Concept of Correlation and It’s Uses in Educational
Research
A correlation coefficient is a numerical
measure of some type of correlation, meaning a statistical relationship between two variables. The
variables may be two columns of a given data
set of observations, often called
a sample, or two components of a multivariate random variable with a known distribution.
Several types
of correlation coefficient exist, each with their own definition and own range
of usability and characteristics. They all assume values in the range from −1
to +1, where +1 indicates the strongest possible agreement and −1 the strongest
possible disagreement. As tools of analysis, correlation coefficients present
certain problems, including the propensity of some types to be distorted by outliers and the possibility of incorrectly being used to infer a causal relationship between the variables. Correlation is a statistical technique that can show
whether and how strongly pairs of variables are related. For example, height
and weight are related; taller people tend to be heavier than shorter people.
The relationship isn't perfect. People of the same height vary in weight, and
you can easily think of two people you know where the shorter one is heavier
than the taller one. Nonetheless, the average weight of people 5'5'' is less
than the average weight of people 5'6'', and their average weight is less than
that of people 5'7'', etc. Correlation can tell you just how much of the
variation in peoples' weights is related to their heights. Although this
correlation is fairly obvious your data may contain unsuspected correlations.
You may also suspect there are correlations, but don't know which are the
strongest. An intelligent correlation analysis can lead to a greater
understanding of your data.
Types of Correlation
·
Positive Correlation
·
Negative Correlation
·
Partial Correlation
·
Linear Correlation
·
Zero Order Correlation
·
Scatter Plot Correlation
·
Spearman's Correlation
·
Non Linear Correlation
·
Weak Correlation
Positive
correlation
A positive
correlation is a correlation in the same direction.
Negative
correlation
A negative
correlation is a correlation in the opposite direction
Partial correlation
The correlation is
partial if we study the relationship between two variables keeping all other variables constant
Linear correlation
When the change in one
variable results in the constant change in the other variable, we say the
correlation is linear. When there is a linear correlation, the points plotted
will be in a straight line
Zero order correlation
A zero correlation suggests that the correlation statistic did not
indicate a relationship between the two variables.
Scatter plot correlation
A scatter plot is a type
of mathematical diagram using cartesian coordinates to
display values for two variables for a set of data. Scatter plots will often
show at a glance whether a relationship exists between two sets of data.
Spearman's correlation
Spearman's rank correlation coefficient allows us
to identify easily the strength of correlation within a data set of two
variables, and whether the correlation is positive or negative.
Non linear correlation
When the amount of
change in one variable is not in a constant ratio to the change in the other
variable, we say that the correlation is non linear.
Weak correlation
The range of the
correlation coefficient between -1 to +1. If the linear
correlation coefficient takes values close to 0, the correlation is
weak.
Uses in Educational Research
·
In correlational research we do not (or at least try not to) influence
any variables but only measure them and look for relations (correlations)
between some set of variables.
·
In experimental research, we manipulate some variables and then measure
the effects of this manipulation on other variables.
·
Experimental data may potentially provide qualitatively better information.
·
Only experimental data can conclusively demonstrate causal relations
between variable.
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