## A macro to execute PROC TTEST for multiple binary grouping variables in SAS (and sorting t-test statistics by their absolute values)

In SAS, you can perform PROC TTEST for multiple numeric variables in the same procedure.  Here is an example using the built-in data set SASHELP.BASEBALL; I will compare the number of at-bats and number of walks between the American League and the National League.

proc ttest
data = sashelp.baseball;
class League;
var nAtBat nBB;
ods select ttests;
run;

Here are the resulting tables.

Method Variances DF t Value Pr > |t|
Pooled Equal 320 2.05 0.0410
Satterthwaite Unequal 313.66 2.06 0.04

Method Variances DF t Value Pr > |t|
Pooled Equal 320 0.85 0.3940
Satterthwaite Unequal 319.53 0.86 0.3884

What if you want to perform PROC TTEST for multiple grouping (a.k.a. classification) variables?  You cannot put more than one variable in the CLASS statement, so you would have to run PROC TTEST separately for each binary grouping variable.  If you do put LEAGUE and DIVISION in the same CLASS statement, here is the resulting log.

1303 proc ttest
1304 data = sashelp.baseball;
1305 class league division;
--------
22
202
ERROR 22-322: Expecting ;.
ERROR 202-322: The option or parameter is not recognized and will be ignored.
1306 var natbat;
1307 ods select ttests;
1308 run;

There is no syntax in PROC TTEST to use multiple grouping variables at the same time, so this tutorial provides a macro to do so.  There are several nice features about my macro:

1. It allows you to use multiple grouping variables at the same time.
2. It sorts the t-test statistics by their absolute values within each grouping variable.
3. It shows the name of each continuous variable in the output table, unlike the above output.

Here is its basic skeleton.

## Remove leading blanks when creating macro variables using PROC SQL in SAS

I regularly use PROC SQL to create macro variables in SAS, and I recently noticed a strange phenomenon when resolving a macro variable within double quotation marks in the title of a plot.  Thankfully, I was able to replicate this problem using the SASHELP.BASEBALL data set, which is publicly available.  I was then able to send the code and the strange result to SAS Technical Support for their examination.

proc sql;
select count(name)
into   :hitters_100plusHR
from   sashelp.baseball
where  CrHome > 100;
quit;

proc sgplot
data = sashelp.baseball;
histogram Salary;
title1 'Distribution of salaries';
title2 "Restricted to the &hitters_100plusHR hitters with more than 100 career home runs";
run;

Here is the resulting plot.  Notice the extra spaces before “72” in the title of the plot.

SAS Technical Support informed me that

• this problem is commonly known.
• there is no way of predicting when it will occur
• for now, the best way to deal with it is to remove the leading blanks using one of several ways.

## A SAS macro to automatically label variables using another data set

#### Introduction

When I write SAS programs, I usually export the analytical results into an output that a client will read.  I often cannot show the original variable names in these outputs; there are 2 reasons for this:

• The maximal length of a SAS variable’s name is 32 characters, whereas the description of the variable can be much longer.  This is the case for my current job in marketing analytics.
• Only letters, numbers, and underscores are allowed in a SAS variable’s name.  Spaces and special characters are not allowed.  Thus, if a variable’s name is quite long and complicated to describe, then the original variable name would be not suitable for presentation or awkward to read.  It may be so abbreviated that it is devoid of practical meaning.

This is why labelling variables can be a good idea.  However, I usually label variables manually in a DATA step or within PROC SQL, which can be very slow and prone to errors.  I recently worked on a data set with 193 variables, most of which require long descriptions to understand what they mean.  Labelling them individually and manually was not a realistic method, so I sought an automated or programmatic way to do so.

## Sorting correlation coefficients by their magnitudes in a SAS macro

#### Theoretical Background

Many statisticians and data scientists use the correlation coefficient to study the relationship between 2 variables.  For 2 random variables, $X$ and $Y$, the correlation coefficient between them is defined as their covariance scaled by the product of their standard deviations.  Algebraically, this can be expressed as

$\rho_{X, Y} = \frac{Cov(X, Y)}{\sigma_X \sigma_Y} = \frac{E[(X - \mu_X)(Y - \mu_Y)]}{\sigma_X \sigma_Y}$.

In real life, you can never know what the true correlation coefficient is, but you can estimate it from data.  The most common estimator for $\rho$ is the Pearson correlation coefficient, which is defined as the sample covariance between $X$ and $Y$ divided by the product of their sample standard deviations.  Since there is a common factor of

$\frac{1}{n - 1}$

in the numerator and the denominator, they cancel out each other, so the formula simplifies to

$r_P = \frac{\sum_{i = 1}^{n}(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i = 1}^{n}(x_i - \bar{x})^2 \sum_{i = 1}^{n}(y_i - \bar{y})^2}}$.

In predictive modelling, you may want to find the covariates that are most correlated with the response variable before building a regression model.  You can do this by

1. computing the correlation coefficients
2. obtaining their absolute values
3. sorting them by their absolute values.