1. How to Interpret a 2-Way ANOVA

2. 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 20
Reading Program
5.2500
Total
4.0250 40
Grade 7
5.1000
7.1500
6.1250
Grade 8
5.7000
3.2500
4.4750
4.5333 60
5.2167
4.8750
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 Prog
5.25
7.15
3.25
5.22
4.03
6.12
4.47
4.88
6 Points

3. 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
74.033
5.149
.007
Error
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)

4. 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
Books_Read
LSD
(I) Grade
(J) Grade
Mean Difference (I-J)
Std. Error
Sig.
Grade 6
Grade 7 *
.84792
.015
Grade 8
-.4500
.597
2.1000*
1.6500
.044
.4500
Books_Read
LSD
(I) Grade
(J) Grade
Mean Difference (I-J)
Std. Error
Sig.
Grade 6
Grade 7 *
.84792
.015
Grade 8
-.4500
.597
2.1000*
1.6500
.044
.4500
Books_Read
LSD
(I) Grade
(J) Grade
Mean Difference (I-J)
Std. Error
Sig.
Grade 6
Grade 7 *
.84792
.015
Grade 8
-.4500
.597
2.1000*
1.6500
.044
.4500
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

5. 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
74.033
5.149
.007
Error
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 Prog
5.25
7.15
3.25
5.22
4.03
6.12
4.47
4.88

6. 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
74.033
5.149
.007
Error
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 Prog
5.25
7.15
3.25
5.22
4.03
6.12
4.47
4.88

7. 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 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)
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 38
6.341

8. 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 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)
Grade 6 students read more books with the reading program (F(1,38) = 9.47, p = .004). (1 point)
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 38
33.641

9. 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 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)
Grade 6 students read more books with the reading program (F(1,38) = 9.47, p = .004). (1 point)
There is no difference between the reading program and the control for the Grade 7 students. (1 point)
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 38
3.157

10. Should the reading program be used
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)