**[R] ladder** -- Ladder of powers

__Syntax__

Ladder of powers

**ladder** *varname* [*if*] [*in*] [**,** __g__**enerate(***newvar***)** __noa__**djust**]

Ladder-of-powers histograms

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

Ladder-of-powers quantile-normal plots

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

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

__Menu__

__ladder__

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

__gladder__

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

__qladder__

**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.

__Options for ladder__

+------+
----+ 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**.

__Options for gladder__

*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*).

__Options for qladder__

*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
**. ladder tempjuly**

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:
Addison-Wesley.