In Research or business studies, often one may be interested to know whether two variables under study are related to each other in any way? For example, in a growth study of children, a researcher wants to know whether the heights and weights of the children are related? In another study, a social scientist wants to know whether the age of the marriage and the number of children is related to each other? In business, one may be interested to know whether there exists a relationship between the amount spent on the advertisement of the product and its sale? The answer to all such questions can be answered by studying the correlation among those two variables.

Two variables X and Y are said to be correlated if a change in one variable causes a change in another variable. Moreover, Whenever, we are dealing with two numerical variables and we are interested in studying the relationship among them then we make use of Pearson correlation. The formula I am not going to describe here. You can find it on internet, easily.

The interpretation of 'r' when found between two numerical variables, can be as follows:

· The r can be positive or negative.

· If r is positive then we can say that changes in x and y are in same direction. Example: Height and Weight, Family Income and Expenditure

· If r is negative then we can say that changes in x and y are in opposite direction. Example: Price and demand, Family size and per capita income

· The r may always lie between -1 and +1.

· When close to 1 (say, 0.8), we say that the correlation is very strong and positive.

· When close to -1 (say, 0.8), we say that the correlation is very strong and neative.

· r^2 indicates the % variation explained in y (dependent variable) due to x (Independent variable).

· The linear relationship between x and y can be given by the equation y=a + bx where a is the intercept and b is the slope.

· a is the value when x is 0. b is termed as the slope and gives the change in y for a unit change in x.

· If r=0.8 then r^2= (0.8)^2 = 0.64 which means x is explaining 64% variation in y.

· Correlation is 0 does not mean there exist no relationship between x and y. The relationship may be quadratic in nature (y = ax^2 + bx+c)

· There should be always a reason to believe that x and y are likely to be related then only correlation should be attempted.

· Attempting the correlation between any two variables and getting some correlation has no meaning like rise in the circulation of certain newspaper and the rise in the number of suicides. In this case even if we get r=0.6 and it is significant, we cannot attach any meaning to it.

· The correlation does not mean causation.

· Only when r is significant, then only any meaning should be attached to it otherwise not.

Hello Riane,

Recommendations for qualitative interpretations of the strength of correlation may well be different depending on: (a) the discipline; and (b) the specific variables involved. While guidelines may be found in abundance, one size does not fit all cases.

Here are two simple examples:

What is the correlation between measures of adult human stature via: (a) hospital height gauge; and (b) using a toothpick, counting "how many toothpicks tall" a person is, then multiplying by the measured length of the toothpick? The correlation won't be perfect, largely because of the error introduced by having to gauge the number of toothpick units of height. However, it's still likely to be in the .90s. Is that strong? In an absolute sense, yes; relative to the precision you'd like for measuring physical properties, it's low.

What is the correlation between shoe size and maze solving score among adult females? An observed correlation of +/- .20 might be considered remarkably high, given that there's no reason physiologically or psychologically to expect a relationship other than zero.

My suggestion would be to look for interpretive conventions in your discipline that would apply to the pair of variables you're evaluating.

Good luck with your work.

Interpreting the Pearson Correlation Coefficient involves considering the magnitude and sign of the coefficient: