# Reliability and Item Analysis Introductory Overview - Sum Scales

What will happen when we sum up several more or less reliable items designed to measure prejudice against foreign-made cars? Suppose the items were written so as to cover a wide range of possible prejudices against foreign-made cars. If the error component in subjects' responses to each question is truly random, then we may expect that the different components will cancel each other out across items. In slightly more technical terms, the expected value or mean of the error component across items will be zero. The true score component remains the same when summing across items. Therefore, the more items are added, the more true score (relative to the error score) will be reflected in the sum scale.

Number of items and reliability. This conclusion describes a basic principle of test design. Namely, the more items there are in a scale designed to measure a particular concept, the more reliable will the measurement (sum scale) be. Perhaps a somewhat more practical example will further clarify this point. Suppose you want to measure the height of 10 persons, using only a crude stick as the measurement device. Note that we are not interested in this example in the absolute correctness of measurement (i.e., in inches or centimeters), but rather in the ability to distinguish reliably between the 10 individuals in terms of their height. If you measure each person only once in terms of multiples of lengths of your crude measurement stick, the resultant measurement may not be very reliable. However, if you measure each person 100 times, and then take the average of those 100 measurements as the summary of the respective person's height, then you will be able to make very precise and reliable distinctions between people (based solely on the crude measurement stick).

See Cronbach's Alpha to look at some of the common statistics that are used to estimate the reliability of a sum scale.