This document discusses correlation and the correlation coefficient. It defines correlation as a measure of the relationship between two variables, but notes that correlation does not imply causation. The correlation coefficient, r, quantifies the strength of the linear relationship between two variables on a scale of -1 to 1. Values closer to 1 or -1 indicate stronger correlations, while values closer to 0 indicate weaker or no correlation. Examples of using correlation in descriptive and experimental research are provided.

1. MEASURE OF RELATIONSHIP:
CORRELATION COEFFICIENT
Prepared by:
Ms. Lady Asrah A. Carim

2. Correlation
• In Statistics, this is commonly concerned to as the correlation
coefficient.
• A value of correlation coefficient (r) represents the whole group
and tells a story the same with mean and standard deviation.
• For instance, the weight-height relationship of fourth year high
school students in certain school has a correlation coefficient (r)
of 0.89, high relationship. This means that the heavier the
weight, the taller is the student and the lighter the weight, the
short the student.

3. Smith/Davis (c) 2005 Prentice Hall
The Nature of Correlation
• Often used as means for
prediction, correlation tells us
how related two variables are.
• However, note that even though
two variables may be highly
correlated, you should not
assume that one variable causes
the other.
• CORRELATION DOES NOT
IMPLY CAUSATION.
• For example, there is the third
variable possibility (i.e., there
may be additional variable(s) that
are causing the two things you are
investigating to be related to each
other).
“There’s a significant
NEGATIVE correlation
between the number of mules
and the number of academics in
a state, but remember,
correlation is not causation”

4. Measures of Correlation
• These are used both in descriptive and experimental researches.
• Some examples of descriptive researches on correlation are as
follows:
1. Correlation Between Achievement and Economic Status of Fourth
Year High School Students
2. IQ and Personality Relationship of Fourth Year High School Students
3. Correlation Between Mathematics and English Achievements of
Second Year Students

5. Measures of Correlation
• Some examples of experimental researches on correlation are as
follows:
1. Weight-Length Relationship of Mudcrab (Alimango) Cultured in the
Backyard Fishpond Using Bread Meal as Supplemental Feed
2. The Height-Weight Relationship of Bottle-Fed Infants Using the
Same Milk Brand
3. Weight-Length Relationship of Tilapia Cultured in Backyard
Fishpond Using Trash Fish as Supplemental Feed

6. Smith/Davis (c) 2005 Prentice Hall
The Scatterplot: Graphing Correlations
• Also known as the scatter diagram, the scatterplot
allows us to visually see the relation between two
variables.
• One variable is plotted on the ordinate and the
other on the abscissa.
• Although you can list either variable on either axis, it is
common to place the variable you are attempting to
predict on the ordinate.
• Positive correlations – occur when both variables move
in the same direction (e.g., as NAT scores increase, so to
do GPAs).
• Negative Correlations – occur when one variable
increases, the other decreases (e.g., as age increases, the
number of speeding tickets decrease).

7. Smith/Davis (c) 2005 Prentice Hall
The Range of r Values
• The Range of r – correlation
coefficients can range in value
from -1.00 to +1.00.
• Perfect positive correlation occurs
when you have a value of +1.00 and
as we see an increase of one unit in
one variable, we always see a
proportional increase in the other
variable.
• The existence of a perfect
correlation indicates there are no
other factors present that influence
the relation we are measuring. This
situation rarely occurs in real life.

8. • There are traditionally assigned values ranging from -1 to +1.
Smith/Davis (c) 2005 Prentice Hall
The Range of r Values
• The Range of r – correlation
coefficients can range in value from -
1.00 to +1.00.
• A correlation of -1.00 indicates a
perfect negative correlation between
the two variables of interest. That is,
whenever there is an increase of one
unit in one variable, there is always
the same proportional decrease in the
other variable.

9. Smith/Davis (c) 2005 Prentice Hall
The Range of r Values
• The Range of r – correlation
coefficients can range in value
from -1.00 to +1.00.
• A zero correlation means there is
little or no relation between the
two variables. That is, as scores on
one variable increase, scores on
the other variable may increase,
decrease, or not change at all.

10. Y
Strong relationships Weak relationships
X
Y
X
Y
Y
X
X
Linear Correlation
Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall

11. Linear Correlation
Y
X
Y
X
No relationship
Slide from: Statistics for Managers Using Microsoft® Excel 4th Edition, 2004 Prentice-Hall

12. Smith/Davis (c) 2005 Prentice Hall
The Pearson Product Moment Correlation Coefficient
• The correlation coefficient is the single number that
represents the degree of relation between two variables.
• The Pearson Product-Moment Correlation Coefficient
(symbolized by r) is the most common measure of
correlation; researchers calculate it when both the X
variable and the Y variable are interval or ration scale
measurements.
• The raw score formula for r is:

13. Interpretation:
Value of r Interpretation/Classification
0.00 to ±ퟎ. ퟐ0 negligible
±0.21 to ±ퟎ. ퟒퟎ slight
±0.41 to ±ퟎ. ퟕ0 moderate
±0.71 to ±ퟎ. ퟗ0 high
±0.91 to ±ퟎ. ퟗퟗ very high
±ퟏ Perfect