Open Daily: 10am - 10pm | Alley door pickup 10am - 7pm 3038 Hennepin Ave Minneapolis, MN
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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Small Sample Confidence Intervals in Log Space Back-Transformed From Normal Space

Small Sample Confidence Intervals in Log Space Back-Transformed From Normal Space

Tisdel, Jason E.

Paperback

General EducationGeneral MathematicsProbability & Statistics

ISBN10: 1288294832
ISBN13: 9781288294831
Publisher: Biblioscholar
Published: Nov 13 2012
Pages: 74
Weight: 0.26
Height: 0.15 Width: 6.14 Depth: 9.21
Language: English
The logarithmic transformation is commonly applied to a lognormal data set to improve symmetry, homoscedasticity, and linearity. Simple to implement and easy to understand, the logarithm function transforms the original data to closely resemble a normal distribution. Analysis in the normal space provides point estimates and confidence intervals, but transformation back to the original space using the naive approach yields confidence intervals of impractical width. The naive approach applies the exponential function e to the parameter of interest in normal space to obtain the corresponding parameter of interest in the original space. The naive approach offers results that are often inadequate for practical purposes. We present an alternative approach that provides improved results in the form of decreased interval width, increased confidence level, or both. Our alternative approach yields dramatically improved results at small sample sizes drawn from the right tail of the lognormal distribution.

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