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Where: ∑ X
∑ X n
n Note:
痀
: the coefficient of reliability : the proportion of correct response on a single item
: the proportion of incorrect response on the same item : the variance of scores on the total test
e : the number of valid item
To know whether the instrument was reliable or not, 痀
or 痀 was
compared with 痀 . If 痀
痀 , the instrument was reliable, but if 痀 痀 , the
instrument was not reliable.
E. The Technique of Analyzing Data
The data were collected from the experimental and control group in the form of scores. Before the data were analyzed, the sample was grouped based on
the student’s linguistic intelligence scores. First of all, the student’s linguistic intelligence scores were ranked by the researcher from the greatest to the smallest.
Then, the students were divided into two groups by taken 50 of the greatest scores as a group of students with high linguistic intelligence and 50 of the
smallest scores as a group of students with low linguistic intelligence. In analyzing the data, the scores of the student’s reading test were
described and analyzed by using the descriptive statistics and inferential statistics.
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Descriptive statistics covered the frequency distribution, mean, mode, median, standard deviation, histogram and polygon of the student’s scores. After the data
were described, the inferential statistics was used. It was used to analyze the normality and homogeneity of the data; both were the analysis requirements of
using ANOVA test. Because this research was a 2 x 2 factorial design, a 2 x 2 multifactor
Analysis of Variance ANOVA was used to test the statistical hypothesis of the research. It was used to find out the significance difference between columns and
rows of the groups of sample. By using this design, it was possible to analyze the interaction effect between two treatments, which each treatment was affected by
moderator variable. If there was an interaction, where the effect of the student’s linguistic
intelligence level upon the student’s reading competence depended on the variation of the teaching techniques, the Tukey test was used as further test to
know the difference between cells. However, if there was no interaction, it was not necessary to use the Tukey test. Thus, the following steps were conducted in
analyzing the data.
1. Normality Test
To ensure whether or not the data obtained had normal distribution. According to Gamst, et al. 2008: 52, “Normality is the assumption that the error
components associated with the scores are normally distributed. If the residual errors are normally distributed, then the distribution of scores will follow suit
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by being distributed in a normal manner”. It means that the data for each group must be distributed normally. The
scores were obtained from the student’s reading test score. To examine the normal distribution of the data, the researcher
used the following procedure. a.
Determining the hypothesis H
o
: the sample did not come from normal population. H
: the sample came from normal population. b.
Computing the data
m 1 w痀
∑ ∑
m m 1
w痀 ∑
m 1 5
痀ame m
c. Test result
H
o
was accepted and H
was rejected, if L
o
L
t
. It means that the data were not distributed normally.
H
was accepted and H
o
was rejected, if L
o
L
t
. It means that the data were distributed normally.
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2. Homogeneity Test
To check whether the research population had the same variance, the researcher examined the data by using homogeneity test. According to Gamst, et
al. 2008: 57, “The homogeneity assumption requires that the distribution of residual errors for each group have equal variances.” The procedure in examining
the data was as follows: a.
Determining the hypothesis H
o
: the data were not homogenous. H
: the data were homogenous, they had the same variance. b.
Computing the data ∑
∑ m
m 1 ∑
∑ m
m 1 ∑
∑ m
m 1 ∑
∑ m
m 1 ∑ m
1 ∑ m
1 铘w
铘w ∑ m
1 ∑ m
1 log
m 1
铘m1 m
1 log
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c. Test result
H
o
was accepted and H
was rejected, if . It means that the data
were not homogeneous. H
was accepted and H
o
was rejected, if . It means that the data
were homogeneous.
3. ANOVA Two-Way Factorial Design Test
To investigate whether there were a significance difference and an interaction between the variables and the variances, it was necessary to use
ANOVA test. Mackay and Gass 2005: 274 state, “Many research designs require comparisons with more than two groups and ANOVA may be appropriate
in this context. ANOVA results provide an F value, which is a ratio of the amount of variation between the groups to the amount of variation within the groups.”
This kind of test was used to analyze the data gained for different groups. This test analyzed different groups between columns and between rows. Groups
between columns were the student’s reading test result for different teaching techniques, while groups between rows were the student’s reading test result for
different level of linguistic intelligence. After gaining the values of those analyses, the value of the interaction effect was possible to be calculated. It was to describe
the effect of the teaching techniques on the level of student’s linguistic intelligence. The design of the ANOVA was illustrated as follows.
