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Correlation

The statistical methods, discussed so far, are used to analyses the data involving only one variable. Often an analysis of data concerning two or more quantitative variables is needed to look for any statistical relationship or association between them that can describe specific numerical features of the association. The knowledge of such a relationship is important to make inferences from the relationship between variables in a given situation. Few instances where the knowledge of an association or a relationship between two variables would be helpful to make decision are as follows:

  • Family income and expenditure on luxury cars
  • Sales revenue and expenses incurred on advertising
  • Weight and height of individuals
  • Frequency of smoking and lung damage

A statistical technique that is used to analyse the strength and direction of the relationship between two quantitative variables is called correlation analysis.

Correlation Coefficient

Correlation coefficient is a number that indicates the strength and direction of statistical relationship between two variables.

  • The strength of the relationship is determined by the closeness of the points to a straight line when a pair of values of two variables are plotted on a graph. A straight line is used as the frame of reference for evaluating the relationship.
  • The direction is determined by whether one variable generally increases or decreases when the other variable increases.

Types of Correlation

There are three broad types of correlation

  • Positive and negative
  • Linear and non-linear
  • Simple, partial and multiple
  • Positive correlation refers to an association between two variables where their values change in the same direction.
     
    Negative correlation refers to an association between two variables where there values change in the opposite direction.
     
    A linear correlation refers to an association between two variables where variation in their values is either proportional or fixed. The following pattern of variation in the values of two variables x and y reveals linear correlation.
    x: 10 20 30 40 50
    y: 40 60 80 100 120
  • A non-linear correlation refers to association between two variables where variation of their values is neither proportional nor fixed. The following pattern of variation in the values of two variables x and y reveals non-linear correlation.
    x: 8 9 9 10 10 28 29 30
    y: 80 130 170 150 230 560 460 600
  • If only two variables are chosen to study correlation between them, then such a correlation is referred to as simple correlation.
  • In partial correlation, two variables are chosen to study the correlation between them but effect of other influencing variable is kept constant.
  • In multiple correlations, more than two variables are chosen to study the correlation between them.

Methods of Correlation Analysis

Methods of calculating a correlation coefficient between two variables x and y are as follows:

  • Scatter diagram method
  • Karl Pearson’s coefficient of correlation method
  • Bivariate frequency distribution
  • Spearman’s rank correlation method
  • Concurrent deviation method





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