# 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)

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