Phi: Phi coefficient of correlation
In SICSresearch/IRTpp: Estimating IRT Parameters using the IRT Methodology

Description Usage Arguments Details Value References Examples

The phi coefficient of is a correlation coefficient applied to dichotomous data. Given a two x two table of counts | a | b | R1 | | c | d | R1 | |—|—|—-| |C1 | C2| n | or a vector c(a,b,c,d) of frequencies.

phi(x)

`x`	a 1 x 4 vector or a matrix 2 x 2 of frequencies.

The coefficient phi is calculated from

(ad - bc)/√{p_qp_2q_1q_2}

where $p_i$ and $q_i$ are the ratios of the dichotomous variables.

the value of the phi coefficient correlation.

Warrens, Matthijs (2008), On Association Coefficients for 2x2 Tables and Properties That Do Not Depend on the Marginal Distributions. Psychometrika, 73, 777-789.

Yule, G.U. (1912). On the methods of measuring the association between two attributes. Journal of the Royal Statistical Society, 75, 579-652.