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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

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

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

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

Probit analysis is similar to Logistic Regression Analysis.

Relationship between Logit and Probit

Logit and Probit is similar. Logit is wide.
logit and probit

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

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