Original Program from program editor.
**********************************************;
*** t-tests done with SAS Proc Univariate ***;
**********************************************;
OPTIONS LS=99 PS=256 nocenter nonumber nodate;
TITLE1 'One sample t-tests';
DATA monkeys; INFILE CARDS MISSOVER;
TITLE2 'Analysis of Blood Pressure change in Rhesus Monkies';
INPUT BPChange;
CARDS; RUN;
0
4
-3
2
0
1
-4
5
-1
4
;
PROC PRINT DATA=monkeys;
TITLE3 'Raw data listing';
RUN;
PROC UNIVARIATE DATA=monkeys PLOT; VAR BPChange;
TITLE3 'Proc Univariate on Blood Pressure Change';
RUN;
PROC ttest DATA=monkeys; VAR BPChange;
TITLE3 'Proc TTEST on Blood Pressure Change';
RUN;
****************************************************************;
*** A shipment of apples are supposed to have a diameter of ***;
*** at least 2.5 inches. Sample 12 apples and test the ***;
*** hypothesis that the mean size is equal 2.5 inches. ***;
*** Reject the shipment if LESS THAN 2.5 inches. ***;
****************************************************************;
OPTIONS LS=99 PS=256 nocenter nonumber nodate;
TITLE1 'One sample t-tests';
TITLE2 'Test the diameter of apples against 2.5 inches';
data apples; infile cards missover;
LABEL diam = 'Diameter of the apple';
input diam; diff = diam - 2.5;
cards; run;
2.9
2.1
2.4
2.8
3.1
2.8
2.7
3.0
2.4
3.2
2.3
3.4
;
proc print data=apples; var diam diff;
TITLE3 'Raw data listing';
run;
proc univariate data=apples plot; var diam;
TITLE3 'Proc Univariate on Apple size';
run;
proc univariate data=apples plot; var diff;
TITLE3 'Proc Univariate on Apple size difference';
run;
proc ttest data=apples H0=2.5; var diam;
TITLE3 'Proc TTEST on Apple size';
run;
*********************************************************************;
*** Test for differences in seed production at two levels on a ***;
*** plant (top and bottom). We have ten vigorous plants bearing ***;
*** lucerne flowers. We want to test for differences in the ***;
*** number of seeds for the average of two pods in each position. ***;
*********************************************************************;
OPTIONS LS=99 PS=256 nocenter nonumber nodate;
TITLE1 'One sample t-tests';
TITLE2 'Test comparing seed production for lucerne flowers';
data flowers; infile cards missover;
TITLE3 'Seed production for top and bottom flowers';
LABEL top = 'Flowers from the top of the plant';
LABEL bottom = 'Flowers from the bottom of the plant';
LABEL diff = 'Difference between top and bottom';
input top bottom;
diff = top - bottom;
cards; run;
4.0 4.4
5.2 3.7
5.7 4.7
4.2 2.8
4.8 4.2
3.9 4.3
4.1 3.5
3.0 3.7
4.6 3.1
6.8 1.9
;
proc print data=flowers; var top bottom diff;
TITLE4'Raw data listing';
run;
proc univariate data=flowers plot; var diff;
TITLE4'Proc Univariate on difference between top and bottom';
run;
proc ttest data=flowers; paired top*bottom;
TITLE4'Proc Univariate on difference between top and bottom';
run;
Below is output from the SAS log (bold) and output from the SAS Output window.
1 **********************************************;
2 *** t-tests done with SAS Proc Univariate ***;
3 **********************************************;
4
5 OPTIONS LS=99 PS=256 nocenter nonumber nodate;
6 TITLE1 'One sample t-tests';
7
8 DATA monkeys; INFILE CARDS MISSOVER;
9 TITLE2 'Analysis of Blood Pressure change in Rhesus Monkies';
10 INPUT BPChange;
11 CARDS;
NOTE: The data set WORK.MONKEYS has 10 observations and 1 variables.
