{smcl}
{* 2004-12-07 JRC}{...}
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help for {hi:fieller}{right:Version 1.0 2004-12-07}
{hi:fielleri}
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{title:Confidence interval of a quotient by Fieller's method (for unpaired data)}
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{cmd:fieller}
{it:varname}
[{cmd:if} {it:exp}]
[{cmd:in} {it:range}]
{cmd:,}
{cmd:by(}{it:grouping_varname}{cmd:)}
[{cmdab:l:evel:(}{it:real}{cmd:)}
{cmdab:rev:erse}]
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{cmd:fielleri}
{it:numerator_mean numerator_SD numerator_n denominator_mean denominator_SD denominator_n}
[{cmd:,}
{cmdab:L:evel:(}{it:real}{cmd:)}]
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{cmd:by} {it:...}{cmd::} may be used with {cmd:fieller}; see help {help by}.
{title:Description}
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{cmd:fieller} calculates the confidence interval for a quotient of two independent samples of normally distributed data in {it:varname}. The samples are identified by the grouping variable in the {cmd:by()} option.
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{cmd:fielleri} is the immediate form of the command. Means, standard deviations and {it:n}s are given sequentially, with the numerator's statistics first.
{title:Options}
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{cmd:by()} is required for {cmd:fieller}. It identifies the grouping variable, which may be either numeric or string. The smallest value defines the group that will go into the numerator and the next-smallest value is the group in the denominator.
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{cmd:reverse} (for {cmd:fieller}) allows the user to invert the quotient should the {cmd:by()} variable be coded such that the group intended to be in the denominator is the lesser value.
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{cmd:level} allows the user to choose the level of the confidence interval. It defaults to {cmd:c(level)}. See help {help creturn}.
{title:Remarks}
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The confidence interval is calculated as described in Motulsky (1995). The method is based upon an eponymous theorem by Edgar C. Fieller.
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The method is intended for normally distributed data, but variances need not be identical between the two groups. {cmd:fieller} and {cmd:fielleri} are for uncorrelated data (independent groups). Confidence intervals for quotients of paired data should be calculable by the official Stata command {cmd:pkequiv} with the {cmd:fieller} option, if the dataset can be arranged to meet the requirements of the command. See help {help pkequiv}.
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The confidence interval relies upon the solution to a quadratic equation, which doesn't necessarily have both roots real; therefore, the confidence interval might not always be calculable. This will happen when the quotient is not statistically signficsignficantly different from zero at the specified level of Type I error rate—the mean of the denominator should be "large" in comparison to its standard deviation.
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{title:Reference}
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Harvey Motulsky, {it:Intuitive Biostatistics} Oxford: Oxford University Press, 1995. pp. 285–86.
{title:Examples}
{p 4 8 2}{cmd:. sysuse bplong}
{p 4 8 2}{cmd:. // A recommended preliminary: -regress- and plot residuals with, for example, -pnorm-}
{p 4 8 2}{cmd:. bysort when: fieller bp, by(sex) level(90)}
{p 4 8 2}{cmd:. fieller bp if when == 2, by(sex)}
{p 4 8 2}{cmd:. // An alternative approach (for large samples) using the delta method; less favorably considered}
{p 4 8 2}{cmd:. tabulate sex, generate(Sex)}
{p 4 8 2}{cmd:. regress bp Sex1 Sex2 if when == 2, noconstant}
{p 4 8 2}{cmd:. nlcom _b[Sex1] / _b[Sex2]}
{p 4 8 2}{cmd:. // Another alternative, using generalized linear modeling (again, for large samples)}
{p 4 8 2}{cmd:. glm bp Sex1 if when == 2, family(gaussian) link(log) eform nolog}
{p 4 8 2}{cmd:. fielleri 278 5.5 4 254 2.88 4, level(99)}
{title:Author}
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E-mail {browse "mailto:jcoveney@bigplanet.com":Joseph Coveney} if you observe any problems.
{title:Also see}
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Manual: {hi:[R] pkequiv}
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Online: help for {help pkequiv}