Determining the Equation for Converting a Score to a Probability with a Logistic Distribution

probability =

= 1 / (1 + EXP((-1) * Y))

where

• The probability is 0.5 when Y = 0. Positive values for Y are associated with higher probabilities and negative values with smaller (opposite effects since multiply by -1).

Rearranging this:

Y =

= (-1) * LN((1 - (probability)) / (probability)) =

= LN ((probability) / (1 - (probability)))

Y =

= (constant) + ((coefficient) * (score))

coefficient =

= SLOPE((linear array of Y's), (linear array of scores))

constant =

= INTERCEPT((linear array of Y's). (linear array of scores))

Once these values are known:

probability =

= 1 / (1 + EXP((-1) * ((constant) + ((coefficient) * (score)))))