swamp pH example: cell means model 1 08:34 Monday, March 11, 2013 The GLM Procedure Class Level Information Class Levels Values loc 2 away near type 3 mesic north shrub Number of Observations Read 35 Number of Observations Used 35 swamp pH example: cell means model 2 08:34 Monday, March 11, 2013 The GLM Procedure Dependent Variable: ph Sum of Source DF Squares Mean Square F Value Model 6 1556.203667 259.367278 1334.49 Error 29 5.636333 0.194356 Uncorrected Total 35 1561.840000 Source Pr > F Model <.0001 Error Uncorrected Total R-Square Coeff Var Root MSE ph Mean 0.300852 6.616660 0.440859 6.662857 Source DF Type I SS Mean Square F Value loc*type 6 1556.203667 259.367278 1334.49 Source Pr > F loc*type <.0001 Source DF Type III SS Mean Square F Value loc*type 6 1556.203667 259.367278 1334.49 Source Pr > F loc*type <.0001 Contrast DF Contrast SS Mean Square F Value loc main effect 1 1.00971645 1.00971645 5.20 type main effect 2 0.50903840 0.25451920 1.31 interaction 2 0.60773900 0.30386950 1.56 Contrast Pr > F loc main effect 0.0302 type main effect 0.2854 interaction 0.2266 swamp pH example: cell means model 3 08:34 Monday, March 11, 2013 The GLM Procedure Dependent Variable: ph Contrast DF Contrast SS Mean Square F Value loc main effect 1 1.00971645 1.00971645 5.20 type main effect 2 0.50903840 0.25451920 1.31 wt loc main effect 1 0.77487218 0.77487218 3.99 wt type main effect 2 0.48187013 0.24093506 1.24 wt m-s contrast 1 0.04255584 0.04255584 0.22 wt n-(m+s) contrast 1 0.43931429 0.43931429 2.26 Contrast Pr > F loc main effect 0.0302 type main effect 0.2854 wt loc main effect 0.0553 wt type main effect 0.3044 wt m-s contrast 0.6433 wt n-(m+s) contrast 0.1435 Standard Parameter Estimate Error t Value Pr > |t| away mean 6.85000000 0.13075228 52.39 <.0001 near mean 6.47055556 0.10304181 62.80 <.0001 a-n contrast 0.37944444 0.16647454 2.28 0.0302 mesic mean 6.60833333 0.11904543 55.51 <.0001 north mean 6.86250000 0.17426467 39.38 <.0001 shrub mean 6.51000000 0.13347658 48.77 <.0001 m-s contrast 0.09833333 0.17885137 0.55 0.5867 n-(m+s) contrast 0.30333333 0.19587018 1.55 0.1323 wt away mean 6.82500000 0.11021465 61.92 <.0001 wt near mean 6.52631579 0.10113990 64.53 <.0001 wt a-n contrast 0.29868421 0.14958793 2.00 0.0553 wt mesic mean 6.62857143 0.11782442 56.26 <.0001 wt north mean 6.84000000 0.13941174 49.06 <.0001 Parameter 95% Confidence Limits away mean 6.58258157 7.11741843 near mean 6.25981140 6.68129971 a-n contrast 0.03896578 0.71992310 mesic mean 6.36485808 6.85180858 north mean 6.50608873 7.21891127 shrub mean 6.23700975 6.78299025 m-s contrast -0.26745878 0.46412545 n-(m+s) contrast -0.09726617 0.70393284 wt away mean 6.59958572 7.05041428 wt near mean 6.31946146 6.73317012 wt a-n contrast -0.00725747 0.60462589 wt mesic mean 6.38759343 6.86954943 wt north mean 6.55487098 7.12512902 swamp pH example: cell means model 4 08:34 Monday, March 11, 2013 The GLM Procedure Dependent Variable: ph Standard Parameter Estimate Error t Value Pr > |t| wt shrub mean 6.54545455 0.13292387 49.24 <.0001 wt m-s contrast 0.08311688 0.17762700 0.47 0.6433 wt n-(m+s) contrast 0.24800000 0.16495419 1.50 0.1435 Parameter 95% Confidence Limits wt shrub mean 6.27359470 6.81731439 wt m-s contrast -0.28017112 0.44640489 wt n-(m+s) contrast -0.08936920 0.58536920 Standard Parameter Estimate Error t Value Pr > |t| loc*type away mesic 6.750000000 0.15586706 43.31 <.0001 loc*type away north 6.900000000 0.31173412 22.13 <.0001 loc*type away shrub 6.900000000 0.17997978 38.34 <.0001 loc*type near mesic 6.466666667 0.17997978 35.93 <.0001 loc*type near north 6.825000000 0.15586706 43.79 <.0001 loc*type near shrub 6.120000000 0.19715797 31.04 <.0001 Parameter 95% Confidence Limits loc*type away mesic 6.431216070 7.068783930 loc*type away north 6.262432139 7.537567861 loc*type away shrub 6.531900024 7.268099976 loc*type near mesic 