EPGY Math Aptitude Test Score Reporting

An aptitude test measures different quantities from an achievement test or standard curriculum. In a mathematics course in school, each student is assessed after learning a topic. This kind of learning is achievement learning; a student works toward a specific goal. Aptitude testing assesses a student's capabilities without any standard training. Like IQ scores, the EPGY Aptitude Tests attempt to measure a variable that does not depend on what a student has been explicitly taught.

Raw scores can be misleading for this test. A raw score on an aptitude test or an achievement test does not mean much on its own. It does not indicate how many items were answered correctly or how many total test items there were. A raw score of 38 on one test and 78 on another test does not mean that the student performed better on the second test. Since the raw scores do not include the total number of items on either test, there is no way of assessing which test score performance was higher. Of course, another issue in making any comparison is the relative difficulty of items on the two tests.

If it were known that the first test consisted of 40 questions and the second test consisted of 100 questions, the percentage correct could be calculated. The first test score would be 38/40 = 95%, and the second test score would be 78/100 = 78%. Based on the percentage correct, the student scored higher on the first test. Thus, knowing the context of the test is important for interpreting the meaning of the score. However, we are still faced with making a judgment of relative difficulty for any adequate evaluation.

To help make such a judgement, standardized tests use percentiles and not percentages in reporting students' scores. Unlike classroom assessment, where the percentage correct corresponds to the student's score, standardized tests rank a student's test performance by comparing each student's score to all other students who took the test through use of percentiles. Unlike the above example where 38/40 = 95%, the 95th percentile indicates that the student performed better than 95% of the population who took the test. All of the students who took the EPGY Mathematics Aptitude Test on January 18th, 2004 were at the top of their class, so these students already have a very high percentile ranking relative to the general population.

Since standardized tests target the average student, the results produce a normal curve (also known as the bell curve - see below.) The highest part of the normal curve is at the 50th percentile. The majority of scores will fall close to the 50th percentile. They are close to the mean, or average for the population. The farther away from the middle of the curve, the rarer the scores are. Therefore, the graph tails off at the lower and upper ends. All of the students who took the EPGY Mathematics Aptitude Test on January 18th, 2004 would be at the upper tail end of a curve whose x-axis is mathematical ability among the general population.

Unlike the other standardized tests that are normed on the general population, the EPGY Mathematics Aptitude Test was normed on and geared toward the gifted population. In other words, the EPGY Mathematics Aptitude Test generates a normal curve among students who already perform in the top 1-5%. These tests evaluate a subgroup of highly able students and the curve generated from the EPGY Mathematics Aptitude Test results refers to this population alone. If a student performed in the 12th percentile on the EPGY Mathematics Aptitude Test, it means that this student performed better than 12% of the selected high-performing students who took the test on January 18th, 2004. This type of norming is rarely done, as there are rarely opportunities for such analyses. In addition, there are rarely any tests that are aimed at assessing this high level of aptitude.

Since the EPGY Aptitude test is given to students of multiple ages, the test is also normed by each student's age. The age level is based on the date of the test and the birthdate information that the student submitted at the time of testing. For the Form A Test, there are three age groups: (1) between 11 and 12, (2) between 12 and 13, and (3) between 13 and 14 years old. For the Form B Test, there are four age groups: (1) between 7 and 8, (2) between 8 and 9, (3) between 9 and 10, and (4) between 10 and 11 years old. Each student's percentile score is calculated based on students in the same age group. If a 7-year-old student submits the Form B Test, his or her percentile is not based on how he or she did against 10-year olds. The percentile and corresponding figure is relative to the performance of other 7-year-old students. If a student took the wrong form of the test for the student's age group, then the student is normed with the closest age group possible. For example, if a 10-year old student took the Form A test, then that student would be normed with the 11-year old age group.

Remember, the results of the EPGY Mathematical Aptitude Test have no bearing on a student's standing in EPGY or in his or her school or district. If you have questions about the development of the test or would like to know more about other studies that are being pursued or have been completed in Hong Kong, please refer to the EPGY website at:

http://www.infokids.com.hk/epgy/index.html

You are also welcome to send any questions or comments to epgy-testing@epgy.stanford.edu. Thank you!

EPGY Testing