``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152``` ```***************************************** ** ** ** Hotelling's T**2 & Profile Analysis ** ** ** ***************************************** * Input matrix of raw scores for group X. MATRIX. COMPUTE X = { 7, 5, 9, 8; 8, 8, 5, 6; 16, 18, 11, 9; 8, 3, 7, 9; 6, 3, 13, 9; 11, 8, 10, 10; 12, 7, 9, 8; 8, 11, 9, 3; 14, 12, 11, 4; 13, 13, 13, 6; 13, 9, 9, 9; 13, 10, 15, 7; 14, 11, 12, 8; 15, 11, 11, 10; 13, 10, 15, 9; 10, 5, 8, 6; 10, 3, 7, 7; 17, 13, 13, 7; 10, 6, 10, 7; 10, 10, 15, 8; 14, 7, 11, 5; 16, 11, 12, 11; 10, 7, 14, 6; 10, 10, 9, 6; 10, 7, 10, 10; 7, 6, 5, 9; 15, 12, 10, 6; 17, 15, 15, 8; 16, 13, 16, 9; 13, 10, 17, 8; 13, 10, 17, 10; 19, 12, 16, 10; 19, 15, 17, 11; 13, 10, 7, 8; 15, 11, 12, 8; 16, 9, 11, 11; 14, 13, 14, 9 }. COMPUTE NX = NROW(X). COMPUTE KX = NCOL(X). PRINT {NX, KX} /TITLE "No. of Cases, No. of Vars. in X". * Input matrix of raw scores for group Y. COMPUTE Y = { 9, 5, 10, 8; 10, 0, 6, 2; 8, 9, 11, 1; 13, 7, 14, 9; 4, 0, 4, 0; 4, 0, 6, 0; 11, 9, 9, 8; 5, 3, 3, 6; 9, 7, 8, 6; 7, 2, 6, 4; 12, 10, 14, 3; 13, 12, 11, 10 }. COMPUTE NY = NROW(Y). COMPUTE KY = NCOL(Y). PRINT {NY, KY} /TITLE "No. of Cases, No. of Vars. in Y". * Calculate sample means. COMPUTE UNITX = MAKE (NX, 1, 1.0). COMPUTE MEANSX = T(UNITX) * X &* (1.0 / NX). PRINT MEANSX /TITLE "Sample means for group X". COMPUTE UNITY = MAKE (NY, 1, 1.0). COMPUTE MEANSY = T(UNITY) * Y &* (1.0 / NY). PRINT MEANSY /TITLE "Sample means for group Y". COMPUTE DIFF = MEANSX - MEANSY. PRINT DIFF /TITLE "Differences". * Calculate mean-corrected SSCP matrices. COMPUTE BXX = SSCP(X). COMPUTE SX = BXX - ((1/NX) &* (T(X) * UNITX) * (T(UNITX) * X)). COMPUTE BYY = SSCP(Y). COMPUTE SY = BYY - ((1/NY) &* (T(Y) * UNITY) * (T(UNITY) * Y)). * Calculate covariance-variance matrices. COMPUTE CX = (1/(NX-1.0)) &* SX. COMPUTE CY = (1/(NY-1.0)) &* SY. * Pooled covariance matrix. COMPUTE COV = (((NX-1) &* CX) + ((NY-1) &* CY)) &/ (NX+NY-2). COMPUTE ICOV = INV(COV). * "Hotelling's T**2 statistic". COMPUTE T2 = (NX * NY * DIFF * ICOV * T(DIFF)) / (NX+NY). PRINT /TITLE " ========== Hotelling's Two-Sample T**2 Test of Means ========== ". PRINT T2 /TITLE "Hotelling's T**2 Statistic". COMPUTE F = T2 * (NX+NY-KX-1) / ((NX+NY-2)*KX). PRINT { F, KX, NX+NY-KX-1 } /Title "Equivalent F & d.f.". COMPUTE P = 1.0 - FCDF(F, KX, NX+NY-KX-1). PRINT P /TITLE "P-value" /FORMAT = F10.9. PRINT /TITLE " ========== Hotelling's Profile Analysis ========== ". * Create Design Matrix C for successive contrasts. COMPUTE V1 = { 1, -1 }. COMPUTE