6.098566691 6.834766643 loc*type near north 6.506216070 7.143783930 loc*type near shrub 5.716766680 6.523233320 swamp pH example: cell means model 5 08:34 Monday, March 11, 2013 Plot of resid*cellmean. Legend: A = 1 obs, B = 2 obs, etc. resid | | 0.6 + | | A | | E 0.4 + | B | A A | C | 0.2 + | B | C | A | 0.0 +----------------------------------------------------------------- | A | A C | | -0.2 + | A | C A | | -0.4 + | B | | | B -0.6 + | | | | -0.8 + | | | A | -1.0 + | | | | A -1.2 + | ---+-----------+-----------+-----------+-----------+-----------+-- 6.0 6.2 6.4 6.6 6.8 7.0 cellmean swamp pH example: cell means model 6 08:34 Monday, March 11, 2013 Plot of cellmean*loc. Symbol is value of type. 6.9 + n | | | | n | 6.8 + | | | m | | 6.7 + | | cellmean | | | 6.6 + | | | | | 6.5 + | | m | | | 6.4 + | | | | | 6.3 + | | | | | 6.2 + | | | | | s 6.1 + ---+----------------------------------------+-- away near loc NOTE: 30 obs hidden. swamp pH example: cell means model 7 08:34 Monday, March 11, 2013 Plot of cellmean*type. Symbol is value of loc. 6.9 + a a | | | | n | 6.8 + | | | a | | 6.7 + | | cellmean | | | 6.6 + | | | | | 6.5 + | | n | | | 6.4 + | | | | | 6.3 + | | | | | 6.2 + | | | | | n 6.1 + ---+---------------------+---------------------+-- mesic north shrub type NOTE: 29 obs hidden. swamp pH example: cell means model 8 08:34 Monday, March 11, 2013 The UNIVARIATE Procedure Variable: resid Moments N 35 Sum Weights 35 Mean 0 Sum Observations 0 Std Deviation 0.40715416 Variance 0.16577451 Skewness -0.9370495 Kurtosis 0.68280491 Uncorrected SS 5.63633333 Corrected SS 5.63633333 Coeff Variation . Std Error Mean 0.06882161 Basic Statistical Measures Location Variability Mean 0.000000 Std Deviation 0.40715 Median 0.100000 Variance 0.16577 Mode 0.450000 Range 1.68333 Interquartile Range 0.60000 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 0 Pr > |t| 1.0000 Sign M 1.5 Pr >= |M| 0.7359 Signed Rank S 37.5 Pr >= |S| 0.5465 Quantiles (Definition 5) Quantile Estimate 100% Max 0.533333 99% 0.533333 95% 0.450000 90% 0.450000 75% Q3 0.333333 50% Median 0.100000 25% Q1 -0.266667 10% -0.550000 5% -0.920000 1% -1.150000 0% Min -1.150000 Extreme Observations -----Lowest---- ------Highest----- Value Obs Value Obs -1.150 23 0.450000 25 -0.920 16 0.450000 26 swamp pH example: cell means model 9 08:34 Monday, March 11, 2013 The UNIVARIATE Procedure Variable: resid Extreme Observations -----Lowest---- ------Highest----- Value Obs Value Obs -0.550 27 0.450000 28 -0.550 22 0.450000 29 -0.425 8 0.533333 10 Stem Leaf # Boxplot 4 555553 6 | 2 8880388 7 +-----+ 0 800088 6 *--+--* -0 00072 5 | | -2 07772 5 +-----+ -4 5522 4 | -6 | -8 2 1 | -10 5 1 | ----+----+----+----+ Multiply Stem.Leaf by 10**-1 Normal Probability Plot 0.5+ **+** * * | *****+ | ****++ | *+** -0.3+ **+** | **+*+ | +++++ | +++++ * -1.1++ * +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 swamp pH example: cell means model 10 08:34 Monday, March 11, 2013 Plot of nscore*resid. Legend: A = 1 obs, B = 2 obs, etc. | | 2.5 + | | | A 2.0 + | | | R 1.5 + a | n | E k | 1.0 + f | B o | A r | A 0.5 + C V | a | B r | B i 0.0 + A a | A A b | A l | B e -0.5 + A A | r | C e | A s -1.0 + B i | d | | B -1.5 + | A | | -2.0 + | A | | -2.5 + | --+-----------+-----------+-----------+-----------+-----------+-- -1.5 -1.0 -0.5 0.0 0.5 1.0 resid swamp pH example: effects model loc first 11 08:34 Monday, March 11, 2013 The GLM Procedure Class Level Information Class Levels Values loc 2 away near type 3 mesic north shrub Number of Observations Read 35 Number of Observations Used 35 swamp pH example: effects model loc first 12 08:34 Monday, March 11, 2013 The GLM Procedure Dependent Variable: ph Sum of Source DF Squares Mean Square F Value Model 5 2.42538095 0.48507619 2.50 Error 29 5.63633333 0.19435632 Corrected Total 34 8.06171429 Source Pr > F Model 0.0536 Error Corrected Total R-Square