## Stata 15 help for qladder

```

Syntax

ladder varname [if] [in] [, generate(newvar) noadjust]

gladder varname [if] [in] [, histogram_options combine_options]

qladder varname [if] [in] [, qnorm_options combine_options]

by is allowed with ladder; see [D] by.

Statistics > Summaries, tables, and tests > Distributional plots and
tests > Ladder of powers

Statistics > Summaries, tables, and tests > Distributional plots and
tests > Ladder-of-powers histograms

Statistics > Summaries, tables, and tests > Distributional plots and
tests > Ladder-of-powers quantile-normal plots

Description

ladder searches a subset of the ladder of powers (Tukey 1977) for a
transform that converts varname into a normally distributed variable.

gladder and qladder each display a graph matrix.  gladder displays nine
histograms of transforms of varname according to the ladder of powers.
qladder displays the quantiles of transforms of varname according to the
ladder of powers against the quantiles of a normal distribution.

+------+
----+ Main +-------------------------------------------------------------

generate(newvar) saves the transformed values corresponding to the
minimum chi-squared value from the table.  We do not recommend using
generate() because it is literal in interpreting the minimum, thus
ignoring nearly equal but perhaps more interpretable transforms.

noadjust is the noadjust option to sktest; see [R] sktest.

histogram_options affect the rendition of the histograms across all
relevant transformations; see [R] histogram.  Here the normal option
is assumed, so you must supply the nonormal option to suppress the
overlaid normal density.  Also, gladder does not allow the width(#)
option of histogram.

combine_options are any of the options documented in [G-2] graph combine.
These include options for titling the graph (see [G-3] title_options)
and for saving the graph to disk (see [G-3] saving_option).

qnorm_options affect the rendition of the quantile-normal plots across
all relevant transformations.  See options2 in [R] diagnostic plots.

combine_options are any of the options documented in [G-2] graph combine.
These include options for titling the graph (see [G-3] title_options)
and for saving the graph to disk (see [G-3] saving_option).

Examples

Setup
. sysuse citytemp

Search ladder of powers for a function that transforms tempjuly to
normality

Draw histogram for each transformation; remove axis labels
. gladder tempjuly, l1title("") ylabel(none) xlabel(none)

Draw quantile-normal plot for each transformation; remove axis labels
. qladder tempjuly, ylabel(none) xlabel(none)

Stored results

ladder stores the following in r():

Scalars
r(N)                number of observations
r(invcube)          chi-squared for inverse-cubic transformation
r(P_invcube)        p-value for normality test after inverse-cubic
transformation
r(invsq)            chi-squared for inverse-square transformation
r(P_invsq)          p-value for normality test after inverse-square
transformation
r(inv)              chi-squared for inverse transformation
r(P_inv)            p-value for normality test after inverse
transformation
r(invsqrt)          chi-squared for inverse-root transformation
r(P_invsqrt)        p-value for normality test after inverse-root
transformation
r(log)              chi-squared for log transformation
r(P_log)            p-value for normality test after log transformation
r(sqrt)             chi-squared for square-root transformation
r(P_sqrt)           p-value for normality test after square-root
transformation
r(ident)            chi-squared for untransformed data
r(P_ident)          p-value for normality test of untransformed data
r(square)           chi-squared for square transformation
r(P_square)         p-value for normality test after square
transformation
r(cube)             chi-squared for cubic transformation
r(P_cube)           p-value for normality test after cubic
transformation

Reference

Tukey, J. W. 1977. Exploratory Data Analysis.  Reading, MA: