# Logit Transformation and Probit Transformation

The range of probibability data is from 0 to 1.

Logit transformation is known as a better method to deal with probability data in
Multi-Variable Analysis
than to use raw data.

##
Logit Transformation

Logit = log( p / (1 - p))

p is the probabitity.
The bottom of log is the number of Napier (=2.71,,,)
This transformation of p is called "Logit Transformation".

By the function of Excel

=Ln(p/(1-p)).

The scatter plot of p and logit shows a curve.
Histgram of logit is similar to normal distribution.

Famous method of
Multi-Variable Analysis
is
Logistic Regression Analysis.

##
Probit Transformation

Probit is the nunber that deal with probability as the part of
standard normal distribution.

By the function of Excel

=norminv(p,0,1.

The scatter plot of p and probit shows a curve.
Histgram of probit shows standard normal distribution.

Probit analysis is similar to
Logistic Regression Analysis.

##
Relationship between Logit and Probit

Logit and Probit is similar.
Logit is wide.

If we use 5 as the bottom of log of logit, the trasnformation is more similar to probit.
By the function of Excel

=log(p/(1-p),**5**)

NEXT Odds Ratio