Poetry | Prose | Psychometry

Return to Table of Contents

Contents: Psychometry

California Math Scale
by Greg A. Grove

Mysterium Exam II by Greg A. Grove

California Math Scale ~
by Greg A. Grove, Ph.D.
Copyright © 1992


Directions:  Some people experience anxiety in math-related situations.  Use the numbers below to indicate how much anxiety you would probably experience throughout each of the following events.  Write your answers on the lines provided.

1 = Very High Anxiety
2 = High Anxiety
4 = Low Anxiety
5 = Very Low Anxiety

_____ (1) Taking a college math placement test.

_____ (2) Learning to figure a new math problem.

_____ (3) Refiguring incorrectly answered problems.

_____ (4) Asking the teacher to repeat the explanation of an equation.

_____ (5) Answering questions based on statistical tables, charts, or graphs.

_____ (6) Solving story problems similar to this one:

                        A train ran 2/5ths of the distance between A and B
                        at an average speed of 24 miles an hour.  For the
                        remainder of the trip, its speed was increased 1/3rd,
                        requiring 12 hours to complete the trip.  What was
                        the distance between A and B?



             Sample:  ____ 3  6  9  12  15  18  ____  ____  ____


Directions:  Look at the sample problem above.  The row has six numbers arranged in some order.  Figure out the numbers that begin and end the series.  Write your answers on the lines provided.

Since the numbers in the Sample increase by 3’s, the series begins with 0 and ends with 21, 24, 27.

You have 5 minutes to fill in the missing numbers below, just as you did the Sample.  Use space on your paper to figure answers.  BEGIN!

____   512   256   128   64   32   16  ____   ____   ____

____  75   57   74   47   73   37   ____   ____   ____  

____  9   3   25   5   49   7   ____   ____   ____

____   89   17   85   13   87   15   ____   ____   ____

____   842   2y   428   5x   284   8w   ____   ____   ____

____   31   34    33    36    34    37    ____   ____   ____



This concludes the California Math Scale

The purpose of the California Math Scale (CMS) is to provide a brief screen of math anxiety and numerical reasoning in adults ages 16 and older.

Math anxiety is defined as a persistent and irrational fear of numbers or computing problems; of learning terms, concepts, and processes, of taking tests; of interacting with the math teacher relative to math instruction, and so forth, that results in physical discomfort such as tension, fatigability, heart pounding, upset stomach, high resting pulse, worry, difficulty in concentrating, and diarrhea.  Numerical reasoning pertains to figuring number sequences using addition, subtraction, multiplication, and division.

Scoring Procedures:  Part I is scored by summing the numbers written to the left of each event.  Items not rated receive no points.  If more than one response to an item is indicated, the lower value is used.  Record your total here: _______  (Range 0-30 points.)

Part II is scored by referring to the answer key below.  Each correct answers receives 1 point.  Wrong answers, or problems not answered, receive no credit.  Sum the number of correctly answered items and record your total here: ________  (Range 0-24 points.)

Answer Key

                                    Row 1:  1024 … 8,  4,  2

                                    Row 2:      67 … 72,   27,   71

                                    Row 3:        1 … 81,   9,   121

                                    Row 4:      15 … 83,   11,   85

                                    Row 5:     -1z … 842,   11v,   428

                                    Row 6:      31 … 34,   37,   33



COMPOSITE SCORE:  Now add both part scores and record your answer here: _______  (Range 0-54 points.)  Refer to the table below to determine your level of performance.

Levels             %iles            Part I            Part II           TOTALS         Grades
Excellent         98-99             26-30              21-24             43-54             A
Superior          91-97             24-25              18-20             40-42             A-
Well-Adjusted  75-90              22-23              15-17             36-39             B
NORMAL          26-74             18-21              10-14             28-35             C
Below Normal    10-25             16-17               7-9               24-27             D
Help Needed      3-9                15                   4-6               21-23             D-
Help Urgent       1-2               0-14                 0-3                0-20              E

Psychometric Data:

The above norms were based on 54 students enrolled in a general education course at a community college in northern California.  The average age was 22.  The average IQ as measured by the Vocabulary subtest of the California Test of Mental Maturity (1963 edition) was IQ 105.  Further statistics follow:


            N = 54             Mean     SD       SEM    Skew   Kurtosis
            Part I                19.6      2.8       .38       .12       2.7
            Part II               11.9      4.4       .59       .05       2.9
            TOTAL               31.5      5.8       .78       .04       2.6


Biserial Item Analysis


            Part I vs. Total Test                                          Part II vs. Total Test
            Item 1              .16                                           Item 1              .36
            Item 2              .48                                           Item 2              .42
            Item 3              .31                                           Item 3              .62
            Item 4              .35                                           Item 4              .44
            Item 5              .35                                           Item 5              .43
            Item 6              .55                                           Item 6              .45
            TOTAL              .66                                           TOTAL              .87


The average item correlation for Part I is .37 and .45 for Part II.  The Pearson correlation between Parts I and II is .23 (p < .09), which suggests that each part is testing a different domain (anxiety vs. computation).  The internal consistency of the Total Test on the sample norming population was .79.  Another administration of the test (N=26) yielded .92.

