2.
In testing teachers are frequently called upon to
describe the relationship between two sets of
measures. These two measures might be
scores by the same set of students on two
separate tests. This chapter shall focus on two
of the most commonly used measures of
relationship in educational measurement and
evaluation, namely: Pearson-Product-Moment
Correlation, Spearman rho.
3.
Correlation
Correlation is the relationship between two or
more paired factors or two or more sets (Best
and Khan, 19980. The degree of relationship is
usually measured and represented by a
correlation coefficient.
4.
A correlation coefficient is numerical measure of the
linear relationship between two factors
or sets of scores (Deauna, 1996). Coefficient can be
identified by either the letter r or the Greek letter
rho. Or other symbols, depending on the manner
the coefficient has been computed. Obtained
correlation coefficient can range from a – 1.00 or a
+ 1.00 toward zero. The sign of the coefficient
indicates the directions of the relationship and the
numerical value of Its strength.
5.
Obtained correlation coefficient can be interpreted
with the use of a scale like the ones presented below
(Best & kahn, 1998).
Correlation Coefficient Degree of Relationship
.00 - .20 Negligible
.21 - .40 Low
.41 - .60 Moderate
.61 - .80 Substantial
.81 – 1.100 High to Very High
6.
The correlation between two sets of scores
can either be4 positive or negative
(Gracia, 2003). Positive correlation means that
high scores in one variable (X) are associated
with high scores in other variable (Y).
Conversely a negative correlation means that
high scores on the variable are associated with
the low scores in another variable vise-versa.
7.
Pearson’s Product-Moment Correlation
This measure of relationship is used
when focus to be correlated are both metric
data. By metric data are meant
measurements, which can be subjected to the
four fundamental operations. To compute the
correlation coefficient using the
aforementioned test statistics, follow these
steps:
8.
1. Compute the sum of each set scores (SX, SY).
2. Square each score and sum the squares
(SX², SY²).
3. Count the number of scores in each group
(N)
4. Multiply each X score by its corresponding Y
score.
5. Sum the cross products of X (SXY).
6. Calculate the correlation, following the
formula.
9.
r = [NSXY- (SX) (SY)]
[(NSX² - (SX²) - (NSY² - (SY) ²)]
Where:
N = Number of paired observation
SXY = sum of the cross products of C and Y
SX = sum of the scores under Variable X
SY = sum of the scores under variable Y
(SX)² = Sum of x scores acquired
(SY) = sum of y equated
SX² = sum of squared X scores
SY² = Sum of squared Y scores
10.
Let us illustrate how Pearson’s is computed.
Table 9.1 shows the computational procedures
in determining the degree of relationship
between test scores of 10 students in English
(x) and mathematics (Y)
11.
TABLE 10.1
Computation of correlation Coefficient Using Pearson’s r
14.
Results of computation of person’s r yielded a
computed r of 0.96. this indicates that a very
high degree of relationship exists between the
test scores in English and mathematics. A
students who scored high in English also
obtained a high score in Mathematics.
15.
Spearman Rho
This measure relationship is used when test scores are ordinal or rank-
ordered. In computing rho, the following steps have to be observed:
1. Rank the process for in distribution X, giving the highest score a rank of 1
2. Repeat the process for the scores in distribution of Y.
3. Obtain the difference between the two sets of ranks (D).
4. Square each of these differences and sum up squared differences (SD²).
5. Solve for rho, the following the formula:
rho = 1 – 6SD²
N³ - N
Where :
rho = rank-order correlation coefficient
D = difference between paired ranks
SD² = number of paired of ranks
The computational procedures for the calculation of rho are reflected in Table 9.2
16.
TABLE 10.2
Computation of Correlation Coefficient
Using Spearman Rho
17.
X Y Rank
of X
Rank
Of Y D D
90 80 1 1 0 0
85 72 2 2 0 0
80 70 3 3 0 0
75 65 4 5 -1 1
70 68 5 4 1 1
65 55 6 7 -1 1
60 60 7 6 1 1
55 50 8 9 -1 1
50 53 9 8 1 1
45 44 10 10 0 0
SD² = 6
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