• by Sir Maurice G. Kendall (1907 - 1983)


    Hiawatha, mighty hunter
    He could shoot ten arrows upwards
    Shoot them with such strength and swiftness
    That the last had left the bowstring
    Ere the first to earth descended.
    This was commonly regarded
    As a feat of skill and cunning.


    One or two sarcastic spirits
    Pointed out to him, however,
    That it might be much more useful
    If he sometimes hit the target.
    Why not shoot a little straighter
    And employ a smaller sample?

    Hiawatha, who at college,
    Majored in applied statistics
    Consequently felt entitled
    To instruct his fellow men on
    Any subject whatsoever,
    Waxed exceedingly indignant
    Talked about the law of error,
    Talked about truncated normals
    Talked of loss of information,
    Talked about his lack of bias
    Pointed out that in the long run
    Independent observations
    Even though they missed the target
    Had an average point of impact
    Very near the spot he aimed at
    (With the possible exception
    Of a set of measure zero.)

    This, they said, was rather doubtful.
    Anyway, it didn't matter
    What resulted in the long run;
    Either he must hit the target
    Much more often than at present
    Or himself would have to pay for
    All the arrows that he wasted.

    Hiawatha, in a temper,
    Quoted parts of R. A. Fisher
    Quoted Yates and quoted Finney
    Quoted yards of Oscar Kempthorne
    Quoted reams of Cox and Cochran
    Quoted Anderson and Bancroft
    Practically in extenso
    Trying to impress upon them
    That what actually mattered
    Was to estimate the error.

    One or two of them admitted
    Such a thing might have its uses
    Still, they said, he might do better
    If he shot a little straighter.

    Hiawatha, to convince them,
    Organized a shooting contest
    Laid out in the proper manner
    Of designs experimental
    Recommended in the textbooks
    (mainly used for tasting tea, but
    Sometimes used in other cases)
    Randomized his shooting order
    In factorial arrangements
    Used in the theory of Galois
    Fields if ideal polynomials
    Got a nicely balanced layout
    And successfully confounded
    Second-order interactions.

    All the other tribal marksmen
    Ignorant, benighted creatures,
    Of experimental setups
    Spent their time of preparation
    Putting in a lot of practice
    Merely shooting at the target.

    Thus it happened in the contest
    That their scores were most impressive
    With one solitary exception
    This (I hate to have to say it)
    Was the score of Hiawatha,
    Who, as usual, shot his arrows
    Shot them with great strength and swiftness
    Managing to be unbiased
    Not, however, with his salvo
    Managing to hit the target.
    There, they said to Hiawatha,
    That is what we all expected.

    Hiawatha, nothing daunted,
    Called for pen and called for paper
    Did analyses of variance
    Finally produced the figures
    Showing beyond all peradventure
    Everybody else was biased
    And the variance components
    Did not differ from each other's
    Or from Hiawatha's
    (This last point, one should acknowledge
    Might have been much more convincing
    If he hadn't been compelled to
    Estimate his own component
    From experimental plots in
    Which the values all were missing.
    Still, they couldn't understand it
    So they couldn't raise objections
    This is what so often happens
    With analyses of variance.)

    All the same, his fellow tribesmen
    Ignorant, benighted heathens,
    Took away his bow and arrows,
    Said that though our Hiawatha
    Was a brilliant statistician
    He was useless as a bowman,
    As for variance components
    Several of the more outspoken
    Made primeval observations
    Hurtful to the finer feelings
    Even of a statistician.

    In a corner of the forest
    Dwells alone my Hiawatha
    Permanently cogitating
    On the normal law of error
    Wondering in idle moments
    Whether an increased precision
    Might perhaps be rather better
    Even at the risk of bias
    If thereby one, now and then, could
    Register upon the target.

  • by W.J. Youden (1900 - 1971)




  • Lyric copyright by Jeff Witmer
    may sing to tune of "Let it Be" (Paul McCartney/Beatles)

    When I find myself with normal data,
    William Gosset comes to me
    Speaking words of wisdom, Use a t.

    If my NP plot is linear
    but sigma isn't known to me
    This is not a problem, Use a t.

    Use a t, use a t, use a t, use a t
    Student knows the answer: Use a t.

    And when the broken hearted students
    in a stats class can't agree
    You can show the answer: Use a t.

    Some want to use a Z test,
    and a chi-square is a mystery
    The truth is very simple: Use a t

    Use a t, use a t, use a t, use a t
    Student knows the answer: Use a t.

    And when your thoughts are cloudy,
    RA Fisher may not hear your plea
    But Gosset will deliver, with a t.

    He knows you are trying
    and he wants to set your mind at ease
    Don't think twice about it, use a t.

    Use a t, use a t, use a t, use a t
    Student knows the answer: Use a t.

  • Lyric copyright ©2006 by Lawrence Mark Lesser
    may be sung to the tune of "Aquarius" (James Rado, Gerome Ragni, Galt MacDermot)

    When you have qualitative data
    And you need to test goodness of fit
    Or do a test of independence,
    Then this fine tool is it!
    This is the dawning of the age of chi-square for us,
    Age of chi-square for us,
    Chi-square for us!
    Chi-square for us!

