If r = 0.65, then the reliability of the whole test using Spearman Brown prophecy formula will be:

The correct answer is 0.788.

Concept:

• The Spearman Brown prophecy formula is an equation used to calculate the reliability coefficient for a test.
• It is based on the idea that if a test is split into two halves, each of these halves should have the same reliability level.
• The formula is expressed as R_whole = (2r)/(1+r), where r is the correlation coefficient between the two halves of the test.
• The formula can be used to calculate the reliability of a whole test given the correlation coefficient of two halves of the test.

Explanation:

The Spearman Brown prophecy formula is :

\(r_{SB} = {nr \over 1+(n-1)r} \)          (n=2)
                                 (r=0.65)

\(= {2(0.65) \over 1+(2-1)0.65} \)

\(= {1.3\over1.65}\)

\( = 0.787878\)

\(r= 0.788\)