How to Interpret a 2 Way ANOVA The

How to Interpret a 2 -Way ANOVA

The Following Tables are the SPSS print-outs for the analysis of the data. Descriptive Statistics Std. Grade Condition Grade 6 control 20 5. 2500 2. 88143 20 Total 4. 0250 2. 77800 40 control 5. 1000 2. 48998 20 7. 1500 7. 81547 20 Total 6. 1250 5. 81857 40 control 5. 7000 1. 80933 3. 2500 Total control Reading Program Total N 2. 09259 Program Grade 8 Deviation 2. 8000 Reading Grade 7 Mean Reading Program Total 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 2. 80 5. 10 5. 7 4. 53 20 Reading Program 5. 25 7. 15 3. 25 5. 22 1. 74341 20 Totals 6. 12 4. 47 4. 88 4. 4750 2. 14820 40 4. 5333 2. 45962 60 5. 2167 5. 08934 60 4. 8750 3. 99488 120 Control 4. 03 6 Points

Two-Way ANOVA TABLE Sum of Squares df Mean Square F Sig. Grade 97. 800 2 48. 900 3. 401 . 037 Condition (reading vs. control) 14. 008 1 14. 008 . 974 . 326 148. 067 2 74. 033 5. 149 . 007 1639. 250 114 14. 379 Source Grade * Condition Error 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 Totals 4. 03 6. 12 4. 47 4. 88 Books_Read LSD LSD (I) Grade 6 Grade 7 Grade 8 Grade 8 (J) Grade 7 Grade 7 8 Grade Grade 8 6 Grade Grade 6 7 Grade 7 Mean Difference (I -J) -J)-2. 1000* * -2. 1000 -. 4500* 2. 1000* * 2. 1000 1. 6500. 4500 -1. 6500 Std. Error. 84792. 84792 Sig. . 015. 597. 015. 044. 597. 044 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 Sum of Squares df Mean Square F Sig. Grade 97. 800 2 48. 900 3. 401 . 037 Condition (reading vs. control) 14. 008 1 14. 008 . 974 . 326 148. 067 2 74. 033 5. 149 . 007 1639. 250 114 14. 379 Source Grade * Condition Error 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 Totals 4. 03 6. 12 4. 47 4. 88

Two-Way ANOVA TABLE Sum of Squares df Mean Square F Sig. Grade 97. 800 2 48. 900 3. 401 . 037 Condition (reading vs. control) 14. 008 1 14. 008 . 974 . 326 148. 067 2 74. 033 5. 149 . 007 1639. 250 114 14. 379 Source Grade * Condition Error 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 Totals 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 Totals 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 Condition Error Sum of Squares df Mean Square 60. 025 1 60. 025 240. 950 38 6. 341 F 9. 466 Sig. . 004

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 Totals 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 Condition Error Sum of Squares df Mean Square 42. 025 1278. 350 38 33. 641 Sig. F 1. 249 . 271

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 Totals 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 Condition Error Sum of Squares df Mean Square 60. 025 119. 950 38 3. 157 F 19. 016 Sig. . 000

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)