SAS Output
The SAS System 236
11:25 Friday, June 26, 1998
Variable N Mean Std Dev Minimum Maximum
--------------------------------------------------------------------
AW 32 40.9184375 5.2845280 28.5556000 52.9545000
AN 32 41.6395438 5.1220170 31.1176000 54.3913000
CXEW 32 41.4576031 5.5310299 28.8856000 54.9234000
CXEN 32 41.3356469 6.0892496 26.8333000 55.4451000
--------------------------------------------------------------------
The SAS System 237
11:25 Friday, June 26, 1998
Detailed descriptive Statistics (each variable individually)
Because of the nature of SAS programming, the detailed descriptive statistics procedure includes normal probability plots and box plots for the individual variables: For interpreting the normal probability plots, In SAS the reference line is denoted by the "+" and the actual data points are plotted with a "*"
Univariate Procedure
Variable=AW
Moments
N 32 Sum Wgts 32
Mean 40.91844 Sum 1309.39
Std Dev 5.284528 Variance 27.92624
Skewness -0.26268 Kurtosis 0.555759
USS 54443.91 CSS 865.7133
CV 12.91478 Std Mean 0.934181
T:Mean=0 43.80138 Pr>|T| 0.0001
Num ^= 0 32 Num > 0 32
M(Sign) 16 Pr>=|M| 0.0001
Sgn Rank 264 Pr>=|S| 0.0001
Variable=AW
Quantiles(Def=5)
100% Max 52.9545 99% 52.9545
75% Q3 44.125 95% 49.7727
50% Med 41.39285 90% 47.0833
25% Q1 38.625 10% 33.7059
0% Min 28.5556 5% 30.1176
1% 28.5556
Range 24.3989
Q3-Q1 5.5
Mode 44.125
Univariate Procedure
Variable=AW
Extremes
Lowest Obs Highest Obs
28.5556( 18) 44.6667( 1)
30.1176( 28) 47.0833( 5)
33.3158( 15) 47.9048( 30)
33.7059( 19) 49.7727( 17)
34.7778( 4) 52.9545( 22)
Univariate Procedure
Variable=AW
Stem Leaf # Boxplot
5 03 2 0
4 5578 4 |
4 000112233334444 15 +--+--+
3 5689999 7 +-----+
3 034 3 0
2 9 1 0
----+----+----+----+
Multiply Stem.Leaf by 10**+1
Univariate Procedure
Variable=AW
Normal Probability Plot
52.5+ +++*++++
| ++++*+*+*+
| *********+** *
| ++*******+
| ++++*+*+**
27.5+++++*
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
Univariate Procedure
Variable=AN
Moments
N 32 Sum Wgts 32
Mean 41.63954 Sum 1332.465
Std Dev 5.122017 Variance 26.23506
Skewness 0.49411 Kurtosis 1.062256
USS 56296.54 CSS 813.2868
CV 12.30085 Std Mean 0.905453
T:Mean=0 45.98751 Pr>|T| 0.0001
Num ^= 0 32 Num > 0 32
M(Sign) 16 Pr>=|M| 0.0001
Sgn Rank 264 Pr>=|S| 0.0001
Univariate Procedure
Variable=AN
Quantiles(Def=5)
100% Max 54.3913 99% 54.3913
75% Q3 43.88095 95% 54.0952
50% Med 42.08335 90% 46.0833
25% Q1 38.2083 10% 34.4118
0% Min 31.1176 5% 34.1765
1% 31.1176
Range 23.2737
Q3-Q1 5.67265
Mode 42.6364
Univariate Procedure
Variable=AN
Extremes
Lowest Obs Highest Obs
31.1176( 18) 45.1304( 9)
34.1765( 19) 46.0833( 32)
34.3125( 15) 49.1739( 30)
34.4118( 28) 54.0952( 17)
37.1364( 4) 54.3913( 22)
Univariate Procedure
Variable=AN
Stem Leaf # Boxplot
54 14 2 0
52
50
48 2 1 |
46 1 1 |
44 0371 4 |
42 36668078 8 +-----+
40 31889 5 | + |
38 1390 4 +-----+
36 125 3 |
34 234 3 |
32 |
30 1 1 |
----+----+----+----+
Univariate Procedure
Variable=AN
Normal Probability Plot
55+ * * +
| ++++
| ++++
| +*++
| +++*
| ++*** *
43+ ***+***
| *****
| ****