Coeff Var Root MSE ph Mean 0.300852 6.616660 0.440859 6.662857 Source DF Type I SS Mean Square F Value loc 1 0.77487218 0.77487218 3.99 type 2 1.04276977 0.52138488 2.68 loc*type 2 0.60773900 0.30386950 1.56 Source Pr > F loc 0.0553 type 0.0853 loc*type 0.2266 Source DF Type II SS Mean Square F Value loc 1 1.33577182 1.33577182 6.87 type 2 1.04276977 0.52138488 2.68 loc*type 2 0.60773900 0.30386950 1.56 Source Pr > F loc 0.0138 type 0.0853 loc*type 0.2266 Source DF Type III SS Mean Square F Value loc 1 1.00971645 1.00971645 5.20 type 2 0.50903840 0.25451920 1.31 swamp pH example: effects model loc first 13 08:34 Monday, March 11, 2013 The GLM Procedure Dependent Variable: ph Source DF Type III SS Mean Square F Value loc*type 2 0.60773900 0.30386950 1.56 Source Pr > F loc 0.0302 type 0.2854 loc*type 0.2266 Source DF Type IV SS Mean Square F Value loc 1 1.00971645 1.00971645 5.20 type 2 0.50903840 0.25451920 1.31 loc*type 2 0.60773900 0.30386950 1.56 Source Pr > F loc 0.0302 type 0.2854 loc*type 0.2266 swamp pH example: effects model loc first 14 08:34 Monday, March 11, 2013 The GLM Procedure Level of --------------ph------------- loc N Mean Std Dev away 16 6.82500000 0.46690470 near 19 6.52631579 0.47239591 Level of --------------ph------------- type N Mean Std Dev mesic 14 6.62857143 0.54268360 north 10 6.84000000 0.29514591 shrub 11 6.54545455 0.54472679 Level of Level of --------------ph------------- loc type N Mean Std Dev away mesic 8 6.75000000 0.64807407 away north 2 6.90000000 0.14142136 away shrub 6 6.90000000 0.20976177 near mesic 6 6.46666667 0.35023801 near north 8 6.82500000 0.32841611 near shrub 5 6.12000000 0.52153619 swamp pH example: effects model loc first 15 08:34 Monday, March 11, 2013 The GLM Procedure Least Squares Means Standard loc ph LSMEAN Error Pr > |t| away 6.85000000 0.13075228 <.0001 near 6.47055556 0.10304181 <.0001 Standard type ph LSMEAN Error Pr > |t| mesic 6.60833333 0.11904543 <.0001 north 6.86250000 0.17426467 <.0001 shrub 6.51000000 0.13347658 <.0001 Standard loc type ph LSMEAN Error Pr > |t| away mesic 6.75000000 0.15586706 <.0001 away north 6.90000000 0.31173412 <.0001 away shrub 6.90000000 0.17997978 <.0001 near mesic 6.46666667 0.17997978 <.0001 near north 6.82500000 0.15586706 <.0001 near shrub 6.12000000 0.19715797 <.0001 swamp pH example: effects model type first 16 08:34 Monday, March 11, 2013 The GLM Procedure Class Level Information Class Levels Values loc 2 away near type 3 mesic north shrub Number of Observations Read 35 Number of Observations Used 35 swamp pH example: effects model type first 17 08:34 Monday, March 11, 2013 The GLM Procedure Dependent Variable: ph Sum of Source DF Squares Mean Square F Value Model 5 2.42538095 0.48507619 2.50 Error 29 5.63633333 0.19435632 Corrected Total 34 8.06171429 Source Pr > F Model 0.0536 Error Corrected Total R-Square Coeff Var Root MSE ph Mean 0.300852 6.616660 0.440859 6.662857 Source DF Type I SS Mean Square F Value type 2 0.48187013 0.24093506 1.24 loc 1 1.33577182 1.33577182 6.87 loc*type 2 0.60773900 0.30386950 1.56 Source Pr > F type 0.3044 loc 0.0138 loc*type 0.2266 Source DF Type II SS Mean Square F Value type 2 1.04276977 0.52138488 2.68 loc 1 1.33577182 1.33577182 6.87 loc*type 2 0.60773900 0.30386950 1.56 Source Pr > F type 0.0853 loc 0.0138 loc*type 0.2266 Source DF Type III SS Mean Square F Value type 2 0.50903840 0.25451920 1.31 loc 1 1.00971645 1.00971645 5.20 swamp pH example: effects model type first 18 08:34 Monday, March 11, 2013 The GLM Procedure Dependent Variable: ph Source DF Type III SS Mean Square F Value loc*type 2 0.60773900 0.30386950 1.56 Source Pr > F type 0.2854 loc 0.0302 loc*type 0.2266 Source DF Type IV SS Mean Square F Value type 2 0.50903840 0.25451920 1.31 loc 1 1.00971645 1.00971645 5.20 loc*type 2 0.60773900 0.30386950 1.56 Source Pr > F type 0.2854 loc 0.0302 loc*type 0.2266