HOTELLING T^2 TEST FOR TWO GENERA OF LIZARDS - YOURNAME 1 DATA FROM Johnson&Wichern Table 6.7 p330 THE DATA AS SAS SEES IT Note that Type appears as genus names Obs Type lnMass lnSVL 1 Cnemidophorus 2.01663 4.30407 2 Cnemidophorus 1.61582 4.24133 3 Cnemidophorus 1.76934 4.27667 4 Cnemidophorus 2.40586 4.38203 5 Cnemidophorus 0.88335 4.02535 6 Cnemidophorus 2.61080 4.54329 7 Cnemidophorus 2.90400 4.55913 8 Cnemidophorus 2.82328 4.60016 9 Cnemidophorus 2.76695 4.57471 10 Cnemidophorus 2.83527 4.50535 11 Cnemidophorus 2.80493 4.51086 12 Cnemidophorus 1.51072 4.20469 13 Cnemidophorus 1.97824 4.31749 14 Cnemidophorus 1.64866 4.24133 15 Cnemidophorus 2.59898 4.51634 16 Cnemidophorus 2.64476 4.51086 17 Cnemidophorus 2.68546 4.49981 18 Cnemidophorus 1.80698 4.29046 19 Cnemidophorus 1.66089 4.24133 20 Cnemidophorus 2.82743 4.54329 21 Sceloporus 2.63268 4.34381 22 Sceloporus 1.65556 4.12713 23 Sceloporus 3.61982 4.68213 24 Sceloporus 3.73244 4.74493 25 Sceloporus 3.46558 4.66344 26 Sceloporus 1.37675 4.02535 27 Sceloporus 1.47408 4.10264 28 Sceloporus 1.11449 3.95124 29 Sceloporus 1.57650 4.09434 30 Sceloporus 1.87564 4.15888 31 Sceloporus 3.11839 4.56435 32 Sceloporus 2.59092 4.37576 33 Sceloporus 1.41318 4.01638 34 Sceloporus 2.51519 4.31749 35 Sceloporus 1.96291 4.16667 36 Sceloporus 3.04818 4.47164 37 Sceloporus 3.76094 4.69135 38 Sceloporus 3.30325 4.56435 39 Sceloporus 3.66102 4.70953 40 Sceloporus 2.98300 4.43675 41 Sceloporus 2.68553 4.38203 42 Sceloporus 1.56653 4.12713 43 Sceloporus 1.61343 4.11904 44 Sceloporus 1.65250 4.12713 45 Sceloporus 1.73871 4.15888 46 Sceloporus 1.91147 4.14313 47 Sceloporus 2.30028 4.26268 48 Sceloporus 2.17827 4.24133 49 Sceloporus 2.25055 4.21213 50 Sceloporus 2.05553 4.18965 51 Sceloporus 1.89987 4.16667 52 Sceloporus 2.48324 4.36945 53 Sceloporus 2.80457 4.43082 HOTELLING T^2 TEST FOR TWO GENERA OF LIZARDS - YOURNAME 2 DATA FROM Johnson&Wichern Table 6.7 p330 THE DATA AS SAS SEES IT Note that Type appears as genus names Obs Type lnMass lnSVL 54 Sceloporus 2.61227 4.39445 55 Sceloporus 2.61740 4.41280 56 Sceloporus 2.33699 4.30407 57 Sceloporus 2.06686 4.22683 58 Sceloporus 2.20860 4.24850 59 Sceloporus 2.58143 4.35028 60 Sceloporus 2.28105 4.24850 HOTELLING T^2 TEST FOR TWO GENERA OF LIZARDS - YOURNAME 3 DATA FROM Johnson&Wichern Table 6.7 p330 PLOT OF TWO LIZARD GENERA: LOG-TRANSFORMED DATA THE LIZARDS SEEM NICELY SEPARATED, BUT THE MARGINAL DISTRIBUTIONS OVERLAP Plot of lnMass*lnSVL. Symbol is value of Type. ‚ 4 ˆ ‚ ‚ SS S ‚ S ‚ S ‚ S ‚ S 3 ˆ S S ‚ S C CC C l ‚ S CC C o ‚ SSSS SS CC g ‚ SC ( ‚ S SS S M ‚ S a 2 ˆ SS S CC s ‚ SSS C s ‚ S S C C ) ‚ S S C C , ‚ SS S ‚ ‚ S 1 ˆ ‚ C ‚ ‚ ‚ ‚ ‚ 0 ˆ Šƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒ 3.8 4.0 4.2 4.4 4.6 4.8 log(Snout-Ventral Length) NOTE: 5 obs hidden. HOTELLING T^2 TEST FOR TWO GENERA OF