NOTE: DATA statement used (Total process time):
real time 0.04 seconds
cpu time 0.04 seconds
11 ! RUN;
22 ;
23 PROC PRINT DATA=monkeys;
24 TITLE3 'Raw data listing';
25 RUN;
NOTE: There were 10 observations read from the data set WORK.MONKEYS.
NOTE: The PROCEDURE PRINT printed page 1.
NOTE: PROCEDURE PRINT used (Total process time):
real time 0.01 seconds
cpu time 0.01 seconds
One sample t-tests
Analysis of Blood Pressure change in Rhesus Monkies
Raw data listing
Obs BPChange
1 0
2 4
3 -3
4 2
5 0
6 1
7 -4
8 5
9 -1
10 4
26
27 PROC UNIVARIATE DATA=monkeys PLOT; VAR BPChange;
28 TITLE3 'Proc Univariate on Blood Pressure Change';
29 RUN;
NOTE: The PROCEDURE UNIVARIATE printed page 2.
NOTE: PROCEDURE UNIVARIATE used (Total process time):
real time 0.07 seconds
cpu time 0.01 seconds
One sample t-tests
Analysis of Blood Pressure change in Rhesus Monkies
Proc Univariate on Blood Pressure Change
The UNIVARIATE Procedure
Variable: BPChange
Moments
N 10 Sum Weights 10
Mean 0.8 Sum Observations 8
Std Deviation 3.01109061 Variance 9.06666667
Skewness -0.157506 Kurtosis -0.9577747
Uncorrected SS 88 Corrected SS 81.6
Coeff Variation 376.386326 Std Error Mean 0.95219046
Basic Statistical Measures
Location Variability
Mean 0.800000 Std Deviation 3.01109
Median 0.500000 Variance 9.06667
Mode 0.000000 Range 9.00000
Interquartile Range 5.00000
NOTE: The mode displayed is the smallest of 2 modes with a count of 2.
Tests for Location: Mu0=0n
Test -Statistic- -----p Value------
Student's t t 0.840168 Pr > |t| 0.4226
Sign M 1 Pr >= |M| 0.7266
Signed Rank S 6.5 Pr >= |S| 0.3984
Quantiles (Definition 5)
Quantile Estimate
100% Max 5.0
99% 5.0
95% 5.0
90% 4.5
75% Q3 4.0
50% Median 0.5
25% Q1 -1.0
10% -3.5
5% -4.0
1% -4.0
0% Min -4.0
Extreme Observations
----Lowest---- ----Highest---
Value Obs Value Obs
-4 7 1 6
-3 3 2 4
-1 9 4 2
0 5 4 10
0 1 5 8
Stem Leaf Boxplot
4 000 3 +-----+
2 0 1 | |
0 000 3 *--+--*
-0 0 1 +-----+
-2 0 1 |
-4 0 1 |
----+----+----+----+
Normal Probability Plot
5+ * *++++*++
| *++++++
| * +*+*++
| ++*++++
| *++++*
-5+ +++++++
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
30 PROC ttest DATA=monkeys; VAR BPChange;
31 TITLE3 'Proc TTEST on Blood Pressure Change';
32 RUN;
NOTE: There were 10 observations read from the data set WORK.MONKEYS.
NOTE: The PROCEDURE TTEST printed page 3.
NOTE: PROCEDURE TTEST used (Total process time):
real time 0.01 seconds
cpu time 0.00 seconds
One sample t-tests
Analysis of Blood Pressure change in Rhesus Monkies
Proc TTEST on Blood Pressure Change
The TTEST Procedure
Statistics
Lower CL Upper CL Lower CL Upper CL
Variable N Mean Mean Mean Std Dev Std Dev Std Dev Std Err Minimum Maximum
BPChange 10 -1.354 0.8 2.954 2.0711 3.0111 5.4971 0.9522 -4 5
T-Tests
Variable DF t Value Pr > |t|
BPChange 9 0.84 0.4226
34
35 ****************************************************************;
36 *** A shipment of apples are supposed to have a diameter of ***;
37 *** at least 2.5 inches. Sample 12 apples and test the ***;
38 *** hypothesis that the mean size is equal 2.5 inches. ***;
39 *** Reject the shipment if LESS THAN 2.5 inches. ***;
40 ****************************************************************;
41
42 OPTIONS LS=99 PS=256 nocenter nonumber nodate;
43 TITLE1 'One sample t-tests';
44 TITLE2 'Test the diameter of apples against 2.5 inches';
45
46 data apples; infile cards missover;
47 LABEL diam = 'Diameter of the apple';
48 input diam; diff = diam - 2.5;
49 cards;
NOTE: The data set WORK.APPLES has 12 observations and 2 variables.
