# Regression – Implementing the Two Step Approach in Linear Regression Analysis

linearmeanregressionspsstwo-way

I have a continuous variable which is not normally distributed i want to transform it to normal using the two step approach method in the link below:

for transforming non-normally distributed continuous variables to
become normally distributed. Step 1 involves transforming the variable
into a percentile rank, which will result in uniformly distributed
probabilities. The second step applies the inverse-normal
transformation to the results of Step 1 to form a variable consisting
of normally distributed z-scores. The approach is little-known outside
the statistics literature, has been scarcely used in the social
sciences, and has not been used in any IS study. The article
illustrates how to implement the approach in Excel, SPSS, and SAS and
explains implications and recommendations for IS research.

https://aisel.aisnet.org/cais/vol28/iss1/4/

Is this method going to reorder the the observations?

• for each value, $$x_i$$ find it's rank $$r_i$$, i.e. the index of this value if $$x_i$$ values were sorted in increasing order,
• transform the ranks to quantile ranks by dividing the ranks by sample size $$q_i = r_i / N$$,
• use standard normal quantile function $$\Phi^{-1}$$ to calculate the $$z$$-scoares $$z_i = \Phi^{-1}(q_i)$$.
As you can see, this doesn't change anything about the ordering of the observations. The order would only change if you actually sorted the $$x_i$$ values, but this is not needed.