Range of correlation coefficient
Correlation:
Correlation
is a statistical technique used measured and describe relationship between two
variables. These variables are neither manipulated nor controlled, rather they
simply are observed as they naturally exist in the environment. Suppose a
researcher is interested in relationship between number of children in a family
and IQ of the individual child.
He would
take a group of students coming from different families. Then he simply observe
or record the number of children in a family and then measure IQ score of each
individual student same group. He will neither manipulate nor control any
variable. Correlation requires two separate scores for each individual. These
scores are normally identified as X and Y and can be present in a table or in a
graph.
Characteristics
of relationship that correlation measures
A
correlation measures three characteristics of the relationship between X and Y.
These are:
1) The direction
of the relationship
The
direction of the relationship can be classified into two basic categories:
positive and negative.
In a
positive correlation both variable tend to change into same direction. When
variable X increases, the variable Y also increases. And if the variable X
decreases, the variable Y also decreases. In other words we can say that both
variables are directly proportional to each other.
In a
negative correlation both variables do not tend to change into same direction.
They go in opposite direction of each other. When the variable X increases, the
variable Y decreases. And if the variable X decreases the variable Y increases.
In other words we can say that both variables are indirectly proportional to
each other.
2) The form of
the relationship
The form of
correlation measures how well the data fit the specific form being considered.
For example a linear correlation measures how well the data points fit on a
straight line.
3) The degree of
the relationship
The degree
of relationship is measured by the numerical value of the correlation. This
value varies from 1.00 to -1.00. A perfect correlation is always identified by
a correlation of 1.00 and indicates a perfect fit.+ 1.00 will indicate perfect
positive correlation and -1.00 will indicate perfect negative correlation. A
correlation of 0 indicates no correlation or no fit at all.
The Pearson
correlation
The most
commonly used correlation is the Pearson correlation. It is also known as
Pearson product moment correlation. It measured the degree and the direction of
linear relationship of between two variables. It is denoted by r, and r= degree
to which X and Y vary together/degree to which X and Y vary separately = co variability
of X and Y / variability of X and Y vary separately.
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