NOTE: DATA statement used (Total process time):
real time 0.03 seconds
cpu time 0.00 seconds
49 ! run;
62 ;
63 proc print data=apples; var diam diff;
64 TITLE3 'Raw data listing';
65 run;
NOTE: There were 12 observations read from the data set WORK.APPLES.
NOTE: The PROCEDURE PRINT printed page 4.
NOTE: PROCEDURE PRINT used (Total process time):
real time 0.01 seconds
cpu time 0.01 seconds
One sample t-tests
Test the diameter of apples against 2.5 inches
Raw data listing
Obs diam diff
1 2.9 0.4
2 2.1 -0.4
3 2.4 -0.1
4 2.8 0.3
5 3.1 0.6
6 2.8 0.3
7 2.7 0.2
8 3.0 0.5
9 2.4 -0.1
10 3.2 0.7
11 2.3 -0.2
12 3.4 0.9
66
67 proc univariate data=apples plot; var diam;
68 TITLE3 'Proc Univariate on Apple size';
69 run;
NOTE: The PROCEDURE UNIVARIATE printed page 5.
NOTE: PROCEDURE UNIVARIATE used (Total process time):
real time 0.01 seconds
cpu time 0.01 seconds
One sample t-tests
Test the diameter of apples against 2.5 inches
Proc Univariate on Apple size
The UNIVARIATE Procedure
Variable: diam (Diameter of the apple)
Moments
N 12 Sum Weights 12
Mean 2.75833333 Sum Observations 33.1
Std Deviation 0.39418116 Variance 0.15537879
Skewness -0.1184219 Kurtosis -0.8352969
Uncorrected SS 93.01 Corrected SS 1.70916667
Coeff Variation 14.2905557 Std Error Mean 0.1137903
Basic Statistical Measures
Location Variability
Mean 2.758333 Std Deviation 0.39418
Median 2.800000 Variance 0.15538
Mode 2.400000 Range 1.30000
Interquartile Range 0.65000
NOTE: The mode displayed is the smallest of 2 modes with a count of 2.
Tests for Location: Mu0=0n
Test -Statistic- -----p Value------
Student's t t 24.2405 Pr > |t| <.0001
Sign M 6 Pr >= |M| 0.0005
Signed Rank S 39 Pr >= |S| 0.0005
Quantiles (Definition 5)
Quantile Estimate
100% Max 3.40
99% 3.40
95% 3.40
90% 3.20
75% Q3 3.05
50% Median 2.80
25% Q1 2.40
10% 2.30
5% 2.10
1% 2.10
0% Min 2.10
Extreme Observations
----Lowest---- ----Highest---
Value Obs Value Obs
2.1 2 2.9 1
2.3 11 3.0 8
2.4 9 3.1 5
2.4 3 3.2 10
2.7 7 3.4 12
Stem Leaf Boxplot
34 0 1 |
32 0 1 |
30 00 2 +-----+
28 000 3 *-----*
26 0 1 | + |
24 00 2 +-----+
22 0 1 |
20 0 1 |
----+----+----+----+
Multiply Stem.Leaf by 10**-1
Normal Probability Plot
3.5+ *+++++
| *+++++
| * +*+++
| * *+*+++
| +*++++
| +*++*
| +++*+
2.1+ +++*+
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
70 proc univariate data=apples plot; var diff;
71 TITLE3 'Proc Univariate on Apple size difference';
72 run;
NOTE: The PROCEDURE UNIVARIATE printed page 6.
