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anscombiser: Create Datasets with Identical Summary Statistics

Description

Anscombe's quartet (Anscombe, 1973) are a set of four two-variable datasetsthat have several common summary statistics but which have very differentjoint distributions. This becomes apparent when the data are plotted, whichillustrates the importance of using graphical displays in Statistics. Thispackage enables the creation of datasets that have identical marginal samplemeans and sample variances, sample correlation, least squares regressioncoefficients and coefficient of determination. The user supplies an initialdataset, which is shifted, scaled and rotated in order to achieve targetsummary statistics. The general shape of the initial dataset is retained.The target statistics can be supplied directly or calculated based on auser-supplied dataset.

Details

The main functions inanscombiser are

• anscombise, which modifies a user-supplied dataset so that it sharessample summary statistics with Anscombe's quartet.

• mimic, which modified a user-supplied dataset so that is sharessample summary statistics with another user-supplied dataset.

Seevignette("intro-to-anscombiser", package = "anscombiser") foran overview of the package.

Author(s)

Maintainer: Paul J. Northropp.northrop@ucl.ac.uk [copyright holder]

References

Anscombe, F. J. (1973). Graphs in Statistical Analysis.The American Statistician 27 (1): 17–21.doi:10.1080/00031305.1973.10478966

See Also

anscombise andmimic

Anscombe's Quartet Separated

Description

Provides Anscombe's Quartet as separate data frames.

Usage

anscombe1anscombe2anscombe3anscombe4

Format

All datasets are objects of classdata.frame with 11 rows and 2columns.

Source

Anscombe's Quartet of 'Identical' Simple Linear Regressions:datasets::anscombe in thedatasets package. Theith dataset isdatasets::anscombe[, c(i, i + 4)].

References

Anscombe, Francis J. (1973). Graphs in statistical analysis.The American Statistician,27, 17-21.doi:10.2307/2682899

Create new versions of Anscombe's quartet

Description

Modifies a datasetx so that it shares sample summary statistics withAnscombe's quartet.

Usage

anscombise(x, which = 1, idempotent = TRUE)

Arguments

Details

The input datasetx is modified by shifting, scaling and rotatingit so that its sample mean and covariance matrix match those of theAnscombe quartet.

The rotation is based on the square root of the sample correlation matrix.Ifidempotent = FALSE then this square root is based on the Choleskydecomposition this matrix, usingchol. Ifidempotent = TRUE thesquare root is based on the spectral decomposition of this matrix, usingthe output fromeigen. This is a minimal rotation square root,which means that if the input datax already have theexactly/approximately the required summary statistics then the returneddataset is exactly/approximately the same as the target dataset.

Value

An object of classc("anscombe", "matrix", "array") withplot andprint methods. This returneddataset has the following summary statistics in common with Anscombe'squartet.

• The sample means of each variable.

• The sample variances of each variable.

• The sample correlation matrix.

• The estimated regression coefficients from least squares linearregressions of each variable on each other variable.

The target and new summary statistics are returned as attributesold_stats andnew_stats and the chosen Anscombe's quartet dataset asan attributeold_data.

See Also

mimic to modify a dataset to share sample summary statisticswith another dataset.

datasets::anscombe for Anscombe's Quartet andanscombe forAnscombe's Quartet as 4 separate datasets.

input_datasets:input1 toinput8 for some input datasestof the same size as those in Anscombe's quartet.

Examples

# Produce Anscombe-like datasets using input1 to input8a1 <- anscombise(input1, idempotent = FALSE)plot(a1)a2 <- anscombise(input2)plot(a2)a3 <- anscombise(input3, idempotent = FALSE)plot(a3)a4 <- anscombise(input4, idempotent = FALSE)plot(a4)a5 <- anscombise(input5, idempotent = FALSE)plot(a5)a6 <- anscombise(input6)plot(a6)a7 <- anscombise(input7, idempotent = FALSE)plot(a7)a8 <- anscombise(input8, idempotent = FALSE)plot(a8)# Old faithful to new faithfulnew_faithful <- anscombise(datasets::faithful, which = 4)plot(new_faithful)# Then check that the sample summary statistics are the sameplot(new_faithful, input = TRUE)# Map of Italygot_maps <- requireNamespace("maps", quietly = TRUE)if (got_maps) {  italy <- mapdata("Italy")  new_italy <- anscombise(italy, which = 4)  plot(new_italy)}

Animation of several Anscombised datasets

Description

Create an animation to show datasets that share sample summary statisticswithAnscombe's quartet.