    It's the oldest test we use now--
    In nineteen-hundred, Pearson showed us how
    Reasoning with simple rat'os
    yield expected frequencies that go in formula summation
    note degrees of libera-ation:
    chi-square for us, Chi-square for us!

    (repeat first section)

  • Lyric copyright by Giles Hooker
    may sing to the tune of "American Pie" (Don McLean)

    Long long time ago,
    Ingram can still remember when
    ANOVA used to be the thing.
    Small samples were all that we had
    And of the Normal we were glad
    And we all said R.A. Fisher was our kin
    But my data would never fit,
    No matter how I transformed it.
    Significance was too low;
    I did not know where to go.
    My referees all called it "crap",
    When a thought hit me with a slap:
    "You should try out the bootstrap."
    That's how I got published.

    CHORUS (slow):
    My, my, this assumptions a lie,
    But if we bootstrap we can use it and the paper will fly.
    We'll resample and kiss the normal goodbye
    Singing "Theory is too hard for this guy".

    Well Tukey in the olden days
    Used to sing the Jack-knife's praise
    'Though no-one knew exactly what it did.
    Mann and Whitney and Signed Ranks
    Received our non-parametric thanks
    When non-normality could not be hid.
    But if the data was over-dispersed
    And transforms seemed to make it worse:
    The Chi-squared wouldn't work
    The doctors went berserk!
    But Brad told us to resample,
    A few hundred times should be ample;
    Use the histogram empirical
    We'll call that the bootstrap.


    Do you know that our confidence
    Can be put in places that make sense
    Even when the distribution is unknown?
    Do you have processing power
    To run this scheme within an hour
    And find a result that's not yet been shown?
    Any applied statistician
    Will almost always say "I can!"
    What ever task you bring
    "We'll bootstrap anything."
    A distribution we can plot
    For any statistic you've got;
    You've stepped into the perfect shop
    Here's the best thing on the lot.


    Twenty-five long years have come and gone
    Since Efron's idea came along
    And now you see it everywhere.
    With computers now so very fast
    Simulation is a blast
    And for all that theory we don't really care.
    Though Donoho still rails away
    At the lack of rigor found today;
    Models are complicated,
    Distributions are not stated.
    And though there is no guarantee
    That the truth is what we'll see,
    When consulting comes to me
    I'll still say "Let's bootstrap".

    CHORUS (x2: soft then fast)

  • Lyrics copyright Nyaradzo Mvududu
    may sing to the tune of "Imagine" (John Lennon)

    Imagine there's no Pearson
    And there's no Spearman too
    No correlation
    Whatever can we do
    Imagine all the factors
    With no way to relate

    Imagine there's no Gosset
    And z test just won't do
    'Coz sigma is a mystery
    For samples you have two
    Imagine all the difference
    Without Student's t

    People said they were dreamers
    How could variance be fun?
    I'm so glad for stats heroes
    For the world is now a better one

    Imagine there's no Fisher
    And more groups to compare
    Do not compound the error
    Probe at the sum of squares
    Imagine the assistance
    From ANOVA man

    People said they were dreamers
    How could variance be fun?
    I'm so glad for stats heroes
    For the world is now a better one

  • Lyric copyright ©2006-2013 by Lawrence Lesser
    may sing to the tune of "Hit Me With Your Best Shot" (Pat Benatar)

    Well you're a real tough cookie in statistics class,
    Doin' just average, enough to pass.
    That's OK, just don't fit a line
    'Til you view the data you're assigned!

    Chorus: Hit me with your best plot!
    Why don't you hit me with your best plot?
    Hit me with your best plot - graph away!

    Come on, you know graphs gotta look fair -
    Like pictogram areas showin' their share.
    Let zero be where the y-axis starts
    And don't have a graph with unlabeled parts!
    (Repeat Chorus)

    Well Hans Rosling took our long history
    And animated data so we could see
    What's a trend or a special case
    As nations move through time and space!
    (Repeat Chorus)

  • Lyric © 2013 Lawrence M. Lesser
    May be sung to the tune of "Beat It!" (Michael Jackson)

    They told him, don't just add the regression errors here:
    The plus and minus cancel and they disappear.
    So make each error positive, make it really clear--
    Just square it, just square it!
    Absolute value doesn't make me a fan:
    A line it gives is not unique, ya understand?
    And that is real tough for a software command,
    So square it, you want to so bad:

    Just square it (square it), square it (square it):
    Get a better line of best fit!
    It's the least you can do to get the best line,
    It really matters how you're inclined:
    Just square it (square it), square it (square it),
    Just square it (square it), square it (square it)

    Oooh! Markov and Gauss, you know that each was the man,
    Showed squaring errors made a better plan.
    They talked 'til they were BLUE 'bout their theorem so grand,
    So square it, just square it.
    Oooh! Well now we know to minimize residuals squared
    'Cause other estimators really can't compare:
    The coefficients' estimates are most precise there,
    So square it, you want to so bad:

    Just square it (square it), square it (square it):
    Now derivatives can bear it!
    It's the least you can do to get the best line,
    It really matters how you're inclined:
    Just square it (square it), square it (square it),
    Just square it (square it), square it (square it)