Two-sample tests: YOUR NAME 00:23 Sunday, September 4, 2005 1 The data as SAS sees it Obs Samp Dat 1 X 9.19 2 X 9.54 3 X 8.65 4 X 7.31 5 X 8.47 6 X 9.78 7 Y 8.73 8 Y 8.17 9 Y 6.40 10 Y 6.31 11 Y 7.09 12 Y 7.99 13 Y 5.89 14 Y 6.38 15 Y 8.24 Two-sample tests: YOUR NAME 00:23 Sunday, September 4, 2005 2 Visualizing the data so that we can see what is going on Frequency 5 + YYYYY | YYYYY | YYYYY | YYYYY | YYYYY 4 + YYYYY | YYYYY | YYYYY | YYYYY | YYYYY 3 + YYYYY YYYYY | YYYYY YYYYY | YYYYY YYYYY | YYYYY YYYYY | YYYYY YYYYY 2 + YYYYY YYYYY YYYYY XXXXX XXXXX | YYYYY YYYYY YYYYY XXXXX XXXXX | YYYYY YYYYY YYYYY XXXXX XXXXX | YYYYY YYYYY YYYYY XXXXX XXXXX | YYYYY YYYYY YYYYY XXXXX XXXXX 1 + YYYYY YYYYY XXXXX XXXXX XXXXX XXXXX | YYYYY YYYYY XXXXX XXXXX XXXXX XXXXX | YYYYY YYYYY XXXXX XXXXX XXXXX XXXXX | YYYYY YYYYY XXXXX XXXXX XXXXX XXXXX | YYYYY YYYYY XXXXX XXXXX XXXXX XXXXX ------------------------------------------------------------------------- 6.0 6.8 7.6 8.4 9.2 10.0 Dat Midpoint Symbol Samp Symbol Samp X X Y Y Two-sample tests: YOUR NAME 00:23 Sunday, September 4, 2005 3 Visualizing the data so that we can see what is going on Frequency 3 + ** ** | ** ** | ** ** | ** ** | ** ** | ** ** | ** ** | ** ** | ** ** | ** ** 2 + ** ** ** ** ** | ** ** ** ** ** | ** ** ** ** ** | ** ** ** ** ** | ** ** ** ** ** | ** ** ** ** ** | ** ** ** ** ** | ** ** ** ** ** | ** ** ** ** ** | ** ** ** ** ** 1 + ** ** ** ** ** ** ** ** | ** ** ** ** ** ** ** ** | ** ** ** ** ** ** ** ** | ** ** ** ** ** ** ** ** | ** ** ** ** ** ** ** ** | ** ** ** ** ** ** ** ** | ** ** ** ** ** ** ** ** | ** ** ** ** ** ** ** ** | ** ** ** ** ** ** ** ** | ** ** ** ** ** ** ** ** ------------------------------------------------------------------ 1 1 Dat Midpoint 6 6 7 8 9 0 6 6 7 8 9 0 . . . . . . . . . . . . 0 8 6 4 2 0 0 8 6 4 2 0 |--------- X --------| |--------- Y --------| Samp Two-sample tests: YOUR NAME 00:23 Sunday, September 4, 2005 4 Two-sample t-test The TTEST Procedure Statistics Lower CL Upper CL Lower CL Variable Samp N Mean Mean Mean Std Dev Std Dev Dat X 6 7.8837 8.8233 9.763 0.5589 0.8954 Dat Y 9 6.4381 7.2444 8.0507 0.7085 1.049 Dat Diff (1-2) 0.4486 1.5789 2.7092 0.7197 0.9927 Statistics Upper CL Variable Samp Std Dev Std Err Minimum Maximum Dat X 2.196 0.3655 7.31 9.78 Dat Y 2.0096 0.3497 5.89 8.73 Dat Diff (1-2) 1.5993 0.5232 T-Tests Variable Method Variances DF t Value Pr > |t| Dat Pooled Equal 13 3.02 0.0099 Dat Satterthwaite Unequal 12 3.12 0.0088 Equality of Variances Variable Method Num DF Den DF F Value Pr > F Dat Folded F 8 5 1.37 0.7570 Two-sample tests: YOUR NAME 00:23 Sunday, September 4, 2005 5 Two-sample Wilcoxon Rank Sum Test The NPAR1WAY Procedure Wilcoxon Scores (Rank Sums) for Variable Dat Classified by Variable Samp Sum of Expected Std Dev Mean Samp N Scores Under H0 Under H0 Score -------------------------------------------------------------------- X 6 69.0 48.0 8.485281 11.500000 Y 9 51.0 72.0 8.485281 5.666667 Wilcoxon Two-Sample Test Statistic 69.0000 Normal Approximation Z 2.4159 One-Sided Pr > Z 0.0078 Two-Sided Pr > |Z| 0.0157 t Approximation One-Sided Pr > Z 0.0150 Two-Sided Pr > |Z| 0.0299 Z includes a continuity correction of 0.5. Kruskal-Wallis Test Chi-Square 6.1250 DF 1 Pr > Chi-Square 0.0133 Two-sample tests: YOUR NAME 00:23 Sunday, September 4, 2005 6 ALTERNATIVE DATA STEPS: Reading data using a switch What the data looks like The important fields are Samp and Dat Note the two records with Dat=Missing Obs Samp zz Dat 1 X X . 2 X 9.19 9.19 3 X 9.54 9.54 4 X 8.65 8.65 5 X 7.31 7.31 6 X 8.47 8.47 7 X 9.78 9.78 8 Y Y . 9 Y 8.73 8.73 10 Y 8.17 8.17 11 Y 6.40 6.40 12 Y 6.31 6.31 13 Y 7.09 7.09 14 Y 7.99 7.99 15 Y 5.89 5.89 16 Y 6.38 6.38 17 Y 8.24 8.24 Two-sample tests: YOUR NAME 00:23 Sunday, September 4, 2005 7 READING DATA IN TWO COLUMNS The records are alternating by sample designator Note the missing Dat values in the last three A records. Obs xx yy Samp Dat 1 9.19 8.73 X 9.19 2 9.19 8.73 Y 8.73 3 9.54 8.17 X 9.54 4 9.54 8.17 Y 8.17 5 8.65 6.40 X 8.65 6 8.65 6.40 Y 6.40 7 7.31 6.31 X 7.31 8 7.31 6.31 Y 6.31 9 8.47 7.09 X 8.47 10 8.47 7.09 Y 7.09 11 9.78 7.99 X 9.78 12 9.78 7.99 Y 7.99 13 . 5.89 X . 14 . 5.89 Y 5.89 15 . 6.38 X . 16 . 6.38 Y 6.38 17 . 8.24 X . 18 . 8.24 Y 8.24