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