The Spearman-Brown prediction formula tells us how the reliability of a test/questionnaire changes if we increase the number of questions in the test/questionnaire.

The Spearman Brown formula is given as,

**Spearman Brown Formula and Split Half Reliability**:

The above formula can be used when we split a test into two halves. The split half reliability of a test is obtained by dividing the test into two equal parts. By substituting the split half reliability obtained in the above formula (putting n=2 since the original test has double the number of questions) we can obtain a score for the reliability of the original test.

**Example**: Suppose that the reliability score of a test is 0.7. If we increase the number of questions in the test by 4 times then what is the new reliability score of the test.

**Solution**: Given R_{0} = 0.7 and n=4

Substituting all these values in the above formula we get,

Predicted reliability R_{1} = 4*0.7/(1+3*0.7) = 0.903

**Predicting the number of questions in the new test**:

We can calculate the factor by which we need to increase the number of questions in order to achieve the desired reliability by using the formula,

**Example**: Suppose that the reliability score of a test having 100 questions is 0.8. If we want to increase the reliability of the test to 0.9 find the factor by which the number of questions must be increased.

**Solution**: Given R_{0} = 0.8 and R_{1} = 0.9

Substituting all these values in the above formula we get,

n = 0.9*(1-0.8)/0.8*(1-0.9) = (0.9*0.2)/(0.8*0.1) = 2.25

So we should increase the number of questions by a factor 0f 2.25 to obtain the desired reliability.

The new test should have 100*2.25 = 225 questions so that we can reach the desired reliability score of 0.9