Statistics with SAS

Technology Short Courses: Fall 2007 (Oct 29, 2007)

Kentaka Aruga

Object of the course

• Performing simple descriptive statistics (proc mean, proc freq, and proc corr)

• Performing basic test statistics (Chi-square test, T-test, F-test)

• Basic commands for regression analysis and how to export the result into a table(proc reg)

Section 1 Preparation

Getting data and importing data

Getting data

• Download the SAS command that will be used in this practice from

http://www.uri.edu/its/research/sasstat.txt

• Download the data file that will be used in this course from

http://www.uri.edu/its/research/auto.xls

http://www.uri.edu/its/research/vote.txt

• Save the files under ‘C:/’ drive of your windows computer.

Importing Excel file to SAS

• Open SAS program and copy and paste the following commands from the file you have just downloaded “sasstat.txt”:libname car ‘c:/’;proc import out= car.autodatafile=“c:/auto.xls”dbms=excel2000 replace;sheet=“auto”;getnames=yes;run;

Then highlight the command line and execute the command.

Proc import

• Look at the ‘trunk’ column

• Do you see an empty column?

• SAS determines the data type based on the most common data type in the first 8 rows. ‘trunk’ column has mixed data.(since the first eight columns are all zero, the remaining columns become all zero)

Proc import

• Add the following statementmixed = yes;

• Now the command line should look likeproc import out= car.autodatafile=“c:/auto.xls”dbms=excel2000 replace;sheet=“auto”;getnames=yes;mixed = yes;run;

• Execute this command

Section 2

Performing simple descriptive statistics (proc mean, proc freq, and proc corr)

How to perform simple descriptive statistics (Review from SAS basics course)

• How would you see the number of obvs, mean, std, min, and max of all numeric variables in SAS?

Ans. proc means data=car.auto;run;

• How do you analyze frequency of the variables?

Ans. proc freq data=car.auto;run;

Proc means• By default “proc means” provides the number of obvs, mean, std,

min, and max of all numeric variables proc means data=car.auto;run;

• Specifying a certain variable– var variable name ;

Q. How would you execute the mean procedure for the variables “price”, “mpg,” and “weight” ?

• Creating an output table– output out= file name

Q. How would you get the output for the mean procedure for the variables “price”, “mpg,” and “weight”?

Proc means (Answers)

proc means data=car.auto;

output out=car.means;

var price mpg weight;

run;

Proc freq• By default this procedure creates frequency tables for all var

iablesproc freq data=car.auto;run;

• Specifying a certain variable– tables variable name

Q. How would you execute the FREQ procedure for the variable “foreign”?

• Creating an output table– /out = file name

Q. How would you get the output for the FREQ procedure for the variable “foreign”?

Proc freq (Answers)

proc freq data=car.auto;

tables foreign /out=car.frn;

run;

Proc freq: Creating a two-way table

• How would you create a two-way

table using the FREQ procedure for the variables “rep78” and “foreign”?

Ans.

proc freq data=sasuser.auto;

tables rep78*foreign;

run;

Proc freq: two-way table

Total % (= 8/13)

Row % (= 8/9)

Column % (= 8/10)

Proc corr

• The CORR procedure generates ‘Simple Statistics’ based on non missing values, and ‘Pearson Correlation Coefficient’, an index that quantifies the linear relationship between a pair of variables

• Insignificant p-value indicates the lack of linear relationship between the two variables.

Proc corr

• Finding correlations between a pair of variables1) All variables

proc corr data=car.auto;run;

2) Three specific variablesproc corr data=car.auto;var price mpg weight;run;

Section 3

Performing basic test statistics

(Chi-square test, T-test, F-test)

Chi-square test of independence

• What is the Chi-square test of independence?Ans. It tests whether the variable in the row and column are independent or related

• What is the null hypothesis?Ans. The variables in the row and column are independent: there is no relationship between row and column frequencies

• The command for SAS to test this is provided in the option of “proc freq”. Simply use chisq.

• To display the expected cell frequency for each cell use the option “expected.”

Chi-square test of independence: exercise

There are 34 students in the classroom and there was a vote on whether they wanted to have a turtle in their classroom as a pet. The data file “vote.txt” contains the result of the vote (Yes=y, No=n), and gender of the students (male=m, female=f).

• Q1 Import the file “vote.txt” into SAS and name the variables “answers” and “gender.”

• Q2 Using the option “chisq,” test whether or not the answers to the vote and gender are associated with each other.

Answers

Q1 data vote;

infile 'c:/vote.txt';

input answers $ gender $;

run;

Q2 proc freq data=vote;

tables answers*gender /expected chisq;

run;

Results

(34)totalTable

(16)totalColumn)15(totalRowFreqExpect

What does the result tell you?

