pickMarble: Simulates the Drawing of A Marble.

In achambaz/simpsons.marbles: Simpson's Marbles

Description

pickMarble simulates the drawing (with replacement) of a marble from a collection of marbles characterized by a tag indicating to which bag each marble belonged to originally, its size and color. The marbles are either poured together in a box, or gathered by similar features in pouches of different textures. Six approaches to the gathering of marbles are available, one for each ordering of the features.

Usage

pickMarble(iter = 10, gather.by = NULL, do.bag = NULL, do.size = NULL,
  do.color = NULL)

Arguments

iter	integer, the number of independent iterations (defaults to 10).
gather.by	either NULL for no gathering (default value) or a character, one among "bsc", "bcs", "sbc", "scb", "cbs", "csb", to specify how the marbles were gathered. The ordering of the first letters of the words bag, size and color determines in which order the marbles are gathered.
do.bag	either NULL for no intervention on bag (default value) or a character to specify the nature of the intervention, either "one" or "two".
do.size	either NULL for no intervention on size (default value) or a character to specify the nature of the intervention, either "large" or "small".
do.color	either NULL for no intervention on color (default value) or a character to specify the nature of the intervention, either "red" or "blue".

Details

pickMarble simulates the drawing (with replacement) of a marble from a collection of marbles characterized a tag indicating to which bag they originate from (bag one or bag two), their size (large or small) and color (red or blue). The marbles are either poured together in a box, or gathered by similar features in pouches of different textures. Six approaches to the gathering are available, one for each ordering of the features of a marble. For a generic approach to gathering described by "xyz" with distinct "x", "y", "z" taken in \{"b", "s", "c"\}, the gathering consists in

1. gathering by bag if x=b, size if x=s, color if x=c,

2. gathering by bag if y=b, size if y=s, color if y=c.

Introduced by J. G. Bennett to discuss Simpson's paradox, the distribution of marbles is the following:

	bag	one		bag	two		the	box
	red	blue		red	blue		red	blue
large	12	18		8	2		20	20
small	3	7		21	9		24	16

where the box contains all the marbles when they are poured together. When the marbles are not poured together, the probabilities to sample the outer pouches on the one hand and conditional probabilities to sample the inner pouches within an outer pouch on the other hand reflect the overall distribution of marbles and are thus possibly unequal. This may represent an unconscious ordering of textures by preference.

Value

A data.frame with iter rows and 3 columns describing the results of the iter independent samplings.

Examples

## draw independently  10 marbles from the box where  all marbles have been
## poured together

pickMarble(10)

## draw independently 10 marbles when the approach to 
## gathering is given by (1) bag, (2) size, (3) color

pickMarble(10, gather.by = "bsc")

## draw independently 10 marbles from bag one when the
## approach to gathering is given by (1) bag, (2) size,
## (3) color

pickMarble(10, gather.by = "bsc", do.bag = "one")

## draw independently 10 large marbles when the approach
## to gathering is given by (1) bag, (2) size, (3) color

pickMarble(10, gather.by = "bsc", do.size = "large")

achambaz/simpsons.marbles documentation built on May 23, 2019, 9 p.m.