Derived scores are obtained by going to a conversion chart in the test manual.  The raw score (# of correct answers) is translated into a score that allows us to compare:
 -one student against others
 -one student against him/herself in various subjects/areas
 

1. Developmental Scores
 a. age equivalents
 b. grade equivalents
 c. Ratio IQ  IQ = Mental age/Chronological age X 100 (to get rid of decimal pt.)
 

2. Scores of Relative Standing
 a. The "iles"
  -percentiles
  -deciles
  -quartile

 b. Standard scores (ways to show distance from mean of a distribution)
  -Z scores
  -T scores
  -Stanines (referring to "Standard nines")
  -Derived IQ (determined by taking the raw score to a translation table)
 

Scores of Relative Standing
(Where you stand in relation to others; How you rate relative to others)
 

Percentiles tell you the % of scores that your score equaled or exceeded
  (did the same or better than)

A score that was ranked in the 40th percentile was as good as or better than 40% of the scores in a group of people.

64th?

81st?

At the mean of the distribution?
 

What is the highest percentile one can obtain?
(99th - - You can do equal to, but NOT better than 100% of the scores)
    (because you can't do better than yourself)
 

What is the lowest percentile into which one's score can fall?
(1st - - You can't perform the same as 0% of the scores)
 

PERCENTILES

Percentiles are widely used and easily calculated.

You figure out how many people fall into each percentile rank by doing what act to the "distribution" of scores?

Divide the total number of scores by "100".
 

So if you have the scores for the 1000 students who took the test, how many scores are in each percentile rank?

If Sam's total score on the achievement test fell into the 90th percentile, that score is equal to or superior to the performance of how many students?
 
 

Because scores are usually normally distributed (normal curve, bell curve), there are more people getting scores near the mean than far from the mean.  Therefore, differences between people appear
 
 -larger in the center of the distribution of scores (not much difference in
   score between two adjacent percentiles - - 50th and 51st)

 -smaller near the extremes of the distribution of scores
          (quite a bit of difference between scores at the 97th and 98th percentiles)
 
 

It's a good idea to also look at other types of scores to get a better idea of what is meant by the percentile.
 
 

Problems:In a "normal distribution" (normal curve), what percentage of people perform within one
  "S" of the average (mean) on that task/trait/test?

What percentage of people perform better than or worse than two S from the mean?

If you are  -2  z-scores  from the mean, you are ___ S from the mean?  Above or below?

Stanines break the normal curve/distribution into how many parts?
 

If you see the numbers "4-3", you know that it represents an __(age or grade?)__ equivalent.

If a student's performance on some task/test falls between the average performance of kids
  who are 9 and 10 years of age.  S/he is given an age equivalent score of "9-6" even
  though no kids of that age ever took the test (and therefore are not part of the norm group to
  which we compare kids).  Which process was conducted? (Interpolation or Extrapolation?)

A student's performance on a test earns him/her an age equivalent of 16 years, even though
  the oldest kids in the norm group were 15 years old.  What process was conducted?
 

Which one(s) of the following are true?  Standard scores allow us to compare:
- The performances of one kid on different tests ("He's better at reading than at math.")
- The performances of many kids on the same test ("When it comes to history, Josh is better than
  Cindy who is better than Wei.)
-The performances of different kids on different subjects/tests ("Hector is a better reader than
  Tyrone is a mathematician.")
 

Percentiles are figured by dividing a group of people who have taken a test into ____
  subgroups or "bands".

How many percentiles are in a decile?

How many percentiles are in a quartile?

The 72nd percentile is equivalent to which decile?      Which quartile?
 
 

Thomas McIntyre at www.BehaviorAdvisor.com