| *+**
| * *+*
| ++++
31+ +*++
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
Univariate Procedure
Variable=CXEW
Moments
N 32 Sum Wgts 32
Mean 41.4576 Sum 1326.643
Std Dev 5.53103 Variance 30.59229
Skewness -0.10474 Kurtosis 0.750866
USS 55947.81 CSS 948.361
CV 13.34141 Std Mean 0.977757
T:Mean=0 42.40071 Pr>|T| 0.0001
Num ^= 0 32 Num > 0 32
M(Sign) 16 Pr>=|M| 0.0001
Sgn Rank 264 Pr>=|S| 0.0001
Univariate Procedure
Variable=CXEW
Quantiles(Def=5)
100% Max 54.9234 99% 54.9234
75% Q3 44.04185 95% 50.7373
50% Med 42.6907 90% 46.8628
25% Q1 38.2984 10% 34.6903
0% Min 28.8856 5% 30.0319
1% 28.8856
Range 26.0378
Q3-Q1 5.74345
Mode 43.0367
Univariate Procedure
Variable=CXEW
Extremes
Lowest Obs Highest Obs
28.8856( 18) 46.2482( 5)
30.0319( 15) 46.8628( 2)
33.6941( 28) 49.8551( 30)
34.6903( 19) 50.7373( 17)
35.2715( 4) 54.9234( 22)
Univariate Procedure
Variable=CXEW
Stem Leaf # Boxplot
5 5 1 0
5 01 2 |
4 5567 4 |
4 02223333333444 14 +--+--+
3 55788899 8 +-----+
3 04 2 |
2 9 1 0
----+----+----+----+
Multiply Stem.Leaf by 10**+1
Univariate Procedure
Variable=CXEW
Normal Probability Plot
57.5+ +
| *++++*+++
| ++++**+*+
42.5+ *************
| *+******+
| ++++*+*+*
27.5+++++*
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
Univariate Procedure
Variable=CXEN
Moments
N 32 Sum Wgts 32
Mean 41.33565 Sum 1322.741
Std Dev 6.08925 Variance 37.07896
Skewness -0.19067 Kurtosis 1.044184
USS 55825.79 CSS 1149.448
CV 14.73123 Std Mean 1.076437
T:Mean=0 38.40042 Pr>|T| 0.0001
Num ^= 0 32 Num > 0 32
M(Sign) 16 Pr>=|M| 0.0001
Sgn Rank 264 Pr>=|S| 0.0001
Univariate Procedure
Variable=CXEN
Quantiles(Def=5)
100% Max 55.4451 99% 55.4451
75% Q3 43.66425 95% 53.7414
50% Med 42.6035 90% 46.3137
25% Q1 38.9432 10% 31.9481
0% Min 26.8333 5% 29.4278
1% 26.8333
Range 28.6118
Q3-Q1 4.72105
Mode 42.6009
Variable=CXEN
Extremes
Lowest Obs Highest Obs
26.8333( 18) 45.1564( 1)
29.4278( 15) 46.3137( 5)
31.7301( 19) 49.8009( 30)
31.9481( 28) 53.7414( 22)
34.4035( 4) 55.4451( 17)
Univariate Procedure
Variable=CXEN
Stem Leaf # Boxplot
5 5 1 0
5 04 2 0
4 5556 4 |
4 00233333333344 14 +--+--+
3 888999 6 +-----+
3 224 3 0
2 79 2 0
----+----+----+----+
Multiply Stem.Leaf by 10**+1
Univariate Procedure
Variable=CXEN
Normal Probability Plot
57.5+ * +++
| +*++++++
| ++*+**+*
42.5+ ************
| +******+
| ++++*+**
27.5+++++*++ *
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
--------------------------------- NAME=an ----------------------------------
Univariate Procedure
Variable=RT
Moments
N 32 Sum Wgts 32
Mean 41.63954 Sum 1332.465
Std Dev 5.122017 Variance 26.23506
Skewness 0.49411 Kurtosis 1.062256
USS 56296.54 CSS 813.2868
CV 12.30085 Std Mean 0.905453
T:Mean=0 45.98751 Pr>|T| 0.0001
Num ^= 0 32 Num > 0 32
M(Sign) 16 Pr>=|M| 0.0001
Sgn Rank 264 Pr>=|S| 0.0001
--------------------------------- NAME=an ----------------------------------
Univariate Procedure
Variable=RT
Quantiles(Def=5)
100% Max 54.3913 99% 54.3913
75% Q3 43.88095 95% 54.0952
50% Med 42.08335 90% 46.0833
25% Q1 38.2083 10% 34.4118
0% Min 31.1176 5% 34.1765
1% 31.1176
