1. Professor : Dr. Dana
Presented by : Omid Sanaei

2.  Correlational research describes the linear
relationship between two or more variables
without any hint of attributing the effect of one
variable on another.
 As a descriptive technique, it is very powerful
because this method indicates whether variables
(such as number of studying and test score) share
something in common with each other. If they do,
the two are correlated (or co – related) with one
another.
*

3. *
 The most frequent measure used to assess degree
of relatedness is the correlation coefficient, which
is a numerical index that reflects the relationship
between two variables.
 Correlation coefficient is expressed as a number
between -1.00 and +1.00, and it increases in
strength as the amount of variance that one
variable shares with another increases.

4.  Correlations can be direct or positive, meaning that as
one variable changes in value, the other changes in the
same direction, such as the relationship between the
number of hours you study and your grade on an exam.
Generally, the more you study, the better your grade
will be. Likewise, the less you study, the worse your
grade will be.
 Correlations can also reflect an indirect or negative
relationship, meaning that as one variable changes in
value in one direction, the other changes in the
opposite direction, such as the relationship between the
speed at which you through multiple-choice items and
your score on the test. Generally, the faster you go, the
lower your score; the slower you go, the higher your
score.

5. ExampleThe correlation isand Y …If X …
The taller one gets (X),
the more
one weighs (Y).
Positive
or direct
Increases
in value
Increases
in value
The fewer mistakes
one makes (X),
the fewer hours
of remedial work
(Y) one participates in.
Positive
or direct
Decreases
in value
Decreases
in value
The better one
behaves (X), the
Fewer in-class
suspensions (Y) one has.
Negative
or indirect
Decreases
in value
Increases
in value
The less time one
spends studying (X), the
more errors one
makes on the test (y).
Negative
or indirect
Decreases
in value
Decreases
in value
Table 9.2 Two types of correlations: positive or direct, negative or indirect

6. *
 The most frequently used measure of relationships
is the Pearson product moment correlation,
represented by letter r followed by symbols
representing the variables being correlated. The
symbol 𝑟𝑥𝑦 represents a correlation between the
variables X and Y.
 Scattergram : A scattergram is a plot of scores in
pairs, in other words the scattergram is a visual
representation of the correlation coefficient of the
relationship between two variables.

7. 0
2
4
6
8
10
0 2 4 6 8 10
Data Set A
3 3
5 6
4 7
6 8
7 7
8 6
6 7
7 9
8 8
9 9
0
2
4
6
8
10
0 2 4 6 8 10
Data Set B
3 3
5 6
4 7
6 5
7 7
8 3
6 7
7 9
8 5
9 9
𝑟𝑥𝑦=.70
𝑟𝑥𝑦= .32

8. 0
2
4
6
8
10
0 2 4 6 8 10
0
1
2
3
4
5
6
0 2 4 6 8 10
Data Set C
3 9
5 8
4 7
6 7
7 6
8 3
6 3
7 4
4 9
5 8
Data Set D
3 2
5 4
4 5
6 4
7 3
8 4
6 5
7 4
8 2
9 3
𝑟𝑥𝑦=− .82
𝑟𝑥𝑦=− .15

9. *
The easiest manual way to compute the correlation between
two variables is through the use of the raw score method.
The formula for 𝑟𝑥𝑦 ( where xy represents the correlation
between x and y ) is as follows:
Where 𝑟𝑥𝑦 = the correlation coefficient between x and y
∑ = the summation sign n = the size of the sample
X = the individual’s score on the X variable
Y = the individual’s score on the Y variable
XY = the product of each X score times its corresponding Y score
𝑋2 = the individual X score, squared
𝑌2 = the individual Y score, squared
𝑟𝑥𝑦 =
𝑛 𝑥𝑦 − 𝑥 𝑦
[𝑛 𝑋 2 − ( 𝑋)2][𝑛 𝑦 2 − ( 𝑌)2]

10.  If you have n variables, then you will have “n
taken two at a time’’ pairs of relationship.

11. *
 The correlation coefficient reflects the degree of
relationship between variables.
 There are two ways to interpret these general
indicators of relationships.
 The first method is the “eyeball’’ method, in which
correlations of a certain value are associated with a
certain nominal degree of relationship such that:
Are said to beCorrelations between
Very strong.8 and 1.0
Strong.6 and .8
Moderate.4 and .6
Weak.2 and .4
Very weak.0 and .2

12.  A sounder method for interpreting the correlation
coefficient is to square its value and then compute the
coefficient of determination. This value, 𝑟 𝑥𝑦2, is the
amount of variance that is accounted for in one variable
by the other.in other words, it allows you to estimate
the amount of variance that can be accounted for in one
variable by examining the amount of variance in another
variable.
 If the correlation between two variables is .40, then the
coefficient of determination is .16. Sixteen percent (16%)
of the variance on one variable can be explained by the
variance in other variable; 84% (100% - 16%)of the
variance is unexplained. This portion of unexplained
variance is referred to as the coefficient of alienation.

13. Table 9.4 Differences in the amount of variance accounted for as a function of different values of the correlation
coefficient .
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5
Value of correlation coefficient
Varianceaccountedfor
Figure 9.2 The proof is the seeing --- relationship between increases in the correlation coefficient
and increases in the amount of variance explain the relationship between two variables.