Interval scales have the properties of identity, magnitude, and equal distance. The equal distance between consecutive scale points allows us to know how many units greater than or less than one case is from another on the characteristic being measured. So we can always be confident that the meaning of the distance between 7 and 10 is the same as the distance between 42 and 45. Interval scales do not have a true zero point; the number "0" is arbitrary.
Many of our standardized tests in psychology use interval scales. An IQ (Intelligence Quotient) score from a standardized test of intelligences is a good example of an interval scale score. 
IQ scores are derived from a lengthy testing process that requires the participant to complete a number of cognitive tasks. Each task is scored and the set of scores is converted into an overall standardized IQ score. IQ scores are created so that a score of 100 represents the average IQ of the population and the standard deviation (or average variability) of scores is 15. A distribution of IQ scores is presented below. 
If one student receives an IQ score of 84 and another student receives and IQ score of 116 we can count on the units having the same meaning in order to make our interpretation. The first student would be 16 points below the mean which would indicate a below average potential for educational pursuits. The second student would be 16 points above the mean which would indicate an above average potential for educational activities. 
There is no zero point for IQ. We do not think of a person as having no intelligence (although we may be tempted to make that evaluation upon occasion). Similarly for standardized scales of personality or other psychological attributes  a zero point is an arbitrary point on a scale and does not indicate the absence of a quality or characteristic. 
You may need to read a test manual or detailed description of scoring procedures to determine whether a standardized test is measured on an interval scale. 
The interval scale of measurement only permits mathematical operations of addition and subtraction. We can combine amounts or remove amounts. We can discuss an amount that is more, less, or equal to another amount. But, we cannot make statements that involve multiplication or division. When measuring IQ, we can say that a person with an IQ score of 110 is 40 points higher than someone with an IQ score of 70, but we would never say that an IQ of 120 means that someone is twice as intelligent as someone with an IQ of 60. A true zero point is required to make valid statements about mathematical operations of multiplication or division of numbers on a scale. 
Other examples of interval scales in psychological research: Most standardized tests of achievement such as SAT, ACT, MCAT. 
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