most appropriate method
    to achieve the organization's objectives.

    According to agency theory, agents of an organization will make decisions
    which are in the agent's interests rather than the organization's interests.
    The theory concludes that compensation must be designed to align the agent's
    interests with the organization's interests.

    And the debate about how to achieve this alignment continues.


  • 6.  NBA Player Heights

    Posted 05-01-2000 13:46
    You guys obviously have too much time on your hands...Since you do, may be
    you could figure out whose going to win the championship based on height to
    individual scoring ratio compared to won/lost records and whether the area
    has a sponsor for its name or not and the beer is served cold.
    :-)
    Ed Brenegar
    ----- Original Message -----
    From: Michael Wolfe <wolfem@STJOHNS.EDU>
    To: <MG-ED-DV@MAELSTROM.STJOHNS.EDU>
    Sent: Monday, May 01, 2000 9:11 AM
    Subject: Re: NBA Player Heights


    > >Just for the heck of it, I went to the NBA player site and obtained the
    > >height of all 410 NBA players. I put them in a spreadsheet and took at
    > >look at some basic stats:
    > >
    > > Mode 6' 9"
    > > Average Height 6' 8"
    > > Median Height 6' 7"
    > >
    > > Range 5' 3" to 7' 7"
    > >
    > >The spreadsheet can be found at http://home.att.net/~nickols/nba.xls if
    > >anyone wants to do any additional crunching. A bar chart is included.
    It
    > >is skewed toward the 6' 9" side of things but you can also see the good
    old
    > >bell curve in there.
    > >
    > >Enjoy...
    > >
    > >--
    > >
    > >Fred Nickols
    > >The Distance Consulting Company
    > >"Assistance at A Distance"
    > >http://home.att.net/~nickols/distance.htm
    > >nickols@worldnet.att.net
    > >(609) 490-0095
    > >
    >
    > 1. As stated earlier in this discussion, the term "bell-shaped curve" is
    not
    > a well-defined concept. Many distributions are unimodal with a well
    defined
    > mode, and hence roughly bell-shaped. Not all such distributions are
    normal.
    > In "real life" the central limit theorem ensures that most random
    > populations are roughly normal (hence the name "normal"). Where the
    > assumptions of the central limit theorem do not hold, it is unlikely that
    > the resultant distribution will be normal.
    >
    > 2. Given a normal population, selecting only members above a cutoff
    > will result in a non-normal distribution that may look roughly
    "bell-shaped"
    > but is not at all normal. Since height is only a (strong) correlate of the
    > actual NBA selection criteria, the resultant distribution, just
    > "eye-balled," looks like a skewed, non-normal distribution.
    >
    > 3. The NBA data have been "histogrammed." If Mr. Nickols has the raw data
    > available, Excel provides one-click skewness and kurtosis (but can we do
    > this in light of the Amazon patent, or do we have to make it more
    > complicated?). Based on other tests already done it appears that the data
    > are very roughly a "good old bell curve" but not at all normal.
    >
    > 4. The normality of the distribution of personnel in an organization is
    not
    > particularly relevant. A distribution with any variance at all, however
    > miniscule, can be mapped to a normal distribution. In statistics, the
    > standard table of random numbers is uniform, and all other distributions
    are
    > generated by mapping them from the uniform distribution. Thus, ratings
    based
    > on a measure with any variance whatsoever can be mapped to fit a normal
    > distribution. There is no need to assume the underlying population is
    normal
    > for the mapping function to "work."
    >
    > 5. The question then becomes whether mapping personnel ratings,
    > compensation, etc., into a given distribution is the most appropriate
    method
    > to achieve the organization's objectives.
    >
    > According to agency theory, agents of an organization will make decisions
    > which are in the agent's interests rather than the organization's
    interests.
    > The theory concludes that compensation must be designed to align the
    agent's
    > interests with the organization's interests.
    >
    > And the debate about how to achieve this alignment continues.
    >


  • 7.  NBA Player Heights

    Posted 05-01-2000 16:40
    Well, to close this off (from my perspective at least) and to respond to Ed
    Brenegar (below), here's the scoop:

    After consulting with the statisticians at my "day job" (ETS) it
    seems that my stats are correct:

    Mean NBA player height 6' 7"
    Median NBA player height 6' 8"
    Mode 6' 9"
    Range 5' 3" to 7' 7"
    Standard Deviation 3.8

    The area covered by one SD either side of the mean is as reported earlier,
    i.e., roughly 77%. By two SDs = 95% and by three SDs = 99.5%.

