Psychometric Entrance Test

The Psychometric Entrance Test (PET, colloquially known in Hebrew as "the Psychometry" - ha-Psixometri, הפסיכומטרי) is a standardized test in Israel, generally taken as a higher education admission exam. The PET covers three areas: quantitative reasoning, verbal reasoning and the English language. It is administered by the Israeli National Institute for Testing and Evaluation (NITE) and is heavily weighed for university admissions.

The test may be taken in Hebrew, Arabic, Russian, French, Spanish, or combined Hebrew/English. There are generally five dates the test may be taken a year; they change from year to year but roughly fall on February, April, July, October, and December. Hebrew may be taken at any date; Arabic at four dates; Russian and combined Hebrew/English at two dates; and French and Spanish at one date. Taking the test on two consecutive dates is not allowed; this results in the test being disqualified. The results are valid for university admission for seven years.

Purpose
According to the National Institute for Testing and Evaluation,


 * The Inter-University Psychometric Entrance Test is a tool for predicting academic performance, and it is used for selecting applicants to institutes of higher learning . When these institutes are unable to admit all applicants, they select those who are most likely to successfully complete their studies. The Psychometric Entrance Test is one way of measuring academic potential. This test enables all applicants to be ranked on a uniform scale and, relative to other selection tools, is less affected by the different background of each applicant or other subjective factors. (The matriculation scores, for example, are based, among other things, on teacher evaluations. Since students are not all evaluated by the same teachers, it is obvious that the various scores cannot be on the same exact scale, and are affected by many different variables.)


 * There is a large body of research indicating that the Psychometric Entrance Test has a high predictive ability. This means that students with high Psychometric Test scores generally do better in their studies than students with low scores. In addition, of all the different combinations of the available selection tools, the combination of the Psychometric Entrance Test and the Matriculation Exams has proved to have the best predictive ability. As a result, most institutes of higher learning in Israel use this combination for selecting applicants.


 * The Psychometric Entrance Test is not a perfect selection tool. While it is able to predict academic success in most cases, there are always exceptions. There may be some people who do not do well on the test and yet are very successful in their studies and vice versa. In addition, the test does not directly measure such factors as creativity, diligence and motivation, which are definitely related to academic success. Nevertheless, it should be noted that some of these elements are measured indirectly, both on the Psychometric Test and also on the Matriculation Exams; thus the final score for selection purposes takes these factors into account to a certain extent. In addition, the results of many studies of the effectiveness of different selection tools indicate that the Psychometric Entrance Test, combined with matriculation scores, is the best and fairest selection tool available at present.[1]

Structure
The test is divided into 8 sections, each typically containing 25 to 30 multiple choice questions of equal weight with 25 minutes alloted (for a total time of 3 hours and 20 minutes). Of the eight sections, only six actually factor into the final test score- two quantitative reasoning chapters, two verbal reasoning chapters and two English chapters. The other two chapters (colloquially known as the "pilots"), which might be of any of the three types, do not affect the test score and are used as a form of quality control to ensure that a question is fair and measure its degree of difficulty in preparation for full-fledged inclusion as a score-affecting question at a later date. This allows the NITE to get a grasp on how challenging a question is, which helps reliably sort the questions in any given subsection in increasing difficulty; and makes possible the factoring of previous test-takers' performance given the same questions into the score of a current test-taker, which helps minimize any unfair systematic differences between one date and another that might affect one's score (such as the overall difficulty of the questions or the overall aptitude of the people taking the test). The NITE strongly encourages test-takers to approach all test sections with equal gravity.

According to the NITE the quantitative reasoning sections jointly determine 40% of the final score, the verbal reasoning sections another 40% and the English sections 20%. Use of calculators, alarm clocks, cellular telephones, beepers, electronic instruments of any kind, dictionaries, books, papers or any other study aids is strictly prohibited.

Quantitative reasoning
Quantitative reasoning sections typically contain 25 sections and thus demand an average of solving a question per minute if one is to answer all of them in the allotted time. They examine the ability to use numbers and mathematical concepts in solving quantitative problems, as well as the ability to analyze data presented in different ways, such as in table or graph form. Only basic mathematical knowledge (the material studied up to 9th - 10th grades in most Israeli high schools) is needed, though that still enables a diverse enough range of topics- including geometry, algebra, percentages, proportions and low-level combinatorics.

Though this is true for the other two types of subsections as well, quantitative reasoning questions in particular often can be tackled by several different approaches. One approach that is useful across many types of questions involves taking advantage of the multiple choice nature of the test by substituting given possible answers into the question and seeing whether the result "works out", or working by elimination. Higher difficulty questions are sometimes phrased in such a way as to make this approach highly impractical (such as requiring the calculation of two independent values X and Y and then asking for their sum - any given sum could have been the result of infinitely many possible values of X and Y and thus it is impossible to conclude, foregoing analysis of the constraints on X and Y, whether a given sum might possibly fit them or not).

