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Continuous or Discreet

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  • March 27, 2012 at 5:06 am #54007

    K S Alok Ranjan
    ★ 10 Years ★
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    Is it not correct to say, Data are never Continuous or Discreet, rather the units that define the data are.

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    March 27, 2012 at 5:35 am #192757

    Robert Butler
    ★ 10 Years ★
    Participant

    From Agresti Categorical Data Analysis 2nd Edition pp. 3 ” Variables are classified as continuous or discrete, according to the number of values they can take. Actual measurements of all variables occurs in a discrete manner, due to precision limitations in measuring instruments. The continuous-discrete classification, in practice, distinguishes between variables that take lots of values and variables that take few values. For instance, statisticians often treat discrete interval variables having a large number of values (such as test scores) as continuous, using them in methods for continuous responses.”

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    March 27, 2012 at 10:14 am #192769

    MBBinWI
    ★ 10 Years ★
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    @ksalokranjan – as Robert quotes, all measurements are inherently discrete due to at some point needing to put a limit on decimals. However, your query postulated that the data units are continuous/discrete. This would be wrong, as the units “degrees” for temperature is clearly continuous (infinite possible values), but the data (recorded observation) is clearly limited in decimal digits having a finite number of reading levels that can be recorded, thus are discrete. So, my answer is exactly opposite of your proposal, and data are always discrete (although we often choose to treat it as continuous), and units can be discrete or continuous.

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    March 27, 2012 at 10:51 am #192775

    Darth
    ★ 10 Years ★
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    I’m not smart enough to understand what was said above but here is how I make the distinction……is it measured or counted? can it logically be divided into units over an essentially infinite scale of measurement.

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    March 27, 2012 at 12:36 pm #192780

    MBBinWI
    ★ 10 Years ★
    Participant

    @Darth – ah, but dear Dr. Darth, what if I’m counting the number of people going to each Brewers game for a season? 10’s of thousands per individual reading and more than a hundred readings – so discrete (counted) or continuous?

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    March 27, 2012 at 1:59 pm #192787

    gomezadams
    ★ 10 Years ★
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    How about superfelous. The Brewers?
    Can’t count them on any scale.

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    March 27, 2012 at 2:05 pm #192789

    Chris Seider
    ★ 10 Years ★
    Participant

    I miss the banter….
    @MBBinWI Let’s say the number of people were counted by ones…I’d treat as continuous as I’m sure you would.

    It’s always an interesting discussion depending on who’s in class and who’s a stickler or who’s a smart alec.

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    March 27, 2012 at 3:24 pm #192792

    Darth
    ★ 10 Years ★
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    @MBBinWI @cseider As Gomez suggested we might only need one hand to count the number of Brewer fans attending a game. I believe we have covered this issue in the past. The underlying characteristic of counting people is definitely discrete. We count, we don’t measure and they are either a person or not. On the other hand, large counts can take on the behavior of continuous data if we have enough and the range of the counts is wide enough. Therefore, in reality, we have discrete and continuous and a Gray World in which counts can be treated as continuous even though that doesn’t change the underlying notion that it is still a discrete count.

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    March 27, 2012 at 9:47 pm #192797

    K S Alok Ranjan
    ★ 10 Years ★
    Participant

    Glad to see so many suggestions. Let me paraphrase my original intent with an example. I wanted to ask,
    “Is it not correct to say, Data (for example 8 or 13) are never Continuous or Discreet, rather the units (for example 8 as in age of a student or 13 as in number of students in section) that define the data are.”
    @MBBinWI, @rbutler got it correct. @rbutler is close to what I wanted to say. He have given the term ‘variable’ to what I referred as ‘units’. And about the unit “degrees”, indeed it is discreet. About one of the reading is continuous, I am not sure!

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    March 27, 2012 at 9:51 pm #192798

    K S Alok Ranjan
    ★ 10 Years ★
    Participant

    And I find @Darth ‘s formula simple and effective. Honestly, I use it. And about number of people going to each Brewer’s game for a season, @MBBinWI, I suppose until it can be counted, it is discreet.. you know, ‘number’ of people.. :-)

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    March 28, 2012 at 7:47 am #192811

    MBBinWI
    ★ 10 Years ★
    Participant

    @ksalokranjan – ah, but if I have sufficient numbers of counted items, and if the counts have sufficient levels, then I can treat them as continuous.
    Likewise, if I have temperature readings (let’s choose deg C as it has a wider coverage range per degree) that I stop the digits at the whole number level (no decimals), then I might only end up with a few different numbers, which I might choose to evaluate as a discrete variable.
    So, in true MBB fashion, my final answer is: It depends!

    And to those of you trying to yank my chain about the Brew Crew, sorry – I’m not invested in the team or their success or lack of. But good try.

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