    The fellow I spoke with said that these data don't reflect a purely normal
    distribution but, as he said, "It isn't crazy far off."

    At 01:46 PM 05/01/2000 -0400, you wrote:
    >You guys obviously have too much time on your hands...Since you do, may be
    >you could figure out whose going to win the championship based on height to
    >individual scoring ratio compared to won/lost records and whether the area
    >has a sponsor for its name or not and the beer is served cold.
    >:-)

    One of the other fellows I spoke with indicated that he, too, had looked at
    the NBA stats and noted that there is no correlation between height and
    points scored.

    Anyway, I'm done with this for now.
    --

    Fred Nickols
    The Distance Consulting Company
    "Assistance at A Distance"
    http://home.att.net/~nickols/distance.htm
    nickols@worldnet.att.net
    (609) 490-0095


  • 8.  NBA Player Heights

    Posted 05-01-2000 18:08
    Hi all - part of the difficulty, as I see it, is that you're using roudned
    off numbers. Height is really a continuous function, but the data you
    have is from measurements that are roudned off to the nearest inch. Ditto
    for your mean value; you rounded it off. In any case, when you apply the
    SD (times 1, 2, or 3), you inadvertently will either include some who
    shouldn't be included or will exclude some, depending on how they're
    measured.

    Within and including the limits you cite, there are only 29 possible whole
    inch values. Whereas this is starting to approach the number of possible
    values required to assume that integer values are continuous, it doesn't
    quite make it. I think if you had real values, perhaps to the nearest 1/4
    inch, you might get a rather different picture. Those data probably are
    not available.

    The other difficulty is that in the upper ranges of the heights you cite,
    you are on the extreme tail of heights of the population as a whole.
    Presumably there aren't many people over 7' available to select from, and
    some of these may not wish to be professional athletes.

    Tim Edlund, Morgan State University

    On Mon, 1 May 2000, Fred Nickols wrote:

    > Well, to close this off (from my perspective at least) and to respond to Ed
    > Brenegar (below), here's the scoop:
    >
    > After consulting with the statisticians at my "day job" (ETS) it
    > seems that my stats are correct:
    >
    > Mean NBA player height 6' 7"
    > Median NBA player height 6' 8"
    > Mode 6' 9"
    > Range 5' 3" to 7' 7"
    > Standard Deviation 3.8
    >
    > The area covered by one SD either side of the mean is as reported earlier,
    > i.e., roughly 77%. By two SDs = 95% and by three SDs = 99.5%.
    >
    > The fellow I spoke with said that these data don't reflect a purely normal
    > distribution but, as he said, "It isn't crazy far off."
    >
    > At 01:46 PM 05/01/2000 -0400, you wrote:
    > >You guys obviously have too much time on your hands...Since you do, may be
    > >you could figure out whose going to win the championship based on height to
    > >individual scoring ratio compared to won/lost records and whether the area
    > >has a sponsor for its name or not and the beer is served cold.
    > >:-)
    >
    > One of the other fellows I spoke with indicated that he, too, had looked at
    > the NBA stats and noted that there is no correlation between height and
    > points scored.
    >
    > Anyway, I'm done with this for now.
    > --
    >
    > Fred Nickols
    > The Distance Consulting Company
    > "Assistance at A Distance"
    > http://home.att.net/~nickols/distance.htm
    > nickols@worldnet.att.net
    > (609) 490-0095
    >


  • 9.  NBA Player Heights

    Posted 05-02-2000 07:21
    That was pointed out by the statistician who looked at my data. He
    suggested Sheppard's correction as a way of compensating for the discrete
    vs continuous data but also estimated that it wouldn't change things by
    more than 5%. Given that my objective was simply to look at the NBA player
    height data to see if they approximated anything at all like a normal
    curve, I'm not going to pursue that option.

