MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 1 VISUALIZE THE DATA BEFORE PROCEEDING: 04:19 Tuesday, September 27, 2005 Frequency 15 + EEEEE EEEEE | EEEEE EEEEE | EEEEE DDDDD | DDDDD DDDDD | DDDDD CCCCC 10 + DDDDD CCCCC | DDDDD CCCCC | EEEEE DDDDD CCCCC | EEEEE CCCCC BBBBB | EEEEE CCCCC BBBBB 5 + DDDDD BBBBB BBBBB BBBBB | DDDDD BBBBB AAAAA BBBBB | CCCCC BBBBB AAAAA AAAAA | CCCCC BBBBB AAAAA AAAAA | EEEEE CCCCC AAAAA AAAAA AAAAA AAAAA ------------------------------------------------------------------ 125 150 175 200 225 250 yy Midpoint Symbol treat Symbol treat Symbol treat A Trt1 B Trt2 C Trt3 D Trt4 E Trt5 MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 2 LIST TREATMENT MEANS AND STANDARD DEVIATIONS: 04:19 Tuesday, September 27, 2005 The MEANS Procedure Analysis Variable : yy N treat Obs N Mean Std Dev Minimum Maximum ------------------------------------------------------------------------- Trt1 9 9 210.0000000 19.7040605 183.0000000 246.0000000 Trt2 9 9 200.3333333 23.2540319 171.0000000 237.0000000 Trt3 9 9 178.7777778 22.3482537 148.0000000 208.0000000 Trt4 9 9 175.7777778 16.2617479 150.0000000 203.0000000 Trt5 9 9 164.6666667 22.5000000 118.0000000 193.0000000 ------------------------------------------------------------------------- MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 3 WHICH TREATMENT DIFFERENCES ARE SIGNIFICANTLY DIFFERENT? MULTIPLE COMPARISON TESTS: 04:19 Tuesday, September 27, 2005 The GLM Procedure Class Level Information Class Levels Values treat 5 Trt1 Trt2 Trt3 Trt4 Trt5 Number of Observations Read 45 Number of Observations Used 45 MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 4 WHICH TREATMENT DIFFERENCES ARE SIGNIFICANTLY DIFFERENT? MULTIPLE COMPARISON TESTS: 04:19 Tuesday, September 27, 2005 The GLM Procedure Dependent Variable: yy Sum of Source DF Squares Mean Square F Value Pr > F Model 4 12538.53333 3134.63333 7.13 0.0002 Error 40 17593.11111 439.82778 Corrected Total 44 30131.64444 R-Square Coeff Var Root MSE yy Mean 0.416125 11.28070 20.97207 185.9111 Source DF Type I SS Mean Square F Value Pr > F treat 4 12538.53333 3134.63333 7.13 0.0002 Source DF Type III SS Mean Square F Value Pr > F treat 4 12538.53333 3134.63333 7.13 0.0002 MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 5 WHICH TREATMENT DIFFERENCES ARE SIGNIFICANTLY DIFFERENT? MULTIPLE COMPARISON TESTS: 04:19 Tuesday, September 27, 2005 The GLM Procedure t Tests (LSD) for yy NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 40 Error Mean Square 439.8278 Critical Value of t 2.02108 Least Significant Difference 19.981 Means with the same letter are not significantly different. t G r o u p i n g Mean N treat A 210.000 9 Trt1 A A 200.333 9 Trt2 B 178.778 9 Trt3 B B 175.778 9 Trt4 B B 164.667 9 Trt5 MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 6 WHICH TREATMENT DIFFERENCES ARE SIGNIFICANTLY DIFFERENT? MULTIPLE COMPARISON TESTS: 04:19 Tuesday, September 27, 2005 The GLM Procedure Duncan's Multiple Range Test for yy NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 40 Error Mean Square 439.8278 Number of Means 2 3 4 5 Critical Range 19.98 21.01 21.68 22.17 Means with the same letter are not significantly different. D u n c a n G r o u p i n g Mean N treat A 210.000 9 Trt1 A A 200.333 9 Trt2 B 178.778 9 Trt3 B B 175.778 9 Trt4 B B 164.667 9 Trt5 MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 7 WHICH TREATMENT DIFFERENCES ARE SIGNIFICANTLY DIFFERENT? MULTIPLE COMPARISON TESTS: 04:19 Tuesday, September 27, 2005 The GLM Procedure Student-Newman-Keuls Test for yy NOTE: This test controls the Type I experimentwise error rate under the complete null hypothesis but not under partial null hypotheses. Alpha 0.05 Error Degrees of Freedom 40 Error Mean Square 439.8278 Number of Means 2 3 4 5 Critical Range 19.981262 24.062536 26.499513 28.236283 Means with the same letter are not significantly different. S N K G r o u p i n g Mean N treat A 210.000 9 Trt1 A A 200.333 9 Trt2 B 178.778 9 Trt3 B B 175.778 9 Trt4 B B 164.667 9 Trt5 MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 8 WHICH TREATMENT DIFFERENCES ARE SIGNIFICANTLY DIFFERENT? MULTIPLE COMPARISON TESTS: 04:19 Tuesday, September 27, 2005 The GLM Procedure Tukey's Studentized Range (HSD) Test for yy NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than REGWQ. Alpha 0.05 Error Degrees of Freedom 40 Error Mean Square 439.8278 Critical Value of Studentized Range 4.03913 Minimum Significant Difference 28.236 Means with the same letter are not significantly