• The null hypothesis that the two variables are independent is rejected at even 1% significance level.

• The two variables “answers” and “gender” are associated with each other (They are dependent).

This is lower than 0.01

Proc ttest• This procedure is used to test the hypothesis of

equality of means for two normal populations from which independent samples have been obtained.

– Three cases in SAS• One-sample t-test

– Computes the sample mean of the variable and compares it with a given number.

• Two-sample t-test– Compares the mean of the first sample minus the

mean of the second sample to a given number.• Pair observations t-test

– Compares the mean of the differences in the observations to a given number.

Assumptions of “proc ttest”

• The observations are random samples drawn from normally distributed populations. This can be tested using the UNIVARIATE procedure – If the normality assumptions are not satisfied: use NPAR1WAY

procedure.• Two populations of a group comparison must be

independent. – If not independent, you should question the validity of a paired

comparison.• The default null hypothesis is set as equal to zero. To

change this you can use H0=‘number’.” e.g. h0=10• The default confidence level is 5%. To change this you can

use alpha=‘confidence level’.” e.g. alpha=0.01

Source: http://www.okstate.edu/sas/v8/saspdf/stat/chap67.pdf

Proc ttest: exercise

• How would you perform a t-test on mpg variable classified by foreign variable?

Hint: use “class” and “var” statement

• What will the null hypothesis be in this case?

Proc ttest (Cont’d)• The command

proc ttest data=car.auto;class foreign;var mpg;run;

– CLASS statement: contains a variable that distinguishes the groups being compared.

– VAR statement: specifies the response variable to be used in calculations.

• The null hypothesis

• The alternative hypothesis

0:H foreigndomestic0

0:H foreigndomestic1

• The first table shows the basic statistics• The second table is the t-test for equal mean. Before using this table

you need to look at the third table to determine if the assumption of equal variances is reasonable

• The third table is a test of equal variances• In this example the null hypothesis of equal variance is not rejected.• Thus you need to look at the “equal variance” in the second table. The

second table suggests there is not a difference in means across domestic and foreign car.

See here

High high p-value

Section 4

Basic commands for regression analysis and how to export the result into a table

(proc reg)

Regression analysis

• Regression analysis : finding a reasonable mathematical model of the relationship between a response variable (y) and a set of explanatory variables (x1, x2,…. xP)

• General model

0 1 1 2 2 p py x x x

Proc reg

• General commandproc reg data = file namemodel DV = IV ; run;DV: dependent variable IV: independent variable

• This procedure also does the following testing:– F-test: Tests the null hypothesis that none of the independent vari

ables has any effect– T-test

Tests for each IV the null hypothesis that the independent variable has no effect toward the dependent variable.

Proc reg: exercise

• Let ‘price’ be a response variable (dependent variable (DV)), and ‘mpg’ and ‘length’ be explanatory variables (independent variables (IV))

Q1 What will be the commands?

Q2 What null hypotheses will be tested?

Q3 Will the model be significant?

Proc reg: answers

Q1 proc reg data = car.auto;

model price = mpg length;

run;

Q2 F-test

T-test

0:0 iH 0:1 iH

00 price:H lengthmpgprice: 2101H

Proc reg

Q3

Proc reg: Confidence and prediction interval• Constructing 95% confidence and predict

ion interval by adding two options, ‘clm’ and ‘cli’

• How would you add these options in the case of previous model?proc reg data=car.auto;model price = mpg length / clm cli;run;

Proc reg: creating an output table

• Add “outest = file name” after the “proc reg” command

proc reg data=car.auto

outest=car.est1;

model price = mpg length /clm cli;

run;

quit;

• In order to see the output data file “car.est1” you need to add the statement “quit” in the end.

• You can drop the categories you do not want to see by using the “keep” or “drop” statemente.g. data car.est2 (keep=intercept mpg length);set car.est1;run;data car.est3 (drop=price _model_ _depvar_ _type_ _RMSE_);set car.est1;run;

Proc reg: creating an output table

• To see other outputs go to “Help” and type in “REG” and go into “The REG procedure.”

Click “Syntax”

Click Here

Exporting the output data to Excel

• General commandsproc export data = Name of the SAS data file

you are exportingoutfile = “The name of the drive or the pass to the folder of your computer”

dbms = excel2000 replace;run;

• How would you export the file “car.est2” into an Excel file?Ans. proc export data = car.est2

outfile = “c:/est.xls" dbms = excel2000 replace; run;

Useful supports: other useful sites

• Online SAS manuals

http://www.uri.edu/sasdoc

This will automatically link you to http://support.sas.com/documentation/onlinedoc/sas9doc.html

• Statbookstore: useful site for finding program examples

http://www.geocities.com/statbookstore/

For further Questions: kentaka@mail.uri.edu