Range 23.2737
Q3-Q1 5.67265
Mode 42.6364
--------------------------------- NAME=an ----------------------------------
Univariate Procedure
Variable=RT
Extremes
Lowest Obs Highest Obs
31.1176( 18) 45.1304( 9)
34.1765( 19) 46.0833( 32)
34.3125( 15) 49.1739( 30)
34.4118( 28) 54.0952( 17)
37.1364( 4) 54.3913( 22)
--------------------------------- NAME=an ----------------------------------
Univariate Procedure
Variable=RT
Stem Leaf # Boxplot
5 44 2 0
4 5569 4 |
4 012222333334444 15 +--+--+
3 7788899 7 +-----+
3 1444 4 |
----+----+----+----+
Multiply Stem.Leaf by 10**+1
--------------------------------- NAME=an ----------------------------------
Univariate Procedure
Variable=RT
Normal Probability Plot
52.5+ *++++*++++
| ++++**+*++
42.5+ *******+******
| +*+******
32.5+ +*++++*+*+*
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
--------------------------------- NAME=aw ----------------------------------
Univariate Procedure
Variable=RT
Moments
N 32 Sum Wgts 32
Mean 40.91844 Sum 1309.39
Std Dev 5.284528 Variance 27.92624
Skewness -0.26268 Kurtosis 0.555759
USS 54443.91 CSS 865.7133
CV 12.91478 Std Mean 0.934181
T:Mean=0 43.80138 Pr>|T| 0.0001
Num ^= 0 32 Num > 0 32
M(Sign) 16 Pr>=|M| 0.0001
Sgn Rank 264 Pr>=|S| 0.0001
--------------------------------- NAME=aw ----------------------------------
Univariate Procedure
Variable=RT
Quantiles(Def=5)
100% Max 52.9545 99% 52.9545
75% Q3 44.125 95% 49.7727
50% Med 41.39285 90% 47.0833
25% Q1 38.625 10% 33.7059
0% Min 28.5556 5% 30.1176
1% 28.5556
Range 24.3989
Q3-Q1 5.5
Mode 44.125
-------------------------------- NAME=aw ----------------------------------
Univariate Procedure
Variable=RT
Extremes
Lowest Obs Highest Obs
28.5556( 18) 44.6667( 1)
30.1176( 28) 47.0833( 5)
33.3158( 15) 47.9048( 30)
33.7059( 19) 49.7727( 17)
34.7778( 4) 52.9545( 22)
--------------------------------- NAME=aw ----------------------------------
Univariate Procedure
Variable=RT
Stem Leaf # Boxplot
5 03 2 0
4 5578 4 |
4 000112233334444 15 +--+--+
3 5689999 7 +-----+
3 034 3 0
2 9 1 0
----+----+----+----+
Multiply Stem.Leaf by 10**+1
--------------------------------- NAME=aw ----------------------------------
Univariate Procedure
Variable=RT
Normal Probability Plot
52.5+ +++*++++
| ++++*+*+*+
| *********+** *
| ++*******+
| ++++*+*+**
27.5+++++*
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
-------------------------------- NAME=cxen ---------------------------------
Univariate Procedure
Variable=RT
Moments
N 32 Sum Wgts 32
Mean 41.33565 Sum 1322.741
Std Dev 6.08925 Variance 37.07896
Skewness -0.19067 Kurtosis 1.044184
USS 55825.79 CSS 1149.448
CV 14.73123 Std Mean 1.076437
T:Mean=0 38.40042 Pr>|T| 0.0001
Num ^= 0 32 Num > 0 32
M(Sign) 16 Pr>=|M| 0.0001
Sgn Rank 264 Pr>=|S| 0.0001
-------------------------------- NAME=cxen ---------------------------------
Univariate Procedure
Variable=RT
Quantiles(Def=5)
100% Max 55.4451 99% 55.4451
75% Q3 43.66425 95% 53.7414
50% Med 42.6035 90% 46.3137
25% Q1 38.9432 10% 31.9481
0% Min 26.8333 5% 29.4278
1% 26.8333
Range 28.6118
Q3-Q1 4.72105
Mode 42.6009
