TWO-WAY ANOVA WITH POSSIBLE INTERACTIONS: Reading and Sex - YOURNAME 1 THE DATA AS SAS SEES IT 22:30 Wednesday, November 16, 2005 Obs Sex Method yy 1 Male Method1 700 2 Male Method1 850 3 Male Method1 820 4 Male Method1 640 5 Male Method1 920 6 Male Method2 480 7 Male Method2 460 8 Male Method2 500 9 Male Method2 570 10 Male Method2 580 11 Male Method3 500 12 Male Method3 550 13 Male Method3 480 14 Male Method3 600 15 Male Method3 610 16 Female Method1 900 17 Female Method1 880 18 Female Method1 899 19 Female Method1 780 20 Female Method1 899 21 Female Method2 590 22 Female Method2 540 23 Female Method2 560 24 Female Method2 570 25 Female Method2 555 26 Female Method3 520 27 Female Method3 660 28 Female Method3 525 29 Female Method3 610 30 Female Method3 645 TWO-WAY ANOVA WITH POSSIBLE INTERACTIONS: Reading and Sex - YOURNAME 2 PROC GLM FOR MAIN EFFECTS only 22:30 Wednesday, November 16, 2005 This is a BAD IDEA if there are significant interactions The GLM Procedure Class Level Information Class Levels Values Method 3 Method1 Method2 Method3 Sex 2 Female Male Number of Observations Read 30 Number of Observations Used 30 TWO-WAY ANOVA WITH POSSIBLE INTERACTIONS: Reading and Sex - YOURNAME 3 PROC GLM FOR MAIN EFFECTS only 22:30 Wednesday, November 16, 2005 This is a BAD IDEA if there are significant interactions The GLM Procedure Dependent Variable: yy Sum of Source DF Squares Mean Square F Value Pr > F Model 3 528619.5667 176206.5222 41.85 <.0001 Error 26 109475.8000 4210.6077 Corrected Total 29 638095.3667 R-Square Coeff Var Root MSE yy Mean 0.828433 10.03803 64.88920 646.4333 Source DF Type I SS Mean Square F Value Pr > F Method 2 503215.2667 251607.6333 59.76 <.0001 Sex 1 25404.3000 25404.3000 6.03 0.0210 Source DF Type III SS Mean Square F Value Pr > F Method 2 503215.2667 251607.6333 59.76 <.0001 Sex 1 25404.3000 25404.3000 6.03 0.0210 TWO-WAY ANOVA WITH POSSIBLE INTERACTIONS: Reading and Sex - YOURNAME 4 INTERACTION PLOT for Method versus Sex 22:30 Wednesday, November 16, 2005 (Full factorial two-way model) CELL MEANS FOR INTERACTION PLOT ARE Cell Obs Method Sex _TYPE_ _FREQ_ Mean 1 Method1 Female 3 5 871.6 2 Method1 Male 3 5 786.0 3 Method2 Female 3 5 563.0 4 Method2 Male 3 5 518.0 5 Method3 Female 3 5 592.0 6 Method3 Male 3 5 548.0 TWO-WAY ANOVA WITH POSSIBLE INTERACTIONS: Reading and Sex - YOURNAME 5 INTERACTION PLOT for Method versus Sex 22:30 Wednesday, November 16, 2005 (Full factorial two-way model) INTERACTION PLOT FOR IPLOTMEANS Plot of CellMean*Method. Symbol is value of Sex. CellMean | 900 + | F | | | 800 + | M | | | 700 + | | | | 600 + F | | F | M | M 500 + ---+----------------------+----------------------+-- Method1 Method2 Method3 Method TWO-WAY ANOVA WITH POSSIBLE INTERACTIONS: Reading and Sex - YOURNAME 6 INTERACTION PLOT for Method versus Sex 22:30 Wednesday, November 16, 2005 (Full factorial two-way model) IN CONTRAST, THE UNRESTRICTED PROC MEAN OUTPUT IS Cell Obs Method Sex _TYPE_ _FREQ_ Mean 1 0 30 646.433 2 Female 1 15 675.533 3 Male 1 15 617.333 4 Method1 2 10 828.800 5 Method2 2 10 540.500 6 Method3 2 10 570.000 7 Method1 Female 3 5 871.600 8 Method1 Male 3 5 786.000 9 Method2 Female 3 5 563.000 10 Method2 Male 3 5 518.000 11 Method3 Female 3 5 592.000 12 Method3 Male 3 5 548.000 TWO-WAY ANOVA WITH POSSIBLE INTERACTIONS: Reading and Sex - YOURNAME 7 TWO-WAY ANOVA with interaction: 22:30 Wednesday, November 16, 2005 (FULL FACTORIAL two-way model) The GLM Procedure Class Level Information Class Levels Values Method 3 Method1 Method2 Method3 Sex 2 Female Male Number of Observations Read 30 Number of Observations Used 30 TWO-WAY ANOVA WITH