Part II

Grade Equivalents


Raw     G.E.                           Raw     G.E.                         Raw     G.E.
          1          2.6                             7         6.5                          19        14.8
          2          3.2                             8         7.3                          20        15.6
          3          3.8                             9         8.1                          21        16.2
          4          4.6                             10        8.7                          22       17.0
          5          5.2                             11        9.3                          23       17.8
          6          6.0                             12       10.4                         24       18.4

Return to Top


Copyright © 2000, 2001
by Greg A. Grove, Ph.D.

Directions: Do not commence testing until you have sufficient time to complete both parts at one sitting. Reference and memory aids are not allowed so that all responses will be entirely your own. An undisturbed environment is recommended for maximum concentration. There is no time limit, however, most people finish the Exam within 15 minutes.

The Mysterium Entrance Examination-2 is intended as an alternate form to the original Exam. A qualifying score at or above the 98th percentile admits to the Mysterium fellowship. To determine your performance level, submit only the answers to Part A and Part B to ggrove141@aol.com, and a score report will reach you within one week. Good luck.


Do not spend too much time on any one question. Make educated guesses if you are not sure of an answer, for there is a correction for haphazard guessing that will nullify credit given for any answer due to pure chance.

Many questions in this part have more than one "good" answer; some have no "good" answer. In either case, select from the choices the one choice per question which you consider the best answer.

1. Dentist is to Caries as Policeman is to ?
        a. Convicts b. Justice c. Crime d. Conduct

2. Satin is to Gingham as Platinum is to ?
        a. Burlap b. Gold c. Lead d. Diamond

3. Principal is to ? as Medium is to Wave.
        a. School b. Interest c. Idea d. Recess

4. Diamond is to Rhinestone as Wool is to ?
        a. Cotton b. Orlon c. Mohair d. Nylon

5. Its is to Babies’ as Their is to ?
        a. You b. Ladies c. Your d. We

6. Streptococci is to Pneumonia as Malnutrition is to ?
        a. Dysentery b. Malaria c. Beri-Beri d. Death

7. Russia is to Steppes as Argentina is to ?
        a. Pampas b. Plateaus c. Valleys d. Moraine

8. Tsar is to Caesar as Kaiser is to ?
        a. President b. Caesar c. Governor d. Napoleon

9. Serfdom is to Feudalism as Entrepreneurs is to ?
        a. Laissez-Faire b. Capitalism c. Socialism d. Mercantilism

10. Spaghetti is to Vodka as ? is to Don.
        a. Florence b. Henry c. Liquor d. Food

11. Einstein is to Dorogi as Yippee is to ?
        a. Chamois b. Hashish c. Kindergarten d. Swipe

12. Toluene is to Rubber as Fountain Pen is to ?
        a. Crayon b. Pencil c. Brush d. Chalk

13. Clairvoyance is to Telepathy as Intuit is to ?
        a. Foresee b. Learn c. Transport d. Imply

14. Humours is to Antiquated as Magic is to ?
        a. Simulated b. Attendant c. Outdated d. Psychological


Write T (True) or F (False) for each statement below.

  1. I would rather be a senator than a philosopher.
  2. I would rather be an efficiency expert than a musician.
  3. I would rather be an engineer than an artist
  4. I get my best ideas by daydreaming rather than relying on books, well-established authorities or other people.
  5. If I had the talent, I would enjoy being a composer.
  6. I would rather edit than write a book.
  7. I would rather be a leader than an inventor.
  8. I prefer teachers who give well-organized courses and clear assignments to those who require independent reports and papers.
  9. I often make judgments by first impressions and feelings rather than by a careful thinking through of the situation.
  10. I solve intellectual problems by careful, logical thinking.
  11. If I had the talent, I would enjoy being a sculptor.
  12. I think I am a practical rather than an imaginative person.
  13. My friends think of me as an objective rather than an emotional person.
  14. I am more of a realist than an idealist.


Return to Top

Poetry | Prose | Psychometry

Return to Top