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

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 printdata=my_data;

We can use 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 univariatedata=my_data normal; 
    histogram x;
run;

From the last table titled Tests for Normality we can see that the 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 printdata=log_data;

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

From the last table titled Tests for Normality we can see that the 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.

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