NOTE: PROCEDURE UNIVARIATE used (Total process time):
real time 0.01 seconds
cpu time 0.00 seconds
One sample t-tests
Test the diameter of apples against 2.5 inches
Proc Univariate on Apple size difference
The UNIVARIATE Procedure
Variable: diff
Moments
N 12 Sum Weights 12
Mean 0.25833333 Sum Observations 3.1
Std Deviation 0.39418116 Variance 0.15537879
Skewness -0.1184219 Kurtosis -0.8352969
Uncorrected SS 2.51 Corrected SS 1.70916667
Coeff Variation 152.586256 Std Error Mean 0.1137903
Basic Statistical Measures
Location Variability
Mean 0.25833 Std Deviation 0.39418
Median 0.30000 Variance 0.15538
Mode -0.10000 Range 1.30000
Interquartile Range 0.65000
NOTE: The mode displayed is the smallest of 2 modes with a count of 2.
Tests for Location: Mu0=0n
Test -Statistic- -----p Value------
Student's t t 2.270258 Pr > |t| 0.0443
Sign M 2 Pr >= |M| 0.3877
Signed Rank S 25 Pr >= |S| 0.0493
Quantiles (Definition 5)
Quantile Estimate
100% Max 0.90
99% 0.90
95% 0.90
90% 0.70
75% Q3 0.55
50% Median 0.30
25% Q1 -0.10
10% -0.20
5% -0.40
1% -0.40
0% Min -0.40
Extreme Observations
----Lowest---- ----Highest---
Value Obs Value Obs
-0.4 2 0.4 1
-0.2 11 0.5 8
-0.1 9 0.6 5
-0.1 3 0.7 10
0.2 7 0.9 12
Stem Leaf Boxplot
8 0 1 |
6 00 2 |
4 00 2 +-----+
2 000 3 *--+--*
0 | |
-0 00 2 +-----+
-2 0 1 |
-4 0 1 |
----+----+----+----+
Multiply Stem.Leaf by 10**-1
Normal Probability Plot
0.9+ ++*++
| *++*++
| *+*+++
| * *++++
| +++++
| *++*+
| *++++
-0.5+ +++++
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
73 proc ttest data=apples H0=2.5; var diam;
74 TITLE3 'Proc TTEST on Apple size';
75 run;
NOTE: There were 12 observations read from the data set WORK.APPLES.
NOTE: The PROCEDURE TTEST printed page 7.
NOTE: PROCEDURE TTEST used (Total process time):
real time 0.01 seconds
cpu time 0.01 seconds
One sample t-tests
Test the diameter of apples against 2.5 inches
Proc TTEST on Apple size
The TTEST Procedure
Statistics
Lower CL Upper CL Lower CL Upper CL
Variable N Mean Mean Mean Std Dev Std Dev Std Dev Std Err Minimum Maximum
diam 12 2.5079 2.7583 3.0088 0.2792 0.3942 0.6693 0.1138 2.1 3.4
T-Tests
Variable DF t Value Pr > |t|
diam 11 2.27 0.0443
77
78 *********************************************************************;
79 *** Test for differences in seed production at two levels on a ***;
80 *** plant (top and bottom). We have ten vigorous plants bearing ***;
81 *** lucerne flowers. We want to test for differences in the ***;
82 *** number of seeds for the average of two pods in each position. ***;
83 *********************************************************************;
84
85 OPTIONS LS=99 PS=256 nocenter nonumber nodate;
86 TITLE1 'One sample t-tests';
87 TITLE2 'Test comparing seed production for lucerne flowers';
88
89 data flowers; infile cards missover;
90 TITLE3 'Seed production for top and bottom flowers';
91 LABEL top = 'Flowers from the top of the plant';
92 LABEL bottom = 'Flowers from the bottom of the plant';
93 LABEL diff = 'Difference between top and bottom';
94 input top bottom;
95 diff = top - bottom;
96 cards;
NOTE: The data set WORK.FLOWERS has 10 observations and 3 variables.
NOTE: DATA statement used (Total process time):
real time 0.01 seconds
cpu time 0.01 seconds
96 ! run;
107 ;
108 proc print data=flowers; var top bottom diff;
109 TITLE4'Raw data listing';
110 run;
NOTE: There were 10 observations read from the data set WORK.FLOWERS.