    At 06:07 PM 05/01/2000 -0400, you wrote:
    >Hi all - part of the difficulty, as I see it, is that you're using roudned
    >off numbers. Height is really a continuous function, but the data you
    >have is from measurements that are roudned off to the nearest inch. Ditto
    >for your mean value; you rounded it off. In any case, when you apply the
    >SD (times 1, 2, or 3), you inadvertently will either include some who
    >shouldn't be included or will exclude some, depending on how they're
    >measured.
    >
    >Within and including the limits you cite, there are only 29 possible whole
    >inch values. Whereas this is starting to approach the number of possible
    >values required to assume that integer values are continuous, it doesn't
    >quite make it. I think if you had real values, perhaps to the nearest 1/4
    >inch, you might get a rather different picture. Those data probably are
    >not available.
    >
    >The other difficulty is that in the upper ranges of the heights you cite,
    >you are on the extreme tail of heights of the population as a whole.
    >Presumably there aren't many people over 7' available to select from, and
    >some of these may not wish to be professional athletes.
    >
    >Tim Edlund, Morgan State University
    >
    >On Mon, 1 May 2000, Fred Nickols wrote:
    >
    > > Well, to close this off (from my perspective at least) and to respond to Ed
    > > Brenegar (below), here's the scoop:
    > >
    > > After consulting with the statisticians at my "day job" (ETS) it
    > > seems that my stats are correct:
    > >
    > > Mean NBA player height 6' 7"
    > > Median NBA player height 6' 8"
    > > Mode 6' 9"
    > > Range 5' 3" to 7' 7"
    > > Standard Deviation 3.8
    > >
    > > The area covered by one SD either side of the mean is as reported earlier,
    > > i.e., roughly 77%. By two SDs = 95% and by three SDs = 99.5%.
    > >
    > > The fellow I spoke with said that these data don't reflect a purely normal
    > > distribution but, as he said, "It isn't crazy far off."
    > >
    > > At 01:46 PM 05/01/2000 -0400, you wrote:
    > > >You guys obviously have too much time on your hands...Since you do,
    > may be
    > > >you could figure out whose going to win the championship based on
    > height to
    > > >individual scoring ratio compared to won/lost records and whether the area
    > > >has a sponsor for its name or not and the beer is served cold.
    > > >:-)
    > >
    > > One of the other fellows I spoke with indicated that he, too, had looked at
    > > the NBA stats and noted that there is no correlation between height and
    > > points scored.
    > >
    > > Anyway, I'm done with this for now.
    > > --
    > >
    > > Fred Nickols
    > > The Distance Consulting Company
    > > "Assistance at A Distance"
    > > http://home.att.net/~nickols/distance.htm
    > > nickols@worldnet.att.net
    > > (609) 490-0095
    > >

    Fred Nickols
    The Distance Consulting Company
    "Assistance at A Distance"
    http://home.att.net/~nickols/distance.htm
    nickols@worldnet.att.net
    (609) 490-0095


  • 10.  NBA Player Heights

    Posted 05-02-2000 08:13
    Is there a moderator on this listserv to exercise communication control?
    Some of us have actual jobs with professional responsiblities and don't have
    e-mail capacity for 7th grade recess talk.