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Table 3.3. 2 x 2 Multifactor Analysis of Variance Main effects
Teaching Technique A Simple effect
Linguistic Intelligence B
Experiment group Note-Taking Pairs
Control group Three-Phase Reading
High Linguistic Intelligence Group 1
Group 2
Low Linguistic Intelligence Group 3
Group 4
Total
For the clear explanation, the steps of ANOVA two-way variance were
described as follows: a.
Determining the hypothesis 1
For groups in between columns teaching techniques H
o
: the difference effect between column was not significant. H
: the difference effect between column was significant. 2
For groups in between rows student’s linguistic intelligence H
o
: the difference effect between rows was not significant. H
: the difference effect between rows was significant. 3
For groups in interaction effect teaching techniques and student’s linguistic intelligence
H
o
: there was no interaction effect. H
: there was an interaction effect.
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b. Computing the data
The analyses were as follows: 1
The total sum of squares: ∑
2 The sum of squares between groups:
∑ m
∑ m
∑ m
∑ m
∑
3 The sum of square within group:
4 The between-columns sum of squares:
Ǵ
∑
Ǵ
m
Ǵ
∑
Ǵ
m
Ǵ
∑
5 The between-rows sum of squares:
∑ m
∑ m
∑
6 The sum-of-squares interaction:
u Ǵ
7 The number of degrees of freedom associated with each source of
variation: df for between-columns sum of squares = C – 1
df for between-rows sum of squares = R – 1 df for interaction = C – 1R – 1
df for between-groups sum of squares = G – 1
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df for within- groups sum of squares = Σ n – 1
df for total sum of squares = N – 1 where:
C = the number of columns R = the number of rows
G = the number of groups n = the number of subjects in one group
N = the number of subjects in all groups c.
Test result 1
For groups in between columns teaching techniques H
o
was accepted and H
was rejected, if at the significance level
α = 0.05. It means that the difference between columns was not significant.
H
was accepted and H
o
was rejected, if at the significance level
α = 0.05. It means that the difference between columns was significant.
2 For groups in between rows student’s linguistic intelligence
H
o
was accepted and H
was rejected, if at the significance level
α = 0.05. It means that the difference between rows was not significant.
H
was accepted and H
o
was rejected, if at the significance level
α = 0.05. It means that the difference between rows was significant.
3 For groups in interaction effect teaching techniques and student’s
linguistic intelligence H
o
was accepted and H
was rejected, if at the significance level
α = 0.05. It means that there was no interaction effect.
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H
was accepted and H
o
was rejected, if at the significance level
α = 0.05. It means that there was an interaction effect.
The following Table 3.4. is the summary of ANOVA test.
Table 3.4. The Summary of a 2 x 2 Multifactor Analysis of Variance Source of variant
SS df
MS F
o
F
t0.05
Between column Teaching techniques: A
1
and A
2
Between rows Linguistic Intelligence: B
1
and B
2
Columns by rows Interaction between A and B Between groups
Within groups error variance SA Total Variance total SS
4. Tukey Test
After knowing the result of computation of ANOVA factorial design, it was needed to use Tukey Test if the result of ANOVA showed that there was an
interaction effect between the teaching techniques and student’s linguistic intelligence. It was used to compare the means of every treatment with the other
means and to identify which means had significance different from the other. It is explained as follow:
a. Note-Taking Pairs technique compared with DR-TA technique.
Ǵ Ǵ
뾸痀痀w痀 �a痀oam |m b.
Students having high linguistic intelligence compared with students having low linguistic intelligence.
뾸痀痀w痀 �a痀oam |m
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c. Note-Taking Pairs technique compared with DR-TA technique for the
students having high linguistic intelligence
Ǵ Ǵ
뾸痀痀w痀 �a痀oam |m d.
Note-Taking Pairs technique compared with DR-TA technique for the students having low linguistic intelligence
Ǵ Ǵ
뾸痀痀w痀 �a痀oam |m or
Ǵ Ǵ
뾸痀痀w痀 �a痀oam |m The analyses of the results of the computation were: 1
was compared with
, if , the difference was significant, and if
, the difference was not significant. 2 To know which one was better, the means were compared.
F. Statistical Hypothesis
