Many statistical tests make the assumption that the values for a particular variable are normally distributed.

However, often values are *not *normally distributed. One way to address this issue is to transform the variable by taking the log of each value.

By performing this transformation, a variable typically becomes closer to normally distributed.

The following example shows how to perform a log transformation on a variable in SAS.

**Example: Log Transformation in SAS**

Suppose we have the following dataset in SAS:

/*create dataset*/ data my_data; input x; datalines; 1 1 1 2 2 2 2 2 2 3 3 3 6 7 8 ; run; /*view dataset*/ proc print data=my_data;

We can use PROC UNIVARIATE to perform normality tests on the variable x to determine if it is normally distributed and also create a histogram to visualize the distribution of values:

**/*create histogram and perform normality tests*/
proc univariate data=my_data normal;
histogram x;
run;**

From the last table titled** Tests for Normality** we can see that the p-value for the Shapiro-Wilk test is less than .05, which provides strong evidence that the variable **x** is not normally distributed.

The histogram also shows that the distribution of values does not appear to be normally distributed:

We can attempt a **log transformation** on the original dataset to see if we can produce a dataset that is more normally distributed.

We can use the following code to create a new dataset in SAS in which we take the log of each of the original x values:

**/*use log transformation to create new dataset*/
data log_data;
set my_data;
x = log(x);
run;
/*view log transformed data*/
proc print data=log_data;**

We can then use **PROC UNIVARIATE** once again to perform normality tests on the transformed variable and produce a histogram as well:

**/*create histogram and perform normality tests*/
proc univariate data=log_data normal;
histogram x;
run;**

From the last table titled** Tests for Normality** we can see that the p-value for the Shapiro-Wilk test is now greater than .05.

The histogram also shows that the distribution of values is slightly more normally distributed than it was before the transformation:

Based on the results of the Shapiro-Wilk test and the histogram shown above, we would conclude that the log transformation created a variable that is much more normally distributed than the original variable.

**Additional Resources**

The following tutorials explain how to perform other common tasks in SAS:

How to Identify Outliers in SAS

How to Calculate Cook’s Distance in SAS

How to Create Histograms in SAS