    -----Original Message-----
    From: Fred Nickols [mailto:nickols@WORLDNET.ATT.NET]
    Sent: Monday, May 01, 2000 4:40 PM
    To: MG-ED-DV@MAELSTROM.STJOHNS.EDU
    Subject: Re: NBA Player Heights


    Well, to close this off (from my perspective at least) and to respond to Ed
    Brenegar (below), here's the scoop:

    After consulting with the statisticians at my "day job" (ETS) it
    seems that my stats are correct:

    Mean NBA player height 6' 7"
    Median NBA player height 6' 8"
    Mode 6' 9"
    Range 5' 3" to 7' 7"
    Standard Deviation 3.8

    The area covered by one SD either side of the mean is as reported earlier,
    i.e., roughly 77%. By two SDs = 95% and by three SDs = 99.5%.

    The fellow I spoke with said that these data don't reflect a purely normal
    distribution but, as he said, "It isn't crazy far off."

    At 01:46 PM 05/01/2000 -0400, you wrote:
    >You guys obviously have too much time on your hands...Since you do, may be
    >you could figure out whose going to win the championship based on height to
    >individual scoring ratio compared to won/lost records and whether the area
    >has a sponsor for its name or not and the beer is served cold.
    >:-)

    One of the other fellows I spoke with indicated that he, too, had looked at
    the NBA stats and noted that there is no correlation between height and
    points scored.

    Anyway, I'm done with this for now.
    --

    Fred Nickols
    The Distance Consulting Company
    "Assistance at A Distance"
    http://home.att.net/~nickols/distance.htm
    nickols@worldnet.att.net
    (609) 490-0095


  • 11.  NBA Player Heights

    Posted 05-02-2000 11:53
    On 2 May 00, at 5:12, Schaefer, Mary wrote:

    > Is there a moderator on this listserv to exercise communication control?
    > Some of us have actual jobs with professional responsiblities and don't
    > have e-mail capacity for 7th grade recess talk.

    Mary, I'm sorry you don't find the conversation interesting, and that
    apparently you aren't clear on the purpose of it. Not all
    conversations can be encompassed in a brief sound-byte.

    There's a couple of points to it (and I commend Fred for making the
    effort to play this out -- something most people can't be bothered to
    do). First, if people want to teach managers basic statistical
    concepts, we have just gone through a mini-process that can be
    used to help that.

    Second, the issue (which I guess goes way over the head of some
    people) has to do with whether we educate managers on the use
    (or misuse) of statistical concepts as they apply to real life
    decisions. Jack Ring's contention that one can assume a normal
    distribution and make decisions that affect real life is one I hope
    nobody here would teach managers. Further, the distribution issue
    has a direct bearing on the use of forced rankings on a normal
    curve sometimes used for appraisals and even in layoffs.


    Visit the work911.com supersite at http://www.work911.com
    for work related articles, or to find almost anything including
    book reviews and suggestions, discussion lists and more.


  • 12.  NBA Player Heights

    Posted 05-02-2000 11:59
    On 2 May 00, at 7:21, Fred Nickols wrote:

    > That was pointed out by the statistician who looked at my data. He
    > suggested Sheppard's correction as a way of compensating for the discrete
    > vs continuous data but also estimated that it wouldn't change things by
    > more than 5%. Given that my objective was simply to look at the NBA
    > player height data to see if they approximated anything at all like a
    > normal curve, I'm not going to pursue that option.

    Well, Fred the sound-byters are getting restless (which I knew
    would happen). Ok, so let's see if we can tease out the real life
    implications of having a distribution that one assumes is normal but
    isn't.

    So let's say we have a distribution at work (on performance or
    ability or whatever) that has 77% of people within 2 SD's (we'll
    assume it's symetrical for now, that's a test we didn't talk about)

    The company, however is assuming that the distribution is normal
    (eg. 68% within the "hump and any other characteristics").

    If the company was handing out rewards based on the normal curve
    (which would be inaccurate for them), what kinds of errors (if any),
    might occur?

    (I don't know the answer to this -- I should be able to muddle
    through it, since it's a logic thing, but my brain is fuzzy right now).

    Anyone?

    What other errors might be made from assuming a normal curve
    when one doesn't exist?