NOTE: The PROCEDURE PRINT printed page 8.
NOTE: PROCEDURE PRINT used (Total process time):
real time 0.00 seconds
cpu time 0.00 seconds
One sample t-tests
Test comparing seed production for lucerne flowers
Seed production for top and bottom flowers
Raw data listing
Obs top bottom diff
1 4.0 4.4 -0.4
2 5.2 3.7 1.5
3 5.7 4.7 1.0
4 4.2 2.8 1.4
5 4.8 4.2 0.6
6 3.9 4.3 -0.4
7 4.1 3.5 0.6
8 3.0 3.7 -0.7
9 4.6 3.1 1.5
10 6.8 1.9 4.9
111
112 proc univariate data=flowers plot; var diff;
113 TITLE4'Proc Univariate on difference between top and bottom';
114 run;
NOTE: The PROCEDURE UNIVARIATE printed page 9.
NOTE: PROCEDURE UNIVARIATE used (Total process time):
real time 0.01 seconds
cpu time 0.00 seconds
One sample t-tests
Test comparing seed production for lucerne flowers
Seed production for top and bottom flowers
Proc Univariate on difference between top and bottom
The UNIVARIATE Procedure
Variable: diff (Difference between top and bottom)
Moments
N 10 Sum Weights 10
Mean 1 Sum Observations 10
Std Deviation 1.59861051 Variance 2.55555556
Skewness 1.66938453 Kurtosis 3.93459317
Uncorrected SS 33 Corrected SS 23
Coeff Variation 159.861051 Std Error Mean 0.50552503
Basic Statistical Measures
Location Variability
Mean 1.000000 Std Deviation 1.59861
Median 0.800000 Variance 2.55556
Mode 0.600000 Range 5.60000
Interquartile Range 1.90000
Tests for Location: Mu0=0n
Test -Statistic- -----p Value------
Student's t t 1.978141 Pr > |t| 0.0793
Sign M 2 Pr >= |M| 0.3438
Signed Rank S 19.5 Pr >= |S| 0.0469
Quantiles (Definition 5)
Quantile Estimate
100% Max 4.90
99% 4.90
95% 4.90
90% 3.20
75% Q3 1.50
50% Median 0.80
25% Q1 -0.40
10% -0.55
5% -0.70
1% -0.70
0% Min -0.70
Extreme Observations
----Lowest---- ----Highest---
Value Obs Value Obs
-0.7 8 1.0 3
-0.4 1 1.4 4
-0.4 6 1.5 9
0.6 7 1.5 2
0.6 5 4.9 10
Stem Leaf Boxplot
4 9 1 0
3
2
1 0455 4 +--+--+
0 66 2 *-----*
-0 744 3 +-----+
----+----+----+----+
Normal Probability Plot
4.5+ * +++++++
| ++++++
| ++++++
| +*++*++* *
| ++*++*
-0.5+ * ++*++*
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
115 proc ttest data=flowers; paired top*bottom;
116 TITLE4'Proc Univariate on difference between top and bottom';
117 run;
NOTE: There were 10 observations read from the data set WORK.FLOWERS.
NOTE: The PROCEDURE TTEST printed page 10.
NOTE: PROCEDURE TTEST used (Total process time):
real time 0.00 seconds
cpu time 0.00 seconds
118
NOTE: SAS Institute Inc., SAS Campus Drive, Cary, NC USA 27513-2414
NOTE: The SAS System used:
real time 7.03 seconds
cpu time 0.48 seconds
One sample t-tests
Test comparing seed production for lucerne flowers
Seed production for top and bottom flowers
Proc Univariate on difference between top and bottom
The TTEST Procedure
Statistics
Lower CL Upper CL Lower CL Upper CL
Difference N Mean Mean Mean Std Dev Std Dev Std Dev Std Err
top - bottom 10 -0.144 1 2.1436 1.0996 1.5986 2.9184 0.5055
T-Tests
Difference DF t Value Pr > |t|
top - bottom 9 1.98 0.0793