Percent2Probit: Probit transformation
In aravind-j/viabilitymetrics: Seed Viability Calculations and Curve Fitting

Description Usage Arguments Details Value References Examples

These functions transform data between percentage, probit and Normal Equivalent Deviate (NED) \insertCitebliss_method_1934,finney_probit_1952viabilitymetrics. \loadmathjax

PercentAdjust(percentage, n)

Percent2NED(percentage)

Percent2Probit(percentage)

Probit2NED(probit)

NED2Probit(NED)

NED2Percent(NED)

Probit2Percent(probit)

`percentage`	The percentage value.
`n`	Sample size for estimation of percentage.
`probit`	The probit value
`NED`	The NED value.

Probit transformation can be used to transform a sigmoid curve of percentage data to a linear one. The probit transformation is defined as \mjseqn\textrmNED + 5. However the two terms probit and NED are used interchangeably in literature.

NED function (\mjseqn\Phi^-1) is is the inverse of the cumulative distribution function (\mjseqn\Phi) of the standard normal distribution (\mjseqnz\sim N(0,1)) or the quantile function associated with the standard normal distribution.

For percentage \mjseqnp,

\mjsdeqn\textrm

NED(p)=\Phi^-1(p)= \sqrt2~\textrmerf^-1(2p-1)

and

\mjsdeqn\textrm

probit(p)=\textrmNED(p)+5

The PercentAdjust function adjusts the percentage values of 0 and 100 to \mjseqn100\times \dfrac0.25n and \mjseqn100\times \dfracn-0.25n respectively, according to the sample size \mjseqnn to avoid infinity values during probit transformation \insertCitemiller_estimation_1944viabilitymetrics.

The transformed value.

\insertRef

bliss_method_1934viabilitymetrics

\insertRef

miller_estimation_1944viabilitymetrics

\insertRef

finney_probit_1952viabilitymetrics

Percent2NED(0:100)
Percent2Probit(0:100)

Percent2NED(25)
Percent2Probit(25)
Percent2NED(25) +5
NED2Probit(-0.6744898)

# Percentage adjustment for 0 and 100
Percent2Probit(100)
Percent2Probit(0)
n = 50
Percent2Probit(PercentAdjust(100, n))
Percent2Probit(PercentAdjust(0, n))