    Visit the work911.com supersite at http://www.work911.com
    for work related articles, or to find almost anything including
    book reviews and suggestions, discussion lists and more.


  • 13.  NBA Player Heights

    Posted 05-02-2000 11:59
    It is quite rude, and inaccurate, to level the name of "sound biters" at
    those who object to you taking up their space with your "down in the noise"
    discussion. But you can only develop and educate some management types so
    far.

    -----Original Message-----
    From: Robert Bacal [mailto:rbacal@ESCAPE.CA]
    Sent: Tuesday, May 02, 2000 11:59 AM
    To: MG-ED-DV@MAELSTROM.STJOHNS.EDU
    Subject: Re: NBA Player Heights


    On 2 May 00, at 7:21, Fred Nickols wrote:

    > That was pointed out by the statistician who looked at my data. He
    > suggested Sheppard's correction as a way of compensating for the discrete
    > vs continuous data but also estimated that it wouldn't change things by
    > more than 5%. Given that my objective was simply to look at the NBA
    > player height data to see if they approximated anything at all like a
    > normal curve, I'm not going to pursue that option.

    Well, Fred the sound-byters are getting restless (which I knew
    would happen). Ok, so let's see if we can tease out the real life
    implications of having a distribution that one assumes is normal but
    isn't.

    So let's say we have a distribution at work (on performance or
    ability or whatever) that has 77% of people within 2 SD's (we'll
    assume it's symetrical for now, that's a test we didn't talk about)

    The company, however is assuming that the distribution is normal
    (eg. 68% within the "hump and any other characteristics").

    If the company was handing out rewards based on the normal curve
    (which would be inaccurate for them), what kinds of errors (if any),
    might occur?

    (I don't know the answer to this -- I should be able to muddle
    through it, since it's a logic thing, but my brain is fuzzy right now).

    Anyone?

    What other errors might be made from assuming a normal curve
    when one doesn't exist?


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    for work related articles, or to find almost anything including
    book reviews and suggestions, discussion lists and more.


  • 14.  NBA Player Heights

    Posted 05-02-2000 12:16
    On 2 May 00, at 8:59, Schaefer, Mary wrote:

    > It is quite rude, and inaccurate, to level the name of "sound biters" at
    > those who object to you taking up their space with your "down in the
    > noise" discussion. But you can only develop and educate some management
    > types so far.

    Mary, what is it exactly, that bothers you about the conversation?
    Is it the detail? The length? The topic? Too Technical?

    I'm really curious here. And what do you think should be content
    you would like to see on the list?


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    for work related articles, or to find almost anything including
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  • 15.  NBA Player Heights

    Posted 05-02-2000 12:31
    This seems clear. It leads to the assumption that a larger proportion of
    "our" employees fall outside the 2 SD range than is actually the case. IF
    we have a forced distribution of rewards, then more people (assuming
    sufficiently large numbers, which is rarely the case) will get the highest
    rewards than deserve them, and more will get the lowest rewards - which
    may be no rewards or even negative rewards - such as layoffs, firing, etc.

    Which brings up another problem - if we use forced distributions to
    de-select those at the bottom, then those people will no longer be
    on-board to occupy the bottom, and some of those previously judged to be
    in the middle range will have to be judged sub-standard the next time the
    exercise is done. For firms forced to frequently retrench, this issue
    will continue to exist.

    An argument for unions, I suppose! They tend to insist on some sort of
    non-judgemental rule to determine who has to go - such as last in, first
    out!

    Tim Edlund, Morgan State University

    On Tue, 2 May 2000, Robert Bacal wrote: [truncated to save space]

    > let's see if we can tease out the real life
    > implications of having a distribution that one assumes is normal but
    > isn't.
    >
    > So let's say we have a distribution at work (on performance or
    > ability or whatever) that has 77% of people within 2 SD's (we'll
    > assume it's symetrical for now, that's a test we didn't talk about)
    >
    > The company, however is assuming that the distribution is normal
    > (eg. 68% within the "hump and any other characteristics").
    >
    > If the company was handing out rewards based on the normal curve
    > (which would be inaccurate for them), what kinds of errors (if any),
    > might occur?
    >
    > (I don't know the answer to this -- I should be able to muddle
    > through it, since it's a logic thing, but my brain is fuzzy right now).
    >
    > Anyone?
    >
    > What other errors might be made from assuming a normal curve
    > when one doesn't exist?