POSSIBLE INTERACTIONS: Reading and Sex - YOURNAME 8 TWO-WAY ANOVA with interaction: 22:30 Wednesday, November 16, 2005 (FULL FACTORIAL two-way model) The GLM Procedure Dependent Variable: yy Sum of Source DF Squares Mean Square F Value Pr > F Model 5 531436.1667 106287.2333 23.92 <.0001 Error 24 106659.2000 4444.1333 Corrected Total 29 638095.3667 R-Square Coeff Var Root MSE yy Mean 0.832848 10.31264 66.66433 646.4333 Source DF Type I SS Mean Square F Value Pr > F Method 2 503215.2667 251607.6333 56.62 <.0001 Sex 1 25404.3000 25404.3000 5.72 0.0250 Method*Sex 2 2816.6000 1408.3000 0.32 0.7314 Source DF Type III SS Mean Square F Value Pr > F Method 2 503215.2667 251607.6333 56.62 <.0001 Sex 1 25404.3000 25404.3000 5.72 0.0250 Method*Sex 2 2816.6000 1408.3000 0.32 0.7314 TWO-WAY ANOVA WITH POSSIBLE INTERACTIONS: Reading and Sex - YOURNAME 9 TWO-WAY ANOVA with interaction: 22:30 Wednesday, November 16, 2005 (FULL FACTORIAL two-way model) The GLM Procedure Duncan's Multiple Range Test for yy NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 24 Error Mean Square 4444.133 Number of Means 2 3 Critical Range 61.53 64.63 Means with the same letter are not significantly different. D u n c a n G r o u p i n g Mean N Method A 828.80 10 Method1 B 570.00 10 Method3 B B 540.50 10 Method2 TWO-WAY ANOVA WITH POSSIBLE INTERACTIONS: Reading and Sex - YOURNAME 10 TWO-WAY ANOVA with interaction: 22:30 Wednesday, November 16, 2005 (FULL FACTORIAL two-way model) The GLM Procedure Duncan's Multiple Range Test for yy NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 24 Error Mean Square 4444.133 Number of Means 2 Critical Range 50.24 Means with the same letter are not significantly different. D u n c a n G r o u p i n g Mean N Sex A 675.53 15 Female B 617.33 15 Male TWO-WAY ANOVA WITH POSSIBLE INTERACTIONS: Reading and Sex - YOURNAME 11 ONE-WAY ANOVA FOR JOINT (METHOD,SEX) CELLS (Note that Model P-value and F-statistic are identical with the full factorial model) 22:30 Wednesday, November 16, 2005 The GLM Procedure Class Level Information Class Levels Values RdCell 6 Method1 Female Method1 Male Method2 Female Method2 Male Method3 Female Method3 Male Number of Observations Read 30 Number of Observations Used 30 TWO-WAY ANOVA WITH POSSIBLE INTERACTIONS: Reading and Sex - YOURNAME 12 ONE-WAY ANOVA FOR JOINT (METHOD,SEX) CELLS (Note that Model P-value and F-statistic are identical with the full factorial model) 22:30 Wednesday, November 16, 2005 The GLM Procedure Dependent Variable: yy Sum of Source DF Squares Mean Square F Value Pr > F Model 5 531436.1667 106287.2333 23.92 <.0001 Error 24 106659.2000 4444.1333 Corrected Total 29 638095.3667 R-Square Coeff Var Root MSE yy Mean 0.832848 10.31264 66.66433 646.4333 Source DF Type I SS Mean Square F Value Pr > F RdCell 5 531436.1667 106287.2333 23.92 <.0001 Source DF Type III SS Mean Square F Value Pr > F RdCell 5 531436.1667 106287.2333 23.92 <.0001 TWO-WAY ANOVA WITH POSSIBLE INTERACTIONS: Reading and Sex - YOURNAME 13 ONE-WAY ANOVA FOR JOINT (METHOD,SEX) CELLS (Note that Model P-value and F-statistic are identical with the full factorial model) 22:30 Wednesday, November 16, 2005 The GLM Procedure Duncan's Multiple Range Test for yy NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 24 Error Mean Square 4444.133 Number of Means 2 3 4 5 6 Critical Range 87.02 91.40 94.21 96.19 97.67 Means with the same letter are not significantly different. D u n c a n G r o u p i n g Mean N RdCell A 871.60 5 Method1 Female A A 786.00 5 Method1 Male B 592.00 5 Method3 Female B B 563.00 5 Method2 Female B B 548.00 5 Method3 Male B B 518.00 5 Method2 Male