How to Interpret a 2-Way ANOVA

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How to Interpret a 2-Way ANOVA

Descriptive Statistics The Following Tables are the SPSS print-outs for the analysis of the data. Descriptive Statistics Grade Condition Mean Std. Deviation N Grade 6 control 2.8000 2.09259 20 Reading Program 5.2500 2.88143 Total 4.0250 2.77800 40 Grade 7 5.1000 2.48998 7.1500 7.81547 6.1250 5.81857 Grade 8 5.7000 1.80933 3.2500 1.74341 4.4750 2.14820 4.5333 2.45962 60 5.2167 5.08934 4.8750 3.99488 120 Design Type. There are 120 student in the entire study. Sixty are in the reading program and the other 60 are in the control group so Reading Program is a ________Subjects Factor. There are 40 students from each grade level. Therefore, Grade Level is a ________Subjects Factor. The design is a __(Reading Program) X __(Grade Level) _______Subjects Factorial Design. There are ___ conditions. Gr 6 Gr 7 Gr 8 Totals Control 2.80 5.10 5.7 4.53 Reading Program 5.25 7.15 3.25 5.22 4.03 6.12 4.47 4.88 6 Points

Two-Way ANOVA TABLE Source Sum of Squares df Mean Square F Sig. Grade 97.800 2 48.900 3.401 .037 Condition (reading vs. control) 14.008 1 .974 .326 Grade * Condition 148.067 74.033 5.149 .007 Error 1639.250 114 14.379 Main Effect of Grade is significant (F(2,114) = 3.40, p = .037). Because we are comparing among 3 grades we need to do LSD’s to determine which grades differ from which other grades. ( 1 point)

Gr 6 Gr 7 Gr 8 Totals Control 2.80 5.10 5.7 4.53 Reading Program 5.25 7.15 3.25 5.22 4.03 6.12 4.47 4.88 Books_Read LSD (I) Grade (J) Grade Mean Difference (I-J) Std. Error Sig. Grade 6 Grade 7 -2.1000* .84792 .015 Grade 8 -.4500 .597 2.1000* 1.6500 .044 .4500 -1.6500 Books_Read LSD (I) Grade (J) Grade Mean Difference (I-J) Std. Error Sig. Grade 6 Grade 7 -2.1000* .84792 .015 Grade 8 -.4500 .597 2.1000* 1.6500 .044 .4500 -1.6500 Books_Read LSD (I) Grade (J) Grade Mean Difference (I-J) Std. Error Sig. Grade 6 Grade 7 -2.1000* .84792 .015 Grade 8 -.4500 .597 2.1000* 1.6500 .044 .4500 -1.6500 Grade 6 students read significantly less books than grade 7 students (p = .015). Grade 6 students do not differ from grade 8 students on the number of books they read. Grade 7 students read significantly more books that grade 8 students do (p = .044) 3 Points

Two-Way ANOVA TABLE Source Sum of Squares df Mean Square F Sig. Grade 97.800 2 48.900 3.401 .037 Condition (reading vs. control) 14.008 1 .974 .326 Grade * Condition 148.067 74.033 5.149 .007 Error 1639.250 114 14.379 Main Effect of Condition is not significant. There is no difference between the number of books read in the control condition compared to the reading program. (1 point) Gr 6 Gr 7 Gr 8 Totals Control 2.80 5.10 5.7 4.53 Reading Program 5.25 7.15 3.25 5.22 4.03 6.12 4.47 4.88

Two-Way ANOVA TABLE Source Sum of Squares df Mean Square F Sig. Grade 97.800 2 48.900 3.401 .037 Condition (reading vs. control) 14.008 1 .974 .326 Grade * Condition 148.067 74.033 5.149 .007 Error 1639.250 114 14.379 The Interaction between reading programs and grade levels is significant (F(2,114) = 5.15, p = .007 Therefore, the effectiveness of the reading program depends on which grade level we are looking at. (1 point) Gr 6 Gr 7 Gr 8 Totals Control 2.80 5.10 5.7 4.53 Reading Program 5.25 7.15 3.25 5.22 4.03 6.12 4.47 4.88

Gr 6 Gr 7 Gr 8 Totals Control 2.80 5.10 5.7 4.53 Reading Program 5.25 7.15 3.25 5.22 4.03 6.12 4.47 4.88 Simple Main Effects Grade 6 students read more books with the reading program (F(1,38) = 9.47, p = .004). (1 point) One Way AVOVA - Grade 6 Source Sum of Squares df Mean Square F Sig. Condition 60.025 1 9.466 .004 Error 240.950 38 6.341

Gr 6 Gr 7 Gr 8 Totals Control 2.80 5.10 5.7 4.53 Reading Prog 5.25 7.15 3.25 5.22 4.03 6.12 4.47 4.88 There is no difference between the reading program and the control for the Grade 7 students. (1 point) One Way AVOVA - Grade 7 Source Sum of Squares df Mean Square F Sig. Condition 42.025 1 1.249 .271 Error 1278.350 38 33.641

Gr 6 Gr 7 Gr 8 Totals Control 2.80 5.10 5.7 4.53 Reading Prog 5.25 7.15 3.25 5.22 4.03 6.12 4.47 4.88 The reading program reduces the number of books students read for the Grade 8 class (F(1,38) = 19.02, p < .001). (1 point) One Way AVOVA - Grade 8 Source Sum of Squares df Mean Square F Sig. Condition 60.025 1 19.016 .000 Error 119.950 38 3.157

Summary Statement Should the reading program be used? It depends on what Grade Level you are teaching. For grade 6 students, it is effective. For Grade 7 students it has no effect. For Grade 8 students it reduces the number of books they read over the summer. (1 Point)