LIZARDS - YOURNAME 4 DATA FROM Johnson&Wichern Table 6.7 p330 T-TESTS FOR LOG-TRANSFORMED MASS AND SVL The two lizard types do not differ significantly in either measure. The TTEST Procedure Statistics Lower CL Upper CL Lower CL Variable Type N Mean Mean Mean Std Dev Std Dev lnMass Cnemidophor 20 1.9618 2.2399 2.518 0.4519 0.5942 us lnMass Sceloporus 40 2.1405 2.3681 2.5958 0.5832 0.7119 lnMass Diff (1-2) -0.499 -0.128 0.2421 0.5719 0.6756 lnSVL Cnemidophor 20 4.319 4.3944 4.4698 0.1225 0.1611 us lnSVL Sceloporus 40 4.2421 4.3081 4.3741 0.169 0.2063 lnSVL Diff (1-2) -0.019 0.0863 0.1919 0.1631 0.1927 Statistics Upper CL Variable Type Std Dev Std Err Minimum Maximum lnMass Cnemidophor 0.8678 0.1329 0.8834 2.904 us lnMass Sceloporus 0.9141 0.1126 1.1145 3.7609 lnMass Diff (1-2) 0.8256 0.185 lnSVL Cnemidophor 0.2353 0.036 4.0254 4.6002 us lnSVL Sceloporus 0.2649 0.0326 3.9512 4.7449 lnSVL Diff (1-2) 0.2354 0.0528 T-Tests Variable Method Variances DF t Value Pr > |t| lnMass Pooled Equal 58 -0.69 0.4911 lnMass Satterthwaite Unequal 44.8 -0.74 0.4654 lnSVL Pooled Equal 58 1.64 0.1072 lnSVL Satterthwaite Unequal 47.4 1.78 0.0820 Equality of Variances Variable Method Num DF Den DF F Value Pr > F lnMass Folded F 39 19 1.44 0.4012 lnSVL Folded F 39 19 1.64 0.2486 HOTELLING T^2 TEST FOR TWO GENERA OF LIZARDS - YOURNAME 5 DATA FROM Johnson&Wichern Table 6.7 p330 CARRYING OUT A HOTELLING T^2 TEST USING PROC IML Design Matrix (X) and Type XX TYPE 2.017 4.304 0 1.616 4.241 0 1.769 4.277 0 2.406 4.382 0 0.883 4.025 0 2.611 4.543 0 2.904 4.559 0 2.823 4.600 0 2.767 4.575 0 2.835 4.505 0 2.805 4.511 0 1.511 4.205 0 1.978 4.317 0 1.649 4.241 0 2.599 4.516 0 2.645 4.511 0 2.685 4.500 0 1.807 4.290 0 1.661 4.241 0 2.827 4.543 0 2.633 4.344 1 1.656 4.127 1 3.620 4.682 1 3.732 4.745 1 3.466 4.663 1 1.377 4.025 1 1.474 4.103 1 1.114 3.951 1 1.577 4.094 1 1.876 4.159 1 3.118 4.564 1 2.591 4.376 1 1.413 4.016 1 2.515 4.317 1 1.963 4.167 1 3.048 4.472 1 3.761 4.691 1 3.303 4.564 1 3.661 4.710 1 2.983 4.437 1 2.686 4.382 1 1.567 4.127 1 1.613 4.119 1 1.652 4.127 1 1.739 4.159 1 1.911 4.143 1 2.300 4.263 1 2.178 4.241 1 2.251 4.212 1 2.056 4.190 1 1.900 4.167 1 2.483 4.369 1 2.805 4.431 1 HOTELLING T^2 TEST FOR TWO GENERA OF LIZARDS - YOURNAME 6 DATA FROM Johnson&Wichern Table 6.7 p330 CARRYING OUT A HOTELLING T^2 TEST USING PROC IML XX TYPE 2.612 4.394 1 2.617 4.413 1 2.337 4.304 1 2.067 4.227 1 2.209 4.248 1 2.581 4.350 1 2.281 4.248 1 NAMES CVALS Table of sizes: MN=M+N 60 Dimension(D) 2 M 20 N 40 The two samples themselves (lnMass then lnSVL): XX1 XX2 2.017 4.304 2.633 4.344 1.616 4.241 1.656 4.127 1.769 4.277 3.620 4.682 2.406 4.382 3.732 4.745 0.883 4.025 3.466 4.663 2.611 4.543 1.377 4.025 2.904 4.559 1.474 4.103 2.823 4.600 1.114 3.951 2.767 4.575 1.577 4.094 2.835 4.505 1.876 4.159 2.805 4.511 3.118 4.564 