Gilbert F. Pollnow
Wisconsin
SCORAN: A Computerized Test
State University
Oshkosh,54901
Scorer and Analyzer
The following program (Code namr SCOKAN) utilizes a special perforated Porta-Punch Card (available from IBM, printing format No. DG1014 and perforation tool No. 160311) developed by Games' which provides for up to 70 questions of the quintuple choice variety on a single card. Unlike the Games program. however, the following one provides for the arbitrary weight,ing of each question with values fmm 1 through 99 which make it particularly useful for science courses where the questions are generally not equal i n difficulty. In addition, the output includes the Z-scorc and percent,ile rank (under switch option). The program is written in Fortran 11-D for the IRlI1620 comput,er equipped with a 1311 Disk Drive and 1443 Printer. The compiled program is stored on the 1311 Disk File and can be loaded into core in a few seconds. Once loaded into core (40IC), the program will handle up to 590 tests in a single section using a floating point mantissa of five digits and a fixed point word length of five digits. Tests are processed at t,he rate of
12 per min without the perceutilc rank routine and 5 per min with it. Output data are rounded to the nearest appropriate number of significant figures as shown in the figure, where the parentheses enclose information added by the operator for the purpose of this description. Each of the output scores have a particular usage and are defined as follows: Snm of Lhe weights for all correct, answers llm Score (100.0) Percentage = S ~ t mof the weight,s for all qmst.ions Percentage - Percentag-n %-score = Percentage Standard Deviation
Ihw Score
=
.
where Z equals t,he Z-score. The percentage score is included for the majority of those instructors who still prefer to assign their grades on a percentage basis. Z-scores are included since they are the most frequently used standard scores for further GIMES,P W LA,, Educational and Psl,chologiral Meas~rrenxnl, statistical correlation procedures, taking into account 25,881,1965. the difficulty of the t,cst through division by the stanUODES,J. A., AND GREITZER. S. L., ' ' S ~ ~ n ~ e r .41mlpis," icd dard deviation.' Ilayden Book Co., Inc., NeaYork, 1964, p. 97. T-scores are preferred by *:US = O psychometrists for most grading purposes since the TSCO~E PE"C'NT'L' student's fairest cummula66.5 45.0 tive test grade a t the end 52.9 6L.3 of the semester weighted for 55.6 71.2 48.3 43.4 individual test difficulty is 41.1 18.6 35.6 7.5 then simply the sum of the T-scores over all tests divided by the number of tests. Another advantage of the T-score is that it avoids the use of negative DECILE STUDENTS PEUCcNT numbers as given by the Z-scores. In general, the 16.7 100.0 1.0 90.0 OUESILON EKIIORS PERCENT E H H O H S use of Z-scores or T-scores 0.0 90.0 0.0 80.0 1 16.7 tends to lower the high 10.7 scores and raise the lower 0 . 0 8 0 . 0 0 . 0 70.0 3 i 16.7 Lh.7 scores, but not as drasti1.0 16.7 60.0 70.0 5 16.7 cally as illustrated in the 3 50." 1.0 16.7 50.0 60.0 7 3 50.0 figure which is a highly ab" 3 50.0 40.0 50.0 1.0 16.7 3 50.0 normal distribution. 10 50.0 As defined above, the 30.0 110.0 0.0 0.0 II 2 33.5 i ?: 33.3 Percentile is the area under 20.0 30.0 0.0 0.0 13 2 33.3 the normal distribution , 33.3 10.0 20.0 1.0 16.7 ii33.3 curve (multiplied by 100) 16 3 110.0 from negative infinity to 0.0 10.0 1.0 16.7 (continued through 70 questions) A portion of tho output d a t a for a n examination. the Z-score. It can also be Zl
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thought of as the percentage of the group (in a normal distribution) having Z-scores less than the one for which the Percentile was computed. Since this index of performance requires a normal distribution to be valid, appropriate precautions must be observed in using it, e.g., the group must be large enough to ensure a normal distribution of Z-scores. A crude profile of the distribution of Percentage scores is also displayed using decile intewals. These intervals, however, can be easily changed by changing
680 / J o w m l o f Chemical Educufion
four cards in the program which define the intervals and their decrements. The final output includes a simple item analysis which gives the number of times and the percentage of the time that each question was marked wrong or omitted. A switch option also provides for a card output containing the identification number of the student along with his Z-score and T-score in the event that further statistical correlations between groups may be desired.
