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i
q
= The proportion of incorrect answer
t
s
= Standard deviation of total score The result of
r
is then compared with
r
table of Product Moment at the level of significance α= 0.05. The item is valid if
r
t
r
, or if
r
is higher than
t
r
. The valid items of reading test are 42 at the level of significance r
o
is higher than r
t
0.339. Then, to know the reliability of reading test, the formula used is as follows:
kk
r
=
÷ ÷
ø ö
ç ç
è æ
- -
å
2
1 1
t
s pq
k k
Where:
kk
r
= Coefficient of reliability
k
= Total of valid items
å
pq
= Sums of all item variance
2
t
s
= Total variance The result of
r
is then compared with
r
table of Product Moment at the level of significance α= 0.05. The instrument is reliable is
r
t
r
, or if
r
is higher than
t
r
. The reliable items of reading test are 42 at the level of significance r
o
is higher than r
t
0.339. After to be tried out there are 43 valid and reliable items at the coefficient of
reliability
kk
r
= 0.93 for self-esteem questionnaire and there are 42 valid and reliable items at the coefficient of reliability
kk
r
= 0.92 for reading test.
F. Technique for Analyzing Data
Technique for analyzing data relates to the experimental design used. When using factorial design, as the researcher did, that included an independent variable,
moderator variable, and dependent variable, the size of the anallysis of variance is equal to the number of independent and moderator variables. The term variable in this
sense is the same as factor. One statistical device that is appropiate for factorial design is analysis of variance ANOVA. In ANOVA it is possible to put more than one
independent variables into a single study. As noted before, moderator variable is
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included into independent variable. Dealing with this study, the researcher uses two independent variables, the teaching methods and students’ self-esteem which is
divided into two levels; high and low levels. Because there are two independent variables, ANOVA would be called as 2x2 ANOVA.
In counting 2x2 ANOVA, there are some steps. These steps have to be done orderly. Here are the steps of 2x2 ANOVA:
Collaborative Strategic Reading
Direct Instruction Method
High Self-esteem Group 1
å
X
X Group 3
å
X
X
å
1
r
X
1 r
X
Low Self-esteem Group 2
å
X
X Group 4
å
X
X
2 r
X
å
2 r
X
Total
å
X
X
1 c
X
å
1 c
X
2 c
X
å
2 c
X Picture : The points on ANOVA
a. The total sum of squares:
= -
=
å å
å
N X
X x
t t
t 2
2 2
b. The sum of squares between gorups
å
2 t
x =
4 2
4 3
2 3
2 2
2 1
2 1
n X
n X
n X
n X
å å
å å
- +
+
c. The sum of squares within groups:
å
2 w
x =
å
2 t
x -
å
2 b
x
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d. The between-colums sum of squares:
å
2 bc
x =
N X
n X
n X
t c
c c
c
å å
å
- +
2 2
2 1
2 1
e. The beween-rows sum of squares:
å
2 br
x =
N X
n X
n X
t r
r r
r
å å
å
- +
2 2
2 1
2 1
f. The number of degerees of freedon associated with each source of variation
df for between-coolums sum of squares :C-1 df for betwwn-rows sum of squaryes :R-1
df for interaction : C-1 R-1 df for between-groups sum of aquares: G-1
df for within-groups sum of squares :
å
- 1
n df for total sum of squares: N-1
Where df is the degeree of freedom
R is the number of rows G is the number of groups
n is the number of subjects on one group N is the number of subjects in all groups
Here is the table for summarizing 2X2 ANOVA :
Source of Variance SS
df MS
Fo Ft.05 Ft.01
Between columns Method of Teaching
Between rows Level of Ability Coloms by rows Interaction
Between groups Within groups
Total Picture: The summary for 2x2 Factorial Design ANOVA
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To find which means are significantly diffferent from on another, there is Tukey’s test. Tukey’s test, named after John Tukey, is a statistical test generally used in
conjunction with an ANOVA. It compares all possible pairs of means, and is based on a studentized range distribution q this distribution is similar to the distribution of t from
the t-test. The test is also known as Tukey’s HSD Honestly Significant Difference test. The test compares the means of every treatment to the means of every other
treatment, and identifies where would be expected to allow. The formula for this test is as follows:
a. Between columns
n iance
error c
X c
X q
var
2 1
- =
b. Between rows
n iance
error r
X r
X q
var
2 1
- =
c. Between columns
HS
n iance
error r
c X
r c
X q
var
1 2
1 1
- =
d. Between columns
LS
n iance
error r
c X
r c
X q
var
2 2
2 1
- =
or
n iance
error r
c X
r c
X q
var
2 1
2 2
- =
G. Statistical Hypotheses
