Raw scores are the direct result of a measurement process. They are numbers. Larger raw scores are usually interpreted to mean more of something.

Test scores are typically interpreted in terms of one of three things that correspond to the labels domain, criterion, and norm referenced interpretations.

Domain. Here the test score is interpreted to be an index of similar tasks. For my tests, a score of 90 might be interpreted that the student could correctly answer 90 percent of the the questions I could ask about the material covered in this course.

Criterion. Here the test score is interpreted to be an index of performance on tasks other than the test. For example, if a student gets a 90 on my test, this could mean that psychology is a good major for them. A lawyer who passed the bar exam could be expected to perform well in a courtroom.

Norm. Here the test score is interpreted in terms of the person's relative standing to others who took the same test. A test score of 90 would be interpreted that the student knows more about the material than a student who got a score of 80.

Most tests provide better information about norms than about domain or criterion information. By that I mean that error in ordering people (norm reference) is less than the error in predicting the domain performance or criterion performance.

Domain -- spelling, vocab in a specific dictionary

Criterion -- welding test, lisence for law

Norm -- SAT, personality.

The 90-80-70 rule is primarily a domain referenced score to me. If you get 90 percent or more of my questions right, I figure you know most of the information. The curve is norm referenced -- it shows how you stack up to others in class. In my classes as an undergrad, my profs assigned grades using proportions of people in the class like these: 10-15-40-15-10 for A thru F, respectively. People who ask for your GPA are using it for criterion purposes, usually. Employers think it taps how smart you are or how hard you work; graduate schools use it to predict how well you will do in graduate schools.

z-score, T-score, A (SAT-type) score

Calculation of the z score

z = (X -Mean)/standard deviation.

For example Bob weighs 185 lb. Suppose the mean weight in the class is 145, and the standard deviation of weight is 15. Bob’s z score is (185-145)/15 or (40/15) or 2.67.

Meaning of the z score

The z score tells you how far the raw score is from the mean in standard deviation units, that is, it tells you the number of standard deivations above or below the mean it takes to get to the raw score.

The T and A scores are simple transformations of the z score.

T = z*10+50 and

A = z*100+500.

Moving from one conversion to another.

z = (A-500)/100

T=((A-500)/10)+50, etc.

or move to z and then back to other scale.