Hardness of Alloys from four Different Processes -- YOURNAME 1 Horizontal Bar Charts for alloy hardnesses Bar chart by `subgroup' 00:15 Tuesday, September 20, 2005 (Treatments are A,B,C,D) hardness Cum. Cum. Midpoint Freq Freq Percent Percent | 100 |DD 1 1 5.00 5.00 | 140 |DDDD 2 3 10.00 15.00 | 180 |AAAABBBBBBBBDD 7 10 35.00 50.00 | 220 |AAAAAABBBBCCCCCCDD 9 19 45.00 95.00 | 260 |CC 1 20 5.00 100.00 | ----+---+---+---+-- 2 4 6 8 Frequency Symbol treat Symbol treat Symbol treat Symbol treat A A B B C C D D Hardness of Alloys from four Different Processes -- YOURNAME 2 Horizontal Bar Charts for alloy hardnesses Bar chart by `group' 00:15 Tuesday, September 20, 2005 (Treatments are A,B,C,D) This output gives a clearer picture of the relative treatment-group variances. treat hardness Cum. Cum. Midpoint Freq Freq Percent Percent | A 100 | 0 0 0.00 0.00 140 | 0 0 0.00 0.00 180 |********** 2 2 10.00 10.00 220 |*************** 3 5 15.00 25.00 260 | 0 5 0.00 25.00 | B 100 | 0 5 0.00 25.00 140 | 0 5 0.00 25.00 180 |******************** 4 9 20.00 45.00 220 |********** 2 11 10.00 55.00 260 | 0 11 0.00 55.00 | C 100 | 0 11 0.00 55.00 140 | 0 11 0.00 55.00 180 | 0 11 0.00 55.00 220 |*************** 3 14 15.00 70.00 260 |***** 1 15 5.00 75.00 | D 100 |***** 1 16 5.00 80.00 140 |********** 2 18 10.00 90.00 180 |***** 1 19 5.00 95.00 220 |***** 1 20 5.00 100.00 260 | 0 20 0.00 100.00 | -----+----+----+----+ 1 2 3 4 Frequency Hardness of Alloys from four Different Processes -- YOURNAME 3 ONE-WAY ANOVA ANALYSIS 00:15 Tuesday, September 20, 2005 Also display treatment means and save residuals The GLM Procedure Class Level Information Class Levels Values treat 4 A B C D Number of Observations Read 20 Number of Observations Used 20 Hardness of Alloys from four Different Processes -- YOURNAME 4 ONE-WAY ANOVA ANALYSIS 00:15 Tuesday, September 20, 2005 Also display treatment means and save residuals The GLM Procedure Dependent Variable: hardness Sum of Source DF Squares Mean Square F Value Pr > F Model 3 13334.46667 4444.82222 5.32 0.0098 Error 16 13365.73333 835.35833 Corrected Total 19 26700.20000 R-Square Coeff Var Root MSE hardness Mean 0.499414 14.84467 28.90257 194.7000 Source DF Type I SS Mean Square F Value Pr > F treat 3 13334.46667 4444.82222 5.32 0.0098 Source DF Type III SS Mean Square F Value Pr > F treat 3 13334.46667 4444.82222 5.32 0.0098 Hardness of Alloys from four Different Processes -- YOURNAME 5 ONE-WAY ANOVA ANALYSIS 00:15 Tuesday, September 20, 2005 Also display treatment means and save residuals The GLM Procedure Level of -----------hardness---------- treat N Mean Std Dev A 5 204.400000 26.5951123 B 6 190.666667 18.1181309 C 4 234.000000 26.9938265 D 5 158.400000 40.9548532 Hardness of Alloys from four Different Processes -- YOURNAME 6 THE CURRENT DATASET AS SAS SEES IT 00:15 Tuesday, September 20, 2005 Note the two extra columns for means and residuals treat hardness means resid A 166 204.400 -38.4000 A 194 204.400 -10.4000 A 211 204.400 6.6000 A 213 204.400 8.6000 A 238 204.400 33.6000 B 169 190.667 -21.6667 B 175 190.667 -15.6667 B 185 190.667 -5.6667 B 195 190.667 4.3333 B 202 190.667 11.3333 B 218 190.667 27.3333 C 205 234.000 -29.0000 C 227 234.000 -7.0000 C 234 234.000 0.0000 C 270 234.000 36.0000 D 102 158.400 -56.4000 D 145 158.400 -13.4000 D 148 158.400 -10.4000 D 195 158.400 36.6000 D 202 158.400 43.6000 Hardness of Alloys from four Different Processes -- YOURNAME 7 PROC UNIVARIATE: Testing for normality 00:15 Tuesday, September 20, 2005 The W (Shapiro-Wilk) test tests for normality The P-value is Prob(W(rand) |t| 1.0000 Sign M -0.5 Pr >= |M| 1.0000 Signed Rank S -3 Pr >= |S| 0.9138 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.969819 Pr < W 0.7510 Kolmogorov-Smirnov D 0.098626 Pr > D >0.1500 Cramer-von Mises W-Sq 0.034884 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.249268 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 43.60000 99% 43.60000 95% 40.10000 90% 36.30000 75% Q3 19.33333 50% Median -2.83333 25% Q1 -14.53333 Hardness of Alloys from four Different Processes -- YOURNAME 8 PROC UNIVARIATE: Testing for normality 00:15 Tuesday, September 20, 2005 The W (Shapiro-Wilk) test tests for normality The P-value is Prob(W(rand) Chi-Square 0.0269