-------------------------------- NAME=cxen ---------------------------------
Univariate Procedure
Variable=RT
Extremes
Lowest Obs Highest Obs
26.8333( 18) 45.1564( 1)
29.4278( 15) 46.3137( 5)
31.7301( 19) 49.8009( 30)
31.9481( 28) 53.7414( 22)
34.4035( 4) 55.4451( 17)
-------------------------------- NAME=cxen ---------------------------------
Univariate Procedure
Variable=RT
Stem Leaf # Boxplot
5 5 1 0
5 04 2 0
4 5556 4 |
4 00233333333344 14 +--+--+
3 888999 6 +-----+
3 224 3 0
2 79 2 0
----+----+----+----+
Multiply Stem.Leaf by 10**+1
-------------------------------- NAME=cxen ---------------------------------
Univariate Procedure
Variable=RT
Normal Probability Plot
57.5+ * +++
| +*++++++
| ++*+**+*
42.5+ ************
| +******+
| ++++*+**
27.5+++++*++ *
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
-------------------------------- NAME=cxew ---------------------------------
Univariate Procedure
Variable=RT
Moments
N 32 Sum Wgts 32
Mean 41.4576 Sum 1326.643
Std Dev 5.53103 Variance 30.59229
Skewness -0.10474 Kurtosis 0.750866
USS 55947.81 CSS 948.361
CV 13.34141 Std Mean 0.977757
T:Mean=0 42.40071 Pr>|T| 0.0001
Num ^= 0 32 Num > 0 32
M(Sign) 16 Pr>=|M| 0.0001
Sgn Rank 264 Pr>=|S| 0.0001
-------------------------------- NAME=cxew ---------------------------------
Univariate Procedure
Variable=RT
Quantiles(Def=5)
100% Max 54.9234 99% 54.9234
75% Q3 44.04185 95% 50.7373
50% Med 42.6907 90% 46.8628
25% Q1 38.2984 10% 34.6903
0% Min 28.8856 5% 30.0319
1% 28.8856
Range 26.0378
Q3-Q1 5.74345
Mode 43.0367
-------------------------------- NAME=cxew ---------------------------------
Univariate Procedure
Variable=RT
Extremes
Lowest Obs Highest Obs
28.8856( 18) 46.2482( 5)
30.0319( 15) 46.8628( 2)
33.6941( 28) 49.8551( 30)
34.6903( 19) 50.7373( 17)
35.2715( 4) 54.9234( 22)
-------------------------------- NAME=cxew ---------------------------------
Univariate Procedure
Variable=RT
Stem Leaf # Boxplot
5 5 1 0
5 01 2 |
4 5567 4 |
4 02223333333444 14 +--+--+
3 55788899 8 +-----+
3 04 2 |
2 9 1 0
----+----+----+----+
Multiply Stem.Leaf by 10**+1
-------------------------------- NAME=cxew ---------------------------------
Univariate Procedure
Variable=RT
Normal Probability Plot
57.5+ +
| *++++*+++
| ++++**+*+
42.5+ *************
| *+******+
| ++++*+*+*
27.5+++++*
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
Univariate Procedure
Schematic Plots
Variable=RT
60 +
| 0
| 0 0 0 0
50 + | | | |
| | | | |
| *-----* +-----+ *-----* *-----*
40 + | + | *--+--* +--+--+ | + |
| +-----+ | | +-----+
| | | 0 |
30 + | 0 0 0
| 0
|
20 +
------------+-----------+-----------+-----------+-----------
NAME an aw cxen cxew
With the box plots, SAS uses a plus sign (+) to mark where the mean of each group falls. In SAS , the median line is drawn with *'s at the ends and the 25th and 75th quantile lines are drawn with +'s at the ends. Here, for many of the groups, the quantile falls so close to the median that SAS could not always draw both the median and the quantiles. This is one of the drawbacks of a textual based output.