Usage

anscombise_gif(  x,  which = 1,  idempotent = TRUE,  theme_name = "classic",  ease = "cubic-in-out",  transition_length = 3,  state_length = 1,  wrap = TRUE)

Arguments

Details

For this function to work the packagesggplot2 andgganimate must be installed.

Value

An object of classc("gganim", "gg", "ggplot") with an additionalattributenew_data that is a data frame with 3 variables,x,y anddataset containing the datasets output fromanscombise.

The returned object may be displayed using by typing its name,e.g.,anim or saved as a GIF file usinganim_save, e.g.,gganimate::anim_save("anscombe.gif", anim).

See Also

anscombise modifies a dataset so that it shares sample summarystatistics withAnscombe's quartet.

input_datasets:input1 toinput8 for some input datasetsof the same size as those in Anscombe's quartet.

Examples

# Animate some Anscombe-like datasets produced using input1 to input8x <- list(input1, input2, input3, input4, input5, input6, input7, input8)idem <- c(FALSE, TRUE, FALSE, FALSE, FALSE, TRUE, FALSE, FALSE)anim <- anscombise_gif(x, idempotent = idem)

Internal anscombiser functions

Description

Internal anscombiser functions

Usage

is_wholenumber(x, tol = .Machine$double.eps^0.5)is_pos_def(x, tol = 1e-06)minimal_rotation(x)make_stats(x, stats, idempotent = FALSE)

Details

These functions are not intended to be called by the user.

Calculate Anscombe's summary statistics

Description

Calculates a particular set of summary statistics for a dataset.

Usage

get_stats(x)

Arguments

Value

A named list of summary statistics containing

• n The sample size.

• means The sample means of each variable.

• variances The sample means of each variable.

• correlation The sample correlation matrix.

• intercepts,slopes,rsquared Matrices whose (i,j)th entries are theestimated regression coefficients in a regression ofx[, i] onx[, j] and the resulting coefficient of determinationR^2.

Examples

get_stats(anscombe[, c(1, 5)])

Input datasets for use by anscombise()

Description

Provides input datasets from whichanscombe will produce transformed datasets that behave likeAnscombe's quartet of datasets, that is, with the same traditional statistical properties but different general behaviours. Useplot(input1), for example, to see the behaviours of the datasets.

Usage

input1input2input3input4input5input6input7input8

Format

All datasets are objects of classmatrix (inherits fromarray) with 11 rows and 2 columns.

Source

None. Created for use in 'anscombiser'.

References

Anscombe, Francis J. (1973). Graphs in statistical analysis.The American Statistician,27, 17-21.doi:10.2307/2682899

Extract longitude and latitude values

Description

Extracts longitude and latitude values for a particular region from theworld map supplied by the maps package.

Usage

mapdata(region = ".", map = "world", exact = FALSE, ...)

Arguments

Value

A dataframe with two columns:long andlat for longitude andlatitude.

Examples

See the examples inmimic.

Modify a dataset to mimic another dataset

Description

Modifies a datasetx so that it shares sample summary statistics witha target datasetx2.

Usage

mimic(x, x2, idempotent = TRUE, ...)

Arguments

Details

The input datasetx is modified by shifting, scaling and rotatingit so that its sample mean and covariance matrix match those of the targetdatasetx2.

The rotation is based on the square root of the sample correlation matrix.Ifidempotent = FALSE then this square root is based on the Choleskydecomposition this matrix, usingchol. Ifidempotent = TRUE thesquare root is based on the spectral decomposition of this matrix, usingthe output fromeigen. This is a minimal rotation square root,which means that if the input datax already have theexactly/approximately the required summary statistics then the returneddataset is exactly/approximately the same as the target datasetx2.

Value

An object of classc("anscombe", "matrix", "array") withplot andprint methods. This returneddataset has the following summary statistics in common withx2.

• The sample means of each variable.

• The sample variances of each variable.

• The sample correlation matrix.

