How does adding items to a questionnaire affect its internal consistency according to the Spearman–Brown prophecy formula?

Adding items to a questionnaire generally increases its internal consistency. The Spearman–Brown prophecy formula is used to estimate the new reliability coefficient after adding items, showing that more items can improve reliability and strengthen the interpretation of results.

The Spearman–Brown prophecy formula helps estimate how the reliability of a questionnaire changes when items are added. This formula calculates a new reliability coefficient by considering the original reliability and the ratio of the new total number of items to the original number of items. For example, if a questionnaire's reliability coefficient is 0.761 and the number of items is doubled, the new reliability coefficient becomes 0.864. This increase indicates that adding items generally enhances the internal consistency of the questionnaire, making its results more reliable and valid, provided the additional items are relevant.