This is the portion of the output of the GLM procedure that is pertinent to repeated measures. SAS produces considerable output that is not needed for this analysis.
General Linear Models Procedure
Repeated Measures Analysis of Variance
Repeated Measures Level Information
Dependent Variable AW AN CXEW CXEN
Level of WORDTYPE 1 1 2 2
Level of PRIME 1 2 1 2
General Linear Models Procedure
Repeated Measures Analysis of Variance
Univariate Tests of Hypotheses for Within Subject Effects
Source: WORDTYPE
Adj Pr > F
DF Type III SS Mean Square F Value Pr > F G - G H - F
1 0.44281108 0.44281108 0.21 0.6468 . .
Source: Error(WORDTYPE)
DF Type III SS Mean Square
31 64.12305123 2.06848552
Source: PRIME
Adj Pr > F
DF Type III SS Mean Square F Value Pr > F G - G H - F
1 2.87184578 2.87184578 1.97 0.1703 . .
Source: Error(PRIME)
DF Type III SS Mean Square
31 45.17844844 1.45736930
Source: WORDTYPE*PRIME
Adj Pr > F
DF Type III SS Mean Square F Value Pr > F G - G H - F
1 5.68603503 5.68603503 4.72 0.0376 . .
Source: Error(WORDTYPE*PRIME)
DF Type III SS Mean Square
31 37.35101570 1.20487147
One sample t-test
How to do this
Analysis Variable : DIFF
N T Prob>|T|
--------------------------
32 2.1723730 0.0376
--------------------------
This is the portion of the output of the GLM procedure that contains the actual
tests associated with the between-within subjects ANOVA. Sections of the SAS output
that are not relevant are skipped.
How this was done.
Repeated Measures Analysis of Variance
Repeated Measures Level Information
Dependent Variable AW AN CXEW CXEN
Level of WORDTYPE 1 1 2 2
Level of PRIME 1 2 1 2
General Linear Models Procedure
Repeated Measures Analysis of Variance
Tests of Hypotheses for Between Subjects Effects
Source DF Type III SS Mean Square F Value Pr > F
SEX 1 49.9468 49.9468 0.42 0.5226
Error 30 3580.2096 119.3403
The SAS System 311
11:25 Friday, June 26, 1998
General Linear Models Procedure
Repeated Measures Analysis of Variance
Univariate Tests of Hypotheses for Within Subject Effects
Source: WORDTYPE
Adj Pr > F
DF Type III SS Mean Square F Value Pr > F G - G H - F
1 0.41933316 0.41933316 0.20 0.6608 . .
Source: WORDTYPE*SEX
Adj Pr > F
DF Type III SS Mean Square F Value Pr > F G - G H - F
1 0.07037487 0.07037487 0.03 0.8572 . .
Source: Error(WORDTYPE)
DF Type III SS Mean Square
30 64.05267636 2.13508921
The SAS System 312
11:25 Friday, June 26, 1998
General Linear Models Procedure
Repeated Measures Analysis of Variance
Univariate Tests of Hypotheses for Within Subject Effects
Source: PRIME
Adj Pr > F
DF Type III SS Mean Square F Value Pr > F G - G H - F
1 2.81167301 2.81167301 1.87 0.1817 . .
Source: PRIME*SEX
Adj Pr > F
DF Type III SS Mean Square F Value Pr > F G - G H - F
1 0.05408118 0.05408118 0.04 0.8509 . .
Source: Error(PRIME)
DF Type III SS Mean Square
30 45.12436725 1.50414558
The SAS System 313
11:25 Friday, June 26, 1998
General Linear Models Procedure
Repeated Measures Analysis of Variance
Univariate Tests of Hypotheses for Within Subject Effects
Source: WORDTYPE*PRIME
Adj Pr > F
DF Type III SS Mean Square F Value Pr > F G - G H - F
1 5.56550868 5.56550868 4.48 0.0426 . .
Source: WORDTYPE*PRIME*SEX
Adj Pr > F
DF Type III SS Mean Square F Value Pr > F G - G H - F
1 0.11018091 0.11018091 0.09 0.7678 . .
Source: Error(WORDTYPE*PRIME)
DF Type III SS Mean Square
30 37.24083479 1.24136116