1.511 4.205 2.591 4.376 1.978 4.317 1.413 4.016 1.649 4.241 2.515 4.317 2.599 4.516 1.963 4.167 2.645 4.511 3.048 4.472 2.685 4.500 3.761 4.691 1.807 4.290 3.303 4.564 1.661 4.241 3.661 4.710 2.827 4.543 2.983 4.437 2.686 4.382 1.567 4.127 1.613 4.119 1.652 4.127 1.739 4.159 1.911 4.143 2.300 4.263 2.178 4.241 2.251 4.212 2.056 4.190 1.900 4.167 2.483 4.369 2.805 4.431 2.612 4.394 HOTELLING T^2 TEST FOR TWO GENERA OF LIZARDS - YOURNAME 7 DATA FROM Johnson&Wichern Table 6.7 p330 CARRYING OUT A HOTELLING T^2 TEST USING PROC IML XX1 XX2 2.617 4.413 2.337 4.304 2.067 4.227 2.209 4.248 2.581 4.350 2.281 4.248 Sample means and sample mean differences: X1BAR X2BAR ZBAR 2.23992 2.36814 -0.12822 4.39443 4.30809 0.08634 Sample covariance matrices within each sample: SS1 SS2 0.3530 0.0942 0.5068 0.1454 0.0942 0.0260 0.1454 0.0426 Sample un-normalized E matrix and pooled covariance matrix: SUMXY SS 26.474859 7.459488 0.45646 0.12861 7.459488 2.152698 0.12861 0.03712 CORR The sample correlation matrix 1.0000 0.9881 0.9881 1.0000 The Hotelling T^2 statistist is TT2 228.190 Table for the Hotelling T^2 test: NAMES TABLEVALS Hotelling T^2 228.18983 Df1 (Num DF) 2 Df2 (Den DF) 57 F value 112.12776 Pvalue (Pr>F) 0 Note that this is very similar to the SAS output below. HOTELLING T^2 TEST FOR TWO GENERA OF LIZARDS - YOURNAME 8 DATA FROM Johnson&Wichern Table 6.7 p330 HOTELLING T^2 TEST FOR TWO LIZARD CLASSES The GLM Procedure Class Level Information Class Levels Values Type 2 Cnemidophorus Sceloporus Number of Observations Read 60 Number of Observations Used 60 HOTELLING T^2 TEST FOR TWO GENERA OF LIZARDS - YOURNAME 9 DATA FROM Johnson&Wichern Table 6.7 p330 HOTELLING T^2 TEST FOR TWO LIZARD CLASSES The GLM Procedure Multivariate Analysis of Variance E = Error SSCP Matrix lnMass lnSVL lnMass 26.474859459 7.4594881118 lnSVL 7.4594881118 2.15269847 Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 58 lnMass lnSVL lnMass 1.000000 0.988099 <.0001 lnSVL 0.988099 1.000000 <.0001 HOTELLING T^2 TEST FOR TWO GENERA OF LIZARDS - YOURNAME 10 DATA FROM Johnson&Wichern Table 6.7 p330 HOTELLING T^2 TEST FOR TWO LIZARD CLASSES The GLM Procedure Multivariate Analysis of Variance Characteristic Roots and Vectors of: E Inverse * H, where H = Type III SSCP Matrix for Type E = Error SSCP Matrix Characteristic Characteristic Vector V'EV=1 Root Percent lnMass lnSVL 3.93430737 100.00 -1.25607268 4.42634950 0.00000000 0.00 0.13687058 0.20327481 MANOVA Test Criteria and Exact F Statistics for the Hypothesis of No Overall Type Effect H = Type III SSCP Matrix for Type E = Error SSCP Matrix S=1 M=0 N=27.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.20266269 112.13 2 57 <.0001 Pillai's Trace 0.79733731 112.13 2 57 <.0001 Hotelling-Lawley Trace 3.93430737 112.13 2 57 <.0001 Roy's Greatest Root 3.93430737 112.13 2 57 <.0001