66
The testing is done to find out whether the data are homogeneous. This test is important because homogeneity of the data shows that the population is well-
formed. To test homogeneity of data, test is used. If
2
o
is lower than
2
t
at the level of significance α=0.05, the data are homogeneous.
Table 12. Homogeneity Test
Group n
i
– 1 1 n
i
– 1 s
i 2
Lns
i 2
n
i
– 1 Lns
i 2
1 10
0.1 40.273
3.696 36.957
2 10
0.1 19.473
2.969 29.690
3 10
0.1 57.655
4.054 40.545
4 10
0.1 54.655
4.001 40.010
40 0.4
147.202
2
=
k N
1 1
n 1
1 k
3 1
1 s
ln 1
n B
i 2
i i
=
40 1
4 .
1 4
3 1
1 202
. 147
461 .
150
= 3.128
2 0. 05
= 7.815 Because
2
o
3.128 is lower than 815
. 7
2
t
, the data are homogeneous.
C. Data Analysis
Hypothesis test can be done after the results of normality and homogeneity test are fulfilled. The test is done by using multifactor analysis of variance 2 x 2.
Ho is rejected if F
o
F
t
meaning that there is a significant difference and an
67
interaction. If Ho is rejected, the analysis is continued to know which group is better by using Tukey test. The multifactor analysis of variance 2 x 2 and Tukey
test are described as below. 1. Summary of a 2 x 2 M ultifactor Analysis of Variance
Table 13. M ultifactor Analysis of Variance Source of variance
SS df
M S F
o
F
t .05
Between columns model
Between rows Intelligence
Columns by rows Interaction
295.364
5324.000
1833.091 1
1 1
295.364
5324.000
1833.091 6.867
123.775
42.617 4.08
Between groups Within groups
7452.455 1720.545
3 40
2484.15
43.014
Total 9173.00
43
a. Because F
o
between columns 6.867 is higher than F
t .05
4.08, the difference between columns is significant. It can be concluded that the
model used differs significantly from one another in their effect on their performance of the subjects in the experiment. The students’ mean of c
1
62.09 is higher than t he students’ mean of c
2
56.90, so the students who are taught by using reciprocal are better in reading skill than students who
are taught by using direct instructional. b. Because F
o
between rows 123.77 is higher than F
t .05
4.08, it means difference between rows is significant. It can be concluded that the
difference between the achievement of those subjects having high
68 intelligence and those having low intelligence is significant. The students’
mean of r
1
70.50 is higher than the students’ mean of r
2
48.50, so the students who have high level of intelligence have better reading skill than
the students who have low intelligence c. Because F
o
interaction 42.617 is higher than F
t .05
4.08, it can be concluded that there is interaction effect between the two variables, the
teaching models and the degree of intelligence. It means that the effect of the teaching model used on the achievement depends on the subjects’ degree or
level of intelligence. 2. Tukey Test.
Tukey test is done to find which model is more effective and which group is better.
q
is found by dividing the difference between the means by the square root of the ration of the within group variation and the sample size.
Table 14. Tukey Test
PAIR TUKEY
CRITICAL A
1
– A
2
3.92 2.95
A
1
B
1
– A
2
B
1
9.18 3.11
A
1
B
2
– A
2
B
2
4.06 3.11
B
1
– B
2
15.8 2.95
A
1
B
1
- A
1
B
2
17.1 3.11
A
2
B
1
- A
2
B
2
4.56 3.11
69
a. Comparing two means between columns to find which model is more effective
1 Comparing two means between columns q
o
is 3.92. The value of q
t
for α = 0.05 and n = 22 is 2.95. Because q
o
3.92 is higher than q
t
2.95 reciprocal teaching differs significantly from direct instructional for
teaching reading. The mean score of students who are taught by using reciprocal teaching 62.09 is higher than who are taught by using direct
instructional 56.90, so reciprocal teaching is more effective than direct instructional for teaching reading.
2 Comparing two means between cells A
1
B
1
and A
2
B
1
. q
o
is 9.18. The value of q
t
for α = 0.05 and n = 11 is 3.11. Because q
o
9.18 is higher than q
t
3.11 reciprocal teaching differs significantly from direct instructional for teaching reading for students having high intelligence. The mean score
of students having high intelligence who are taught by using reciprocal teaching 79.54 is higher than those who are taught by using direct
instructional 61.45, so reciprocal teaching is more effective than direct instructional for teaching reading for students having high intelligence
3 Comparing two means between cells group A
1
B
2
and group A
2
B
2
. q
o
is 3.42. The value of q
t
for α = 0.05 and n = 11 is 3.11. Because q
o
4.06 is higher than q
t
3.11 instructional model differs significantly from reciprocal teaching model to teach reading for students who have low
intelligence. The mean score of students having low intelligence who are taught by using direct instructional 52.36 is higher than those who are
70
taught by using reciprocal teaching 44.63, so direct instructional is more effective than reciprocal teaching for teaching reading for students having
low intelligence. b. Comparing two means between rows to find which group is better
1 Comparing two means between rows group B
1
and group B
2
. q
o
is 15.8. The value of q
t
for α = 0.05 and n = 22 is 2.95. Because q
o
15.8 is higher than q
t
3.95 the students who have high intelligence are significantly different in reading from the students who have low intelligence. The
mean score of students having high intelligence 70.5 is higher than those who have low intelligence 48.5, so the students who have high level of
intelligence have better reading skill than the students who have low intelligence.
2 Comparing two means between cells group A
1
B
1
and group A
1
B
2
. q
o
is 17.7. The value of q
t
for α = 0.05 and n = 11 is 3.11. Because q
o
17.7 is higher than q
t
3.11 the students who have high intelligence who are taught by using reciprocal teaching are significantly different in reading
from the students who have low intelligence who are taught by using reciprocal teaching. The mean score of students having high intelligence
70.5 is higher than those who have low intelligence 48.5, so the students who have high level of intelligence have better reading skill than
the students who have low intelligence those taught by using reciprocal teaching.
71
3 Comparing two means between cells group A
2
B
1
and group A
2
B
2
. q
o
is 4.56. The value of q
t
for α = 0.05 and n = 11 is 3.11. Because q
o
4.56 is higher than q
t
3.11 the students who have high intelligence who are taught by using direct instructional model are significantly different in
reading from the students who have low intelligence who are taught by using direct instructional model. The mean score of students having high
intelligence 61.4 is higher than those who have low intelligence 52.4, so the students who have high level of intelligence have better reading
skill than the students who have low intelligence those taught by using direct instructional model.
D. Discussion
