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Equivalent of std dev for discrete data-set

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  • February 19, 2010 at 3:39 pm #53302

    Anand
    ★ 10 Years ★
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    I have a data-set of 10 discreet categories each one with 20 observations rated on a 5 point rating scale. I now want to analyze the variation within each category and compare them across the different categories. Had this been continuous data, I would have calculated the std dev of each and also graphically depicted the variation across categories with a box plot. What approach should I follow as my data is for 1-5 ratings and not continuous ?

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    February 19, 2010 at 5:48 pm #189549

    SiggySig
    ★ 10 Years ★
    Member

    In a past life I analyzed survey response statistics, and basically treated the data as continuous. Purists may disagree, especially since you’re on a scale of 1-5. I had scales of 1-7 and 1-10 to deal with, which made it a bit easier.

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    February 20, 2010 at 3:13 am #189557

    Tierradentro
    ★ 10 Years ★
    Participant

    You are dealing with a 5 point Likert scale and a sample size of 20. How does getting a statistically shaky measure of dispersoin help you get answers to your critical questions?  I don’t think your findings will be actionable.  And if not actionable, what is the point?

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    February 20, 2010 at 3:24 am #189558

    Tierradentro
    ★ 10 Years ★
    Participant

    But I didnt answer your question.  Perhaps this article will prove helpful: 
    https://www.isixsigma.com/library/content/c040809a.asp?action=print

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    February 20, 2010 at 5:00 pm #189564

    Darth
    ★ 10 Years ★
    Participant

    Usually you just report out the percentage or proportion of the 1-5 scale. If it makes sense you can report out as “top two box (1 & 2)” and “not top two box”. Not real comfortable with treating as continuous. You are aware that you can calculate s.d. for discrete distributions such as Poisson and Binomial?

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