different. Tukey Groupi ng Mean N treat A 210.000 9 Trt1 A B A 200.333 9 Trt2 B B C 178.778 9 Trt3 B C B C 175.778 9 Trt4 C C 164.667 9 Trt5 MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 9 WHICH TREATMENT DIFFERENCES ARE SIGNIFICANTLY DIFFERENT? MULTIPLE COMPARISON TESTS: 04:19 Tuesday, September 27, 2005 The GLM Procedure Scheffe's Test for yy NOTE: This test controls the Type I experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 40 Error Mean Square 439.8278 Critical Value of F 2.60597 Minimum Significant Difference 31.919 Means with the same letter are not significantly different. Scheffe Grouping Mean N treat A 210.000 9 Trt1 A B A 200.333 9 Trt2 B A B A C 178.778 9 Trt3 B C B C 175.778 9 Trt4 C C 164.667 9 Trt5 MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 10 WHICH TREATMENT DIFFERENCES ARE SIGNIFICANTLY DIFFERENT? MULTIPLE COMPARISON TESTS: 04:19 Tuesday, September 27, 2005 The GLM Procedure t Tests (LSD) for yy NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.005 Error Degrees of Freedom 40 Error Mean Square 439.8278 Critical Value of t 2.97117 Least Significant Difference 29.374 Means with the same letter are not significantly different. t Groupi ng Mean N treat A 210.000 9 Trt1 A B A 200.333 9 Trt2 B B C 178.778 9 Trt3 B C B C 175.778 9 Trt4 C C 164.667 9 Trt5 MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 11 WHICH TREATMENT DIFFERENCES ARE SIGNIFICANTLY DIFFERENT? MULTIPLE COMPARISON TESTS: 04:19 Tuesday, September 27, 2005 The GLM Procedure Dependent Variable: yy Contrast DF Contrast SS Mean Square F Value Pr > F C1 with av of C3 C4 1 6424.462963 6424.462963 14.61 0.0005 Av of C3 C4 with C5 1 954.240741 954.240741 2.17 0.1486 C2 with av C3 C4 C5 1 5015.703704 5015.703704 11.40 0.0016 MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 12 ARE TREATMENT-GROUP VARIANCES THE SAME? 04:19 Tuesday, September 27, 2005 PLOT OF RESIDUALS: Plot of resid*treat. Symbol is value of trtsym. resid | 40 + | 1 2 | | 3 4 5 | 3 5 20 + | 1 3 5 | 1 4 | 1 2 4 | 4 5 0 + 1 2 3 5 | 2 3 5 | 4 | 1 2 | 2 4 5 -20 + 1 2 3 | 3 4 | 1 2 | 3 | -40 + | | 5 | | -60 + | ---+------------+------------+------------+------------+-- Trt1 Trt2 Trt3 Trt4 Trt5 treat NOTE: 6 obs hidden. MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 13 PROC UNIVARIATE: Testing normality 04:19 Tuesday, September 27, 2005 LOOK FOR W STATISTIC The UNIVARIATE Procedure Variable: resid Moments N 45 Sum Weights 45 Mean 0 Sum Observations 0 Std Deviation 19.9960855 Variance 399.843434 Skewness 0.0286183 Kurtosis -0.4927882 Uncorrected SS 17593.1111 Corrected SS 17593.1111 Coeff Variation . Std Error Mean 2.98084043 Basic Statistical Measures Location Variability Mean 0.0000 Std Deviation 19.99609 Median -0.7778 Variance 399.84343 Mode -25.7778 Range 83.33333 Interquartile Range 28.55556 NOTE: The mode displayed is the smallest of 3 modes with a count of 2. Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 0 Pr > |t| 1.0000 Sign M -0.5 Pr >= |M| 1.0000 Signed Rank S -8.5 Pr >= |S| 0.9248 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.981691 Pr < W 0.6886 Kolmogorov-Smirnov D 0.065958 Pr > D >0.1500 Cramer-von Mises W-Sq 0.023329 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.206127 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 36.666667 99% 36.666667 95% 36.000000 90% 28.333333 75% Q3 14.222222 50% Median -0.777778 25% Q1 -14.333333 10% -25.777778 MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 14 PROC UNIVARIATE: Testing normality 04:19 Tuesday, September 27, 2005 LOOK FOR W STATISTIC The UNIVARIATE Procedure Variable: resid Quantiles (Definition 5) Quantile Estimate 5% -29.333333 1% -46.666667 0% Min -46.666667 Extreme Observations ------Lowest----- -----Highest----- Value Obs Value Obs -46.6667 37 28.3333 45 -30.7778 19 29.2222 27 -29.3333 10 36.0000 9 -27.0000 1 36.6667 17 -25.7778 28 36.6667 18 Stem Leaf # Boxplot 3 677 3 | 3 | 2 5789 4 | 2 4 1 | 1 5 1 | 1 03444 5 +-----+ 0 7789 4 | | 0 0133 4 | + | -0 44311 5 *-----* -0 86 2 | | -1 43320 5 +-----+ -1 9865 4 | -2 2 1 | -2 9766 4 | -3 1 1 | -3 | -4 | -4 7 1 | ----+----+----+----+ Multiply Stem.Leaf by 10**+1 MULTIPLE COMPARISONS AMONG 5 TREATMENTS - YOURNAME 15 PROC UNIVARIATE: Testing normality 04:19 Tuesday, September 27, 2005 LOOK FOR W STATISTIC The UNIVARIATE Procedure Variable: resid Normal Probability Plot 37.5+ * *++ | ++ | ****+ | *++ | +*+ | **** | *** | +** | *** | +** | *** | *** | +* | *+** | *++ | +++ | ++ -47.5++++* +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2