V2 = MAKE (1, KX-1, 0). COMPUTE V3 = {V1, V2}. COMPUTE V4 = V3. LOOP I = 1 to KX-1. COMPUTE V4 = {V4 ; V3}. END LOOP. COMPUTE C = RESHAPE (V4, KX+1, KX). COMPUTE C = C(1:(KX-1), 1:KX). PRINT C /TITLE "Contrast matrix". * Differences between adjacent scales for group X. COMPUTE DIFF1 = MEANSX * T(C). PRINT DIFF1 /TITLE "Differences between adjacent scales for group X". * Differences Between adjacent scales for group Y. COMPUTE DIFF2 = MEANSY * T(C). PRINT DIFF2 /TITLE "Differences between adjacent scales for group Y". * Pooled covariance matrix of differences. COMPUTE POOL = C * COV * T(C). PRINT POOL /TITLE "Pooled covariance matrix of differences". COMPUTE IPOOL = INV(POOL). PRINT IPOOL /TITLE "Inverted pooled cov. matrix of diff.". PRINT /TITLE " ----- Hypothesis 1: Parallelism (no group X scale interactions) ----- ". COMPUTE PARALLEL = (NX * NY * DIFF * T(C) * IPOOL * C * T(DIFF)) / (NX+NY). PRINT PARALLEL /TITLE "Hotelling's T**2 statistic for Parallelism". COMPUTE F = PARALLEL * (NX+NY-KX) / ((NX+NY-2)*(KX-1)). PRINT { F, KX-1, NX+NY-KX } /TITLE "Equivalent F & d.f.". COMPUTE P = 1.0 - FCDF(F, KX-1, NX+NY-KX). PRINT P /TITLE "P-value" /FORMAT F10.9. PRINT /TITLE " ----- Hypothesis 2: Equal Levels (assuming parallelism) ----- ". * Create design vector J for equal levels. COMPUTE J = MAKE (1, KX, 1.0). * Grand total for group x. COMPUTE GRANDX = MEANSX * T(J). PRINT GRANDX /TITLE "Grand mean for group X". * Grand total for group y. COMPUTE GRANDY = MEANSY * T(J). PRINT GRANDY /TITLE "Grand mean for group Y". * Differences in levels. COMPUTE DIF = J * T(DIFF). PRINT DIF /TITLE "Difference in levels". * Variance of differences. COMPUTE CV = J * COV * T(J). PRINT CV /TITLE "Variance of differences". COMPUTE EQUAL = J * T(DIFF) / (SQRT ( CV * (1/NX + 1/NY) ) ). PRINT { EQUAL, NX+NY-2 } /TITLE "Hotelling's t-test for Equal levels (one-tailed)". COMPUTE P = (1.0 - TCDF(ABS(EQUAL), NX+NY-2 )) * 0.5. PRINT P /TITLE "P-value" /FORMAT F10.9. PRINT /TITLE " ----- Hypothesis 3: Flatness (again assuming parallelism) ----- ". * Total Grand Means. COMPUTE GRAND = ((MEANSX * NX) + (MEANSY * NY)) / (NX + NY). PRINT GRAND /TITLE "Total Group Means". COMPUTE FLAT = (NX+NY) * GRAND * T(C) * IPOOL * C * T(GRAND). PRINT FLAT /TITLE "Hotelling's T**2 statistic for Flat Profiles". COMPUTE F = FLAT * (NX+NY-KX) / ((NX+NY-2) * (KX-1)). PRINT { F, KX-1, NX+NY-KX } /TITLE "Equivalent F & d.f.". COMPUTE P = 1.0 - FCDF( F, KX-1, NX+NY-KX ). PRINT P /TITLE "P-value" /FORMAT F10.9. END MATRIX. ```
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