The SAS System The FREQ Procedure Table of state by color state color Frequency‚ Percent ‚ Row Pct ‚ Col Pct ‚Green ‚Orange ‚Pink ‚Purple ‚ Total ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ ME ‚ 3 ‚ 3 ‚ 3 ‚ 3 ‚ 12 ‚ 6.25 ‚ 6.25 ‚ 6.25 ‚ 6.25 ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ MS ‚ 3 ‚ 3 ‚ 3 ‚ 3 ‚ 12 ‚ 6.25 ‚ 6.25 ‚ 6.25 ‚ 6.25 ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ VTNH ‚ 3 ‚ 3 ‚ 3 ‚ 3 ‚ 12 ‚ 6.25 ‚ 6.25 ‚ 6.25 ‚ 6.25 ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ WY ‚ 3 ‚ 3 ‚ 3 ‚ 3 ‚ 12 ‚ 6.25 ‚ 6.25 ‚ 6.25 ‚ 6.25 ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ 25.00 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Total 12 12 12 12 48 25.00 25.00 25.00 25.00 100.00 The SAS System The MEANS Procedure Analysis Variable : Y N student Obs Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Cath 4 4.9183076 Cris 4 8.9773209 GK 4 17.6153828 Hsiao 4 9.4498211 Huazhi 4 15.2393352 IB 4 5.2335323 Jennifer 4 4.6209499 Lacey 4 8.5154359 Matt 4 15.2169314 Melissa 4 12.2588675 Paras 4 5.4662399 Rob 4 22.0529058 ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ The SAS System The MEANS Procedure Analysis Variable : Y N state Obs Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ ME 12 3.6092295 MS 12 17.6175284 VTNH 12 9.4481681 WY 12 12.5134173 ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ The SAS System The MEANS Procedure Analysis Variable : Y N color Obs Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Green 12 10.7143673 Orange 12 11.3606056 Pink 12 12.7541616 Purple 12 8.3592089 ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ The SAS System The MEANS Procedure Analysis Variable : Y N square Obs Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ 1 16 9.4069097 2 16 9.9322724 3 16 13.0520755 ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ The SAS System The GLM Procedure Class Level Information Class Levels Values student 12 Cath Cris GK Hsiao Huazhi IB Jennifer Lacey Matt Melissa Paras Rob state 4 ME MS VTNH WY color 4 Green Orange Pink Purple square 3 1 2 3 Number of observations 48 The SAS System The GLM Procedure Dependent Variable: Y Sum of Source DF Squares Mean Square F Value Pr > F Model 17 2784.548132 163.796949 1.65 0.1124 Error 30 2979.340432 99.311348 Corrected Total 47 5763.888564 R-Square Coeff Var Root MSE Y Mean 0.483102 92.29813 9.965508 10.79709 Source DF Type I SS Mean Square F Value Pr > F color 3 121.173437 40.391146 0.41 0.7493 state 3 1235.389070 411.796357 4.15 0.0143 square 2 124.247525 62.123763 0.63 0.5418 student(square) 9 1303.738100 144.859789 1.46 0.2085 Source DF Type III SS Mean Square F Value Pr > F color 3 121.173437 40.391146 0.41 0.7493 state 3 1235.389070 411.796357 4.15 0.0143 square 2 124.247525 62.123763 0.63 0.5418 student(square) 9 1303.738100 144.859789 1.46 0.2085 The SAS System The GLM Procedure Tukey's Studentized Range (HSD) Test for Y 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 30 Error Mean Square 99.31135 Critical Value of Studentized Range 3.84540 Minimum Significant Difference 11.062 Means with the same letter are not significantly different. Tukey Grouping Mean N color A 12.754 12 Pink A A 11.361 12 Orange A A 10.714 12 Green A A 8.359 12 Purple The SAS System The GLM Procedure Bonferroni (Dunn) t Tests for Y 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 30 Error Mean Square 99.31135 Critical Value of t 2.82470 Minimum Significant Difference 11.492 Means with the same letter are not significantly different. Bon Grouping Mean N color A 12.754 12 Pink A A 11.361 12 Orange A A 10.714 12 Green A A 8.359 12 Purple