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Estimation

  • Lyrics © 2015 by Larry Lesser, music by Dominic Dousa

    Salary is the variable whose data I tabulate;
    Mean is the parameter I want to estimate.

    When I calculate its counterpart
    From the sample now in hand,
    I wonder if on average,
    The bullseye's where it lands!

    It's unbiased 'cause on average
    the estimate will land
    Centered at the target
    of the population parameter.

  • Lyrics & Music © 2015 Lawrence M. Lesser

    "Will the Steelers win next season's Super Bowl?"
    We asked about 1,000 fans in a scientific poll.
    The margin of error was 3%
    That's roughly the reciprocal of the square root of n.

    17% answered 'YES' in the poll,
    But what could it be for the population as a whole?
    At the 95% level of confidence
    The interval goes from 14 to 20%.

    If we multiply the sample size by a factor of 9,
    The new margin of error that we could find
    Would be a third as large as what we had before.
    Thanks to the formula, you know the score.
    Go Steelers!

  • Lyrics © 2015 by Larry Lesser, music by Dominic Dousa

    For a population, there is a parameter
    We want to learn about it, it's the number that we're after
    Our best guess for its value is the sample statistic
    The method we use to get it should make us optimistic!

    We'll estimate proportions from opinion polls
    Or estimate the mean height from our class rolls.
    We hope our sample targets the parameter unknown;
    We want a likely range stated as a zone.
    When we seek that interval, it's always good to know
    What would make it shrink and what would make it grow.

    The interval gets tighter with increasing n:
    The added information helps us narrow in!
    The interval gets bigger with a larger s,
    That has come from a sample that's a more uncertain mess!
    The interval gets wider for higher confidence
    'Cause you have to cover lots more of your bets!

    Our sample gives us one shot to make a decent guess
    So let's use a method with a high rate of success!
    I'm eighty percent confident my answers are first rate,
    In my estimation, when we estimate!

  • Lyrics © 2015 by Larry Lesser, music by Dominic Dousa

    Greek letters refer to the population.
    Mu (μ) stands for mean, sigma's (σ) standard deviation,
    Greek letters refer to the population.
    Beta (β) is the slope, rho (ρ) is the correlation.

    Description of part, not whole 
    that's what sample statistics are:
    standard deviation's s, the mean is x-bar () ,
    the slope is b, the correlation's r.


    A sample statistic estimates a population parameter;
    Now that we know this, we're sure to be no statistical amateur!
     
  • Music and Lyrics © 2015 Tom Toce (Retrograde Music)

    For deviation, you need the root
    Don't permute
    Take the root
    Sample growth is one thing
    That's absolute
    Your  Standard Error  lags, it shrinks like –
     Standard Error  lags, it shrinks like –
     Standard Error  lags, it shrinks like –
    The root.
    The  square root !

  • Lyrics © Mary McLellan
    may sing to the tune of "I Can See Clearly Now" by Johnny Nash

    The best it can be is if you use true P
    If you don’t have that, you can just use P-hat
    The worst case scenario is those don’t jive.
    Please don’t cry, cry…
    Just use point 5
    Please don’t cry cry…
    Just use point 5

    Repeat

  • Lyrics © Mary McLellan
    may sing to the tune of  "Can't Buy Me Love" by The Beatles

    Confidence level
    Not an interval
    Confidence level
    Oh, oh, oh, oh

    Let’s say 95%, 95%
    Of all 95%, 95%
    Intervals of confidence,
    They contain the TRUE
    Parameter
    Of interest
    Parameter
    Oh, oh, oh, oh

    Repeat with 98%

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