On the flip side, some types of questions might be effectively tackled with methods that are above 9th-10th grade level, such as high-level combinatorics, or even methods that are generally not taught in Israeli high schools at all, such as modular arithmetic. A study conducted by the NITE on groups of students in eight pre-academic preparatory institutes during the academic year 1992-1993 has indicated that performance gains from practice and external coaching in the quantitative reasoning section are the greatest, averaging at about three tenths of a standard deviation.[2]

Verbal reasoning
Verbal reasoning sections typically contain 30 questions and thus demand an average of solving a question per 50 seconds if one is to answer all of them in the allotted time. They examine verbal abilities necessary for academic studies: vocabulary, logical thought processes, the ability to analyze and understand complex texts, and the ability to think clearly and methodically. The reason for the lower average time given for questions than in the quantitative section is mainly that questions earlier in the verbal section often require much less time to answer than even the easiest questions in quantitative reasoning; the first few questions typically constitute a vocabulary quiz, and even in the event of failing to recognize a word it is a matter of seconds to realize the question is a lost cause and skip it (unlike quantitative reasoning questions- the difficulties with which are typically much less immediately obvious, and often inviting of insistent retries). Apart from vocabulary questions the verbal reasoning section contains questions based on deductive and inductive reasoning, analogies, complex multipart sentence completion and reading comprehension.

A peculiarity of the Hebrew verbal reasoning section among similar tests (such as the SAT) is what is informally known as "Petel questions"- a direct translation of which would, frivolously enough, be "Raspberry questions" (the official term used by the NITE is "Letter Substitution"). The majority of nouns and verbs in Hebrew grammar are constructed by applying a specific meter to a specific root; for example, the meter XaXeXet is universally used to indicate some type of disease, and the root K.sˁ.R. (ק.צ.ר) - meaning "short" - substituted into it yields "Kasˁeret" (קצרת), the Hebrew term for Asthma (figuratively, shortness of breath). Letter substitution questions consist of four sentences with one word in each having had its root replaced by the letters Pe, Teth, Lamed, successively (Comprising the fictitious root "PTL", thus earning these questions their informal nickname). Three of these words share the same root and the objective is to find the odd one out, usually by figuring out the original root common to the three others via associative thinking. This is often complicated by one or several "distractor" roots which happen to make sense in the context of two sentences, but not three.

A study conducted by Tamar Kenet-Cohen and Shmuel Bruner on undergraduate students in six Israeli universities has found that among item types therein, analogies have the highest marginal contribution to the verbal reasoning section's predictive ability of academic performance. Reading comprehension and Inductive/Deductive reasoning items were found to have a reasonable contribution, with the latter- generally the most difficult type of item- having a notably high predictive contribution regarding students of highly selective undergraduate study programs. Results concerning the contribution of vocabulary and sentence completion items were inconclusive; letter substitution questions, generally the easiest type of item, were found to have a negative overall contribution.[3]

English
English sections typically contain 29 questions and thus demand an average of solving a question per approximately 50 seconds if one is to answer all of them in the allotted time. They test the applicant's proficiency in the English language as reflected, among other things, by their vocabulary and their ability to read and understand complex sentences and texts on an academic level. The English sections are fundamentally similar to the Verbal reasoning section insofar they concern skills related directly to grasp of the language- types of questions include vocabulary questions, restatements, sentence completion and reading comprehension - though the difficulty level of the questions per se is considerably lower than that of the equivalent Hebrew ones on the verbal section, for obvious reasons. Also unlike the verbal section the English section does not contain any questions related to reasoning, analogies and the like, instead focusing solely on language skills.

Scores
Applicants can usually view their online score report approximately three weeks after administration of the test- though longer delays are not unheard of (the official figure is 45 days; such longer delays are characteristic of more loaded test dates, particularly the April date, which is the latest date accepted by most academic institutions in Israel for application for the Fall semester). The scores are also sent to the applicants separately by mail and forwarded to several major universities - namely Ben-Gurion University of the Negev, Bar-Ilan University, The University of Haifa, Hebrew University of Jerusalem, Tel Aviv University and The Israel Institute of Technology in Haifa (aka the Technion). Additional higher education institutes for the score to be sent to may be specified by the applicant in advance upon registration for undertaking the test.

The distribution of PET scores is commonly believed to be a normalized distribution with a mean of 500 and a standard deviation of 100; this appears to be a misconception, however, or at least not precisely true, as statistics of percentile ranks released by the NITE show that significantly less people are assigned scores below 500 than above, and the mean is actually closer to 540. In fact, the scores- at least in part- do not appear to form a true normal distribution at all (see below, "percentile ranks").

The scores 800 and 200 are absolute and are reserved uniquely for applicants who have answered all questions correctly and none of them correctly, respectively. The latter is exceedingly improbable- on an average test of 252 questions, even guessing every question has an expected value of 63 correct answers. The probability of guessing all the questions incorrectly is $$\left(\tfrac {3} {4} \right)^{252} \approx \tfrac {1} {3.051 \times 10^{31}}$$, or about 800 times as unlikely as winning the Israeli lottery draw four times in a row.

Each of the three sections of the test is given a separate score on a scale of 50-150 (with 50 and 150, again, as absolute scores). An institution focusing on the exact sciences will often assign additional weight to an applicant's quantitative reasoning score; the English score affects the degree to which an undergraduate might be required to take additional English courses during their studies, ranging from a grade of 83 and below- which prevents one from getting accepted into most Israeli universities regardless of the overall score- to a score of 134 and above, which would exempt the applicant from taking any courses at all.

Percentile ranks and their corresponding PET scores[4]
Curiously, the percentile ranks for the scores between 350 and 525 seem to follow a sort of quadratic, rather than normal, cumulative distribution. The formulas tying the scores (S) and percentile ranks (P) in that range appear to be


 * $$P = \frac {{(2S-575)^2}-625} {5000} ; \quad S = \frac {575 + \sqrt {625(8P+1)}} {2}$$

Which implies that the probability density function in that range is linear. Note that this trend does not continue upwards past the mean (~540); and that it cannot indefinitely continue downwards past the score 350, either, as that would put the 0th percentile at a score of 300, and some applicants do receive scores between 200 and 300.