Re: Confidence Intervals

From: Richard Ulrich (Rich.Ulrich_at_comcast.net)
Date: 09/25/04

  • Next message: Frank Iannarilli: "Multiple Regression w/ Polynomial-in-Y?" 
    Date: Fri, 24 Sep 2004 23:06:56 -0400

    On 24 Sep 2004 17:08:33 -0700, petermichaux@yahoo.com (Peter Michaux)
    wrote:

    > I've been reading old threads and it looks like people here generally
    > prefer using confidence intervals to the other option of hypothesis
    > testing. I can find a lot of information about hypothesis testing in
    > text books but interpreting confidence intervals is harder info to
    > find.
    >
    > Suppose I have the mean mass of girls (X) and the mean mass of boys
    > (Y) and have constructed 95% confidence intervals for my samples. I
    > can imagine a bunch of different cases. Four cases are shown below
    > where the mean and confidence intervals are depicted. What conclusions
    > could I make about these cases? (I hope at least in case 1 I can say
    > boys are heavier than girls with 95% confidence. Or something like
    > that.)

    The technical comparison is *not* made by eyeballing
    CIs to see if they overlap - though that can work for
    extremes, and especially if the Ns and variances are
    similar.

    The CI that reproduces a test for the difference between
    two means is a "CI on the difference."

    >
    > Case 1
    > |---------X--------------|
    > |--------------Y---------|
    >
    > Case 2
    > |---------X--------------|
    > |--------------Y---------|
    >
    > Case 3
    > |---------X--------------|
    > |-------------------Y---------|
    >
    > Case 4
    > |---------X--------------|
    > |--------------Y---------|
    >

    I assume these are diagramming respective overlap (or not),
    of means and end-points of the CIs --
    no overlap;
    ends overlap each other;
    one end overlaps a mean;
    two ends overlap means.

    Case 2 and Case 3 are ambiguous. 

    -- 
Rich Ulrich, wpilib@pitt.edu
http://www.pitt.edu/~wpilib/index.html
  • Next message: Frank Iannarilli: "Multiple Regression w/ Polynomial-in-Y?"

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