  • 16.  NBA Player Heights

    Posted 05-02-2000 18:00
    Robert Bacal, responding to Mary Schaefer, first cites Mary:

    > > Is there a moderator on this listserv to exercise communication control?
    > > Some of us have actual jobs with professional responsiblities and don't
    > > have e-mail capacity for 7th grade recess talk.

    My own response to Mary's comment follows: I'm sorry, Mary, but I can't
    make the connection to "7th grade recess talk." Does that tie to boys and
    basketball or to a view of the conversation as immature or what?

    Robert continues:

    >Mary, I'm sorry you don't find the conversation interesting, and that
    >apparently you aren't clear on the purpose of it. Not all
    >conversations can be encompassed in a brief sound-byte.
    >
    >There's a couple of points to it (and I commend Fred for making the
    >effort to play this out -- something most people can't be bothered to
    >do). First, if people want to teach managers basic statistical
    >concepts, we have just gone through a mini-process that can be
    >used to help that.

    I don't know that anyone else has learned a whole lot but I added to my
    store of knowledge.

    >Second, the issue (which I guess goes way over the head of some
    >people) has to do with whether we educate managers on the use
    >(or misuse) of statistical concepts as they apply to real life
    >decisions. Jack Ring's contention that one can assume a normal
    >distribution and make decisions that affect real life is one I hope
    >nobody here would teach managers. Further, the distribution issue
    >has a direct bearing on the use of forced rankings on a normal
    >curve sometimes used for appraisals and even in layoffs.

    I'll echo Robert on this score. I'll also extend the conversation and loop
    it back to the original issue. I grabbed the NBA stats only because they
    were handy. Frankly, I don't watch NBA games and don't plan to start. The
    question I was exploring, via some pretty hard data, was whether or not a
    selected sample might have a distribution approaching anything like a
    normal distribution. In this case, the skewing is apparent but it's not so
    extreme as to be totally unlike a normal distribution. This was in the
    context of Jack Ring's comment about assuming a normal distribution and
    Robert's admonition against doing that. I was testing the proposition, as
    it were.

    What's interesting (to me) about all this is that selecting people on the
    basis of some physical attribute such as height is a very different matter
    (in my view) from selecting them on the basis of some less unambiguously
    measured attribute (e.g., intelligence, mechanical aptitude, and so on).

    So, when we argue against assuming a normal distribution when the
    population is a selected one, I can see how such arguments can be put to
    the test when the selection is based on something that is reliably measured
    (e.g., height) but I don't see how that same argument can be applied when
    the population is selected on the basis of an unreliable measurement or
    assessment of something like attitude, character, performance, potential
    and so forth. It seems to me that if we don't have a reliable and
    unambiguous measurement as the basis for selecting the population in
    question then any arguments about the appropriateness of assuming or not
    assuming a normal distribution are theoretical and what some might term
    academic. In short, it can't be put to the test.

    Anyone care to pick up that thread? (That invitation extends to you, Mary.)

    --

    Fred Nickols
    The Distance Consulting Company
    "Assistance at A Distance"
    http://home.att.net/~nickols/distance.htm
    nickols@worldnet.att.net
    (609) 490-0095


  • 17.  NBA Player Heights

    Posted 05-02-2000 18:29
    On 2 May 00, at 17:59, Fred Nickols wrote:

    > So, when we argue against assuming a normal distribution when the
    > population is a selected one, I can see how such arguments can be put to
    > the test when the selection is based on something that is reliably
    > measured (e.g., height) but I don't see how that same argument can be
    > applied when the population is selected on the basis of an unreliable
    > measurement or assessment of something like attitude, character,
    > performance, potential and so forth. It seems to me that if we don't have
    > a reliable and unambiguous measurement as the basis for selecting the
    > population in question then any arguments about the appropriateness of
    > assuming or not assuming a normal distribution are theoretical and what
    > some might term academic. In short, it can't be put to the test.

