Correlation

Several situations involving pair of measurements. We observe that there exists certain relationship between pairs of variables for example between rainfalls and agriculture yield or height and weight or persons or between production and prices. These relationships often enable us to predict certain things. Thus if we measure both height and weight for a group of school height children we get bivariate data. The data of this kind in which we secure measures of two variables for each individual or a pair is called a bivariate data. The essential feature of the bivariate data is that one observation can be paired with another observation for each member of the group. When Study of bivariate data we should know the degree of relationship is known as correlation.

If we know that there is a high correlation between scores obtained in English and Mathematics, we can predict that a student getting high scores in English is likely to get high scores in Mathematics. This relationship between two variables is expressed in terms of a number which is always less than or equal to 1(one), never greater than one, is called the coefficient of correlation of correlation. Thus a coefficient of correlation is a single number that tells us to what extent the two variables are related and to what extent variations in one variables go with the variation in the second variables. The coefficient of correlation is a number which is less than or equal to one. Zero indicated complete independence between two variables or no correlation between the two variables then variables are said to be statistically independent. Relation may also be negative i.e., a high degree of one trait may be associated with a low degree of another. When negative or inverse relationship is perfect, r = – 1.0.

If there is neither complete presence nor complete absence of correlation between two variables then in such a state we say that there is, limited correlation and it can be positive as well as negative, In this case the coefficient of correlation is more than 0 but less than 1. The limited correlation is of following three degrees:

**High Degree:**If there is sufficient correlation present between two variables, though there is not perfect correlation between them, then this state is said to be that of high degree correlation.**Moderate Degree:**If the correlation is less than that of the high degree but still sufficient to measure then the correlation is said to be of moderate degrees and its coefficient generally lies between + 0.25 and + 0.75.**Low Degree:**If the degree of correlation lies between 0 and the lower limit + 0.25 of moderate degree then the correlation is said to be of low degree.

The line drawn through one data points represents a direct relationship because y increases as x increases. Because the data points are relatively close to this line, we can say that there is a high degree of association between the variables. Since relationship described by the data points is well described by a straight line. Thus, we can say that it is a linear relationship.

When a number of individuals are arranged in order, according to some quality which they all possess to a varying degree, they are said to be ranked. The arranged as a whole is called ranking in which each member has a rank.

Pearson’s product moment coefficient is no doubt the standard index of the amount of relationship between two variables, yet is sometimes not convenient to use it, as it involves heavy calculation. When the number of cases is small say 25 or so, the Spearman’s rank different method is very convenient to apply. However, this method can be applied only when individual scores are given and frequency distribution. As the name suggests all the scores have to be rank ordered, i.e., positions from 1 onwards are given to the scores. It is not always necessary to arrange them in order, but they must be ranked. The individual getting the highest score gets a rank of one, the next individual gets a rank of 2 and so on.

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