• The estimated regression coefficients from least squares linearregressions of each variable on each other variable.

The target and new summary statistics are returned as attributesold_stats andnew_stats.Ifx2 is supplied then it is returned as a attributeold_data.

See Also

anscombise modifies a dataset so that it shares sample summarystatistics withAnscombe's quartet.

Examples

### 2D examples# The UK and a dinosaurgot_maps <- requireNamespace("maps", quietly = TRUE)got_datasauRus <- requireNamespace("datasauRus", quietly = TRUE)if (got_maps && got_datasauRus) {  library(maps)  library(datasauRus)  dino <- datasaurus_dozen_wide[, c("dino_x", "dino_y")]  UK <- mapdata("UK")  new_UK <- mimic(UK, dino)  plot(new_UK)}# Trump and a dinosaurif (got_datasauRus) {  library(datasauRus)  dino <- datasaurus_dozen_wide[, c("dino_x", "dino_y")]  new_dino <- mimic(dino, trump)  plot(new_dino)}## Examples of passing summary statistics# The default is zero mean, unit variance and no correlationnew_faithful <- mimic(faithful)plot(new_faithful)# Change the correlationmat <- matrix(c(1, -0.9, -0.9, 1), 2, 2)new_faithful <- mimic(faithful, correlation = mat)plot(new_faithful)### A 3D examplenew_randu <- mimic(datasets::randu, datasets::trees)# The samples summary statistics are equalget_stats(new_randu)get_stats(datasets::trees)

Animation of several mimicking datasets

Description

Create an animation to show datasets that mimic a target datasetx2.

Usage

mimic_gif(  x,  x2,  idempotent = TRUE,  theme_name = "classic",  ease = "cubic-in-out",  transition_length = 3,  state_length = 1,  wrap = TRUE)

Arguments

Details

For this function to work the packagesggplot2 andgganimate must be installed.

Value

An object of classc("gganim", "gg", "ggplot") with an additionalattributenew_data that is a data frame with 3 variables,x,y anddataset containing the datasets output frommimc.

The returned object may be displayed using by typing its name,e.g.,anim or saved as a GIF file usinganim_save, e.g.,gganimate::anim_save("anscombe.gif", anim).

See Also

mimic to modify a dataset to share sample summary statisticswith another dataset.

input_datasets:input1 toinput8 for some input datasetsof the same size as those in Anscombe's quartet.

Examples

# Create 8 datasets that mimic Anscombe's first datasetx <- list(input1, input2, input3, input4, input5, input6, input7, input8)anim <- mimic_gif(x, anscombe1)

Plot method for objects of class "anscombe"

Description

plot method for objects inheriting from class"anscombe".

Usage

## S3 method for class 'anscombe'plot(x, input = FALSE, stats = TRUE, digits = 3, legend_args = list(), ...)

Arguments

Details

This function is only applicable in 2 dimensions, that is,whenlength(attr(x, "new_stats")$means) = 2.

Value

Nothing is returned.

Examples

See the examples inanscombise andmimic.

See Also

anscombise andmimic.

Print method for objects of class "anscombe"

Description

print method for class "anscombe".

Usage

## S3 method for class 'anscombe'print(x, ...)

Arguments

Details

Just extracts the new dataset fromx and prints it usingprint.

Value

The argumentx, invisibly.

See Also

anscombise andmimic

Create a list of summary statistics

Description

Creates a list of summary statistics to pass tomimic.

Usage

set_stats(d = 2, means = 0, variances = 1, correlation = diag(2))

Arguments

Details

The vectorsmeans andvariances are recycled usingrep_len to have lengthd.

Value

A list containing the following components.

• means ad-vector of sample means.

• variances ad-vector sample variances.

• correlation ad byd correlation matrix.

Examples

# Uncorrelated with zero means and unit variancesset_stats()# Sample correlation = 0.9set_stats(correlation = matrix(c(1, 0.9, 0.9, 1), 2, 2))

Donald Trump

Description

A dataset that provides an image of Donald Trump's face.

Usage

trump

Format

A matrix with 4885 rows and 2 columns:x andy.

Source

This image was created by Accentaur from the Noun Project.https://thenounproject.com/term/donald-trump/727774/

Examples

plot(trump)