Cronbach’s alpha is a numerical quantity that represents how well the different variables in a particular data set are interrelated amongst themselves. It is used as a measure of the reliability of the data.

The value of Cronbach’s alpha always lies between 0 and 1. If the value is greater than 0.6 then the data is considered reliable with a value greater than 0.9 indicating higher reliability. If the value is less than 0.4 then it indicates low reliability.

For example, suppose we conduct various psychological tests on a group of 100 people. We collect information about various variables such as IQ, happiness quotient, gender, etc. We can now calculate Cronbach’s alpha for these variables to understand how related these variables are to each other.

The formula for Cronbach’s alpha is given as,

α = n*c̄/v̄+(n-1)c̄ where,

n is the sample size

v̄ is the average of all the variances and

c̄ is the average of all the covariance obtained pairwise.

**Steps to calculate Cronbach’s alpha by hand**:

- Find the variance for each variable in your data set.
- Take the average of all variances found above. Denote the result as v̄.
- Choose any pair of two variables and calculate their covariance. Do this for every possible pair of variables.
- Take the average of all covariances found above. Denote the result as c̄.
- Substitute all these values in the above formula and obtain the value of α.