Prof. Pearson’s co-efficient of correlation is based on the following assumptions:

**1. Linear relationship**

In devising the formulae, Prof. Pearson has assumed that there is a linear relationship between the variables which means that if the values of the two variables are plotted on a scatter diagram, it will give rise to a straight line.

**2. Cause and effect relationship**

Prof. Pearson has assumed that there is a cause, and effect relationship between the correlated variables which means that a change in the values of one variable is a cause for effecting a change in the value of another variable. According to him, without such relationship, correlation would carry no meaning at all.

**3. Normalcy in distribution**

It is assumed that the populations from which the data are collected are normally distributed.

**4. Multiplicity of causes**

Prof. Pearson has assumed further that each of the variables under study is affected by multiplicity of causes so as to form a normal distribution. Variables like age, height, weight, price, demand, supply, yield, temperature, etc. which are usually taken to study correlation are affected by multiplicity of causes.

**5. Probable error of measurement**

Prof. Pearson has further assumed that there is probability of some error which may creep into the measurement of the co-efficient of correlation. But, the magnitude of such error must lie within a limit which is obtained by the following formula:

PE_{(r)} = .6745 1-r^{2/√n}

Where, r = Co-efficient of correlation, and n = number of pairs of the two variables.

If the constant. 6745 is omitted from the above formula of probable error; we get the standard error of the co-efficient of correlation.

Thus, SE_{(r)} = 1-r^{2/√n}

The above formula of probable error helps us in interpreting the significance of the co-efficient of correlation as follows:

- The correlation is taken to be almost absent, if r < PE
_{(r).} - The correlation is taken to be significant, if r > 6 times PE
_{(r).} - The correlation is taken to be moderate, if r > PE
_{(r)}but < 6 times PE_{(r).} - The limits of the correlation co-efficient of the population, or P
_{(rho)}= r ± PE_{(r).}