# Biased Coin Design Allocation

### Description

Allocates observations sequentially using a biased coin design. If equal numbers have been allocated to treatment and control, the next observation is allocated to treatment with probability 1/2. If there are more units assigned to treatment than control, the next observation is allocated to control with probability p; if there are more units assigned to control than treatment, the next observation is allocated to treatment with probability p.

### Usage

1 | ```
bcdalloc(n, pbcd, tol = 1e-06)
``` |

### Arguments

`n` |
number of observations |

`pbcd` |
probability p used for biased coin |

`tol` |
tolerance used for allocation |

### Value

Vector of zeroes and ones indicating the allocation of each unit to treatment (1) or control (0)

### Author(s)

Xiaoshu Zhu xiaoshuzhu@westat.com and Sharon Lohr

### References

Efron, B. (1971). Forcing a sequential experiment to be balanced. Biometrika, 58(3), 403-417.

Lohr, S. and X. Zhu (2015). Randomized Sequential Individual Assignment in Social Experiments: Evaluating the Design Options Prospectively. Sociological Methods and Research. [Advance online publication: December 27, 2015] doi: 10.1177/0049124115621332.

### Examples

1 | ```
bcdalloc(20,0.7)
``` |