```-------------------------------------------------------------------------------
help for fieller                                         Version 1.0 2004-12-07
fielleri
-------------------------------------------------------------------------------

Confidence interval of a quotient by Fieller's method (for unpaired data)

fieller varname [if exp] [in range] , by(grouping_varname)
[level(real) reverse]

fielleri numerator_mean numerator_SD numerator_n denominator_mean
denominator_SD denominator_n [, Level(real)]

by ...: may be used with fieller; see help by.

Description

fieller calculates the confidence interval for a quotient of two
independent samples of normally distributed data in varname. The samples
are identified by the grouping variable in the by() option.

fielleri is the immediate form of the command. Means, standard deviations
and ns are given sequentially, with the numerator's statistics first.

Options

by() is required for 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.

reverse (for fieller) allows the user to invert the quotient should the
by() variable be coded such that the group intended to be in the
denominator is the lesser value.

level allows the user to choose the level of the confidence interval.  It
defaults to c(level).  See help creturn.

Remarks

The confidence interval is calculated as described in Motulsky (1995).
The method is based upon an eponymous theorem by Edgar C. Fieller.

The method is intended for normally distributed data, but variances need
not be identical between the two groups.  fieller and fielleri are for
uncorrelated data (independent groups).  Confidence intervals for
quotients of paired data should be calculable by the official Stata
command pkequiv with the fieller option, if the dataset can be arranged
to meet the requirements of the command.  See help pkequiv.

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.

Reference

Harvey Motulsky, Intuitive Biostatistics Oxford: Oxford University Press,
1995. pp. 285–86.

Examples

. sysuse bplong

. // A recommended preliminary: -regress- and plot residuals with, for
example, -pnorm-

. bysort when: fieller bp, by(sex) level(90)

. fieller bp if when == 2, by(sex)

. // An alternative approach (for large samples) using the delta method;
less favorably considered

. tabulate sex, generate(Sex)

. regress bp Sex1 Sex2 if when == 2, noconstant

. nlcom _b[Sex1] / _b[Sex2]

. // Another alternative, using generalized linear modeling (again, for
large samples)

. glm bp Sex1 if when == 2, family(gaussian) link(log) eform nolog

. fielleri 278 5.5 4 254 2.88 4, level(99)

Author

E-mail Joseph Coveney if you observe any problems.

Also see

Manual:  [R] pkequiv

```