    I think if we were to talk about this further we'd have to go into all
    kinds of things that are rather esoteric, like measurement error,
    and so forth, which also have statistical components.

    The NBA example was, as you said, an easy one, and purer to
    illustrate the fallacy of normal distributions. But the principle, as far
    as I can figure is the same. In fact it's moreso.

    If you have an unreliable measurement instrument, or one of
    questionable validity, ANY use of math or statistics is going to give
    you bad results, GIGO. Which is why, in fact it is virtually pointless
    to mathematically or statistically manipulate (operate on) appraisal
    data, unless it is measures more precisely.

    In a sense though the issue in practice wouldn't be the normality of
    the curve (which most of us mortals aren't going to have the
    resources to test in real life(, but whether ANY mathematical
    functions should be used on poor data.

    So, you have two issues. Can we assume a normal distribution
    without verfying (No) and Is our data solid enough to use statistical
    functions on them (often no).

    ...but the reason people continue to do that and pretend the data is
    good is that it provides a veneer of scientificiousity to the process,
    which of course employees recognize as complete guano.


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  • 18.  NBA Player Heights

    Posted 05-02-2000 18:57
    First, I'll delete much of what is in the message, and then again add my
    two bits worth:

    As I see it, we face some of the same difficulties with something as
    "unambiguous" as height. Clearly, if the major requirement for being an
    NBA player was height, we'd see a distribution that would be the extreme
    right tail of the general population distribution - i.e., in selecting the
    ten players per team over 30 teams (those numbers may not be right, I
    don't follow BB either), we'd see a distribution of about 300 very tall
    guys with the peak number occurring at the lowest value (or perhaps the
    next to lowest value).

    Based on the data presented, we see something far different. BB ability
    is not solely dependent on height; it is a blend of many factor, including
    desire, training, athletic ability, willingness to be aggressive, etc.
    The wonder is that the distribution is as close as it is. Using height as
    a proxy for ability and selction is imperfect, just as many of the
    apparently more ambiguous measures are.

    We might be able to come up with an hypothesis:
    The more tenuous between the attribute being measured and the
    characteristic it is considered to be a proxy for, the more likely it is
    to be normally distributed, if it is drawn from a normally distributed
    population.

    Or something like that; it's getting late & I'm hungry and tired.

    Tim Edlund, Morgan State U.

    On Tue, 2 May 2000, Fred Nickols wrote: [in part, edited down]

    > What's interesting (to me) about all this is that selecting people on the
    > basis of some physical attribute such as height is a very different matter
    > (in my view) from selecting them on the basis of some less unambiguously
    > measured attribute (e.g., intelligence, mechanical aptitude, and so on).
    >
    > So, when we argue against assuming a normal distribution when the
    > population is a selected one, I can see how such arguments can be put to
    > the test when the selection is based on something that is reliably measured
    > (e.g., height) but I don't see how that same argument can be applied when
    > the population is selected on the basis of an unreliable measurement or
    > assessment of something like attitude, character, performance, potential
    > and so forth. It seems to me that if we don't have a reliable and
    > unambiguous measurement as the basis for selecting the population in
    > question then any arguments about the appropriateness of assuming or not
    > assuming a normal distribution are theoretical and what some might term
    > academic. In short, it can't be put to the test.
    >
    > Anyone care to pick up that thread? (That invitation extends to you, Mary.)
    >
    > --
    >
    > Fred Nickols
    > The Distance Consulting Company
    > "Assistance at A Distance"
    > http://home.att.net/~nickols/distance.htm
    > nickols@worldnet.att.net
    > (609) 490-0095
    >