Page 170 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Moment correlation is designated by the Greek letter rho (?). When computed in a sample, it is
designated by the letter “r” and is sometimes called “Pearson’s r.” Pearson’s correlation reflects
the degree of linear relationship between two variables. It ranges from + 1 to – 1. A correlation
of + 1 means that there is a perfect positive linear relationship between variables. A correlation
of – 1 means that there is a perfect negative linear relationship between variables. A correlation
of 0 means there is no linear relationship between the two variables. Correlations are rarely if
ever 0, 1, or – 1. If you get a certain outcome it could indicate whether correlations were negative
or positive.
• The simplest device for determining relationship between two variables is a special type of dot
chart called scatter diagram. When this method is used the given data are plotted on a graph
paper in the form of dots, i.e., for each pair of X and Y values we put a dot and thus obtain as
many points as the number of observations. By looking to the scatter of the various points we
can form an idea as to whether the variables are related or not. The more the plotted points
“scatter” over a chart, the less relationship there is between the two variables. The more nearly
the points come to falling on a line, the higher the degree of relationship. If all the points lie on
a straight line falling from the lower left-hand corner to the upper right corner, correlation is
said to be perfectly positive (i.e., r = + l) (diagram I).
• It is a simple and non-mathematical method of studying correlation between the variables. As
such it can be easily understood and a rough idea can very quickly be formed as to whether or
not the variables are related.
• Of the several mathematical methods of measuring correlation, the Karl Pearson’s method,
popularly known as Pearsonian coefficient of correlation, is most widely used in practice. The
Pearsonian coefficient of correlation is denoted by the symbol r. It is one of the very few symbols
that is used universally for describing the degree of correlation between two series.
• When the number of observations of X and Y variables is large, the data are often classified into
two-way frequency distribution called a correlation table. The class intervals for Y are listed in
the captions or column headings, and those for X are listed in the stubs at the left of the table
(the order can also be reversed). The frequencies for each cell of the table are determined by
either tallying or sorting just as in the case of a frequency distribution of a single variable.
• The two variables under study are affected by a large number of independent causes so as to
form a normal distribution. Variables like height, weight, price, demand, supply, etc., are affected
by such forces that a normal distribution is formed.
• There is a cause-and-effect relationship between the forces affecting the distribution of the items
in the two series. If such a relationship is not formed between the variables, i.e., if the variables
are independent, there cannot be any correlation. For example, there is no relationship between
income and height because the forces that affect these variables are not common.
• Amongst the mathematical methods used for measuring the degree of relationship, Karl
Pearson’s method is most popular. The correlation coefficient summarises in one figure not
only the degree of correlation but also the direction, i.e., whether correlation is positive or
negative.
• The coefficient of correlation measures the degree of relationship between two sets of figures.
As the reliability estimate depends upon the closeness of the relationship, it is imperative that
utmost care is taken while interpreting the value of coefficient of correlation, otherwise fallacious
conclusion may be drawn.
• The probable error of the coefficient of correlation helps in interpreting its value. With the help
of probable error it is possible to determine the reliability of the value of the coefficient in so far
as it depends on the conditions of random sampling.
• One very convenient and useful way of interpreting the value of coefficient of correlation between

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