Classroom Test Analysis, Center for Teaching Excellence, University of Illinois at Urbana-Champaign

Classroom Test Analysis: The Total Report

Table of Contents


Class Room Test Analysis
Summary of Test Statistics
Test Frequency Distribution
Sample Total Test Program


This program analyzes data consisting of one or more test scores. It can weight items differentially (e.g., 2 points for Item #1, 3 points for Item #2, etc.) and accepts positive, negative and decimal fraction scores.

The TOTAL output consists of three parts: A summary of statistics, a test frequency distribution, and a listing of students' scores. Any or all three parts of the output may be printed. The first part consists of a summary of the following test statistics: The number of items on the test, the mean, median, standard deviation, Kuder-Richardson reliability 21 (KR-21), standard error of measurement, the possible and obtained low and high scores, and the number of scores. Only those scores that fall within the range specified by the user are included in the analysis, so that the user has the option of disregarding certain scores. Blank and invalid scores (those falling outside the specified range) are counted but are omitted from the analysis. (See the ITEM ANALYSIS program description for definitions of the statistical terms mentioned above.)

The second part of the TOTAL output displays a test frequency distribution. The raw scores are ordered from high to low, with the corresponding standard score, percentile rank, percentage of people in the total group tested who received the given score, the frequency, and the cumulative frequency. The accompanying histogram portrays the frequency of the scores at each score value. (See the ITEM ANALYSIS program for a description of the statistical terms mentioned above.)

The first two parts of the TOTAL TEST analysis can be processed overall, i.e., for the entire class or group of data. It can also be processed by groups, such as class sections. The summary of test statistics and the frequency distribution can be processed for one to ten test scores per TOTAL program. Raw and/or standard scores can be summed, optionally applying weights to each score; a new summary of test statistics and a frequency distribution will be produced for the summed scores. Since different examinations usually have unequal standard deviations and different numbers of items on each examination, raw scores cannot be compared directly across examinations. When raw scores are summed to determine final score distributions and grades, the examinations with the larger standard deviations will always carry the most weight in determining the final score distribution. Since standard scores are comparable across examinations, it is strongly recommended to sum standard scores instead of raw scores or percent scores.

The third part of the TOTAL output is a listing of the students, sorted alphabetically or by student number. The raw score, standard score, and percentile rank for each test, and optionally for the summed raw and/or standard scores, is presented for each student. If grades are based on an examination score distribution, the summed raw score distribution, or the summed standard score distribution, or determined by assigning a certain proportion of the class different letter grades, then the assigned grades can print out in the listing of individual scores. However, this method of assigning grades is not recommended. Refer to Ebel & Frisbie (1986) or consult the staff of Measurement and Evaluation if you are interested in learning about valid grading practices.

References


Ebel, R.L., & Frisbee, D.A. (1986). Essentials of educational measurement (4th ed.). Englewood Cliffs, NJ: Prentice-Hall, Inc.

Gronlund, N.E., & Linn, R.L. (1990). Measurement and evaluation in teaching (6th ed.). NY: MacMillan.


                  * * *  MERMAC -- TEST ANALYSIS AND QUESTIONNAIRE PACKAGE  * * *


SUMMARY OF TEST STATISTICS

NUMBER OF ITEMS:
(Number of items on the test.)
   80
MEAN SCORE:
(Arithmetic average; the sum of all scores divided by the number of scores.)
   60.92
MEDIAN SCORE:
(The raw score point that divides the raw score distribution in half; 50% of the scores fall above the median and 50% fall below.)
   63.15
STANDARD DEVIATION:
(Measure of the spread or variability of the score distribution.  The higher the value of the standard deviation, the better the test is discriminating among student performance levels.)
   12.24
RELIABILITY (KR-21)1:
(When item difficulties are approximately equal, is an estimate of test reliability indicating the internal consistency of the test. The range of the reliability is from 0.00 to 1.00. A reliability of .70 or better is desirable for classroom tests.)
   0.915
S.E. OF MEASUREMENT:
(The accuracy of measurement expressed in the test score scale. The larger the standard error, the less precise the measure of student achievement. Two-thirds of the test takers obtained scores falling within one standard error of measurement of their true score.)
   3.58
POSSIBLE LOW SCORE:
(The possible low score.)
   0
POSSIBLE HIGH SCORE: 
(The possible high score.) 		  80
OBTAINED LOW SCORE:
(The obtained low score.)
   0
OBTAINED HIGH SCORE:
(The obtained high score.)
   80
NUMBER OF SCORES:
(The number of answer sheets submitted for scoring.)
   603
BLANK SCORES2:
(Number of test scores that could be not computed.)
   0
INVALID SCORES:
(Number of test scores out of range specified by the user.)
   0
VALID SCORES:
(Only those scores that fall within the range specified by the user are included in the analysis so that the user has the option of disregarding certain scores.)
   603

1KR-20 is given in ITEM ANALYSIS and provides a more accurate estimate of the reliability when item difficulties are not equal.

2Blank and invalid scores (those falling outside the specified range) are counted and are omitted from the analysis. 


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TEST FREQUENCY DISTRIBUTION

RAW SCORE STANDARD SCORE PERCENTILE PERCENT FREQ CUM FREQ EACH * REPRESENTS 1 PERSON
80 656 99 0.2 1 600  *
79 648 99  0.7 4  599 ****
78 639 99 1.3 8 595 ********
77 631 98 1.0 6 587 ******
76 623 97 2.2 13 581 *************
75 615 95 2.7 16 568 ****************
74 607 92 2.5 15  552 ***************
73 599 89 3.7 22 537 **********************
72 590 86 3.2  19 515 *******************
71 582 83 3.2 19 496 *******************
70 574 79 2.8 17 477 *****************
69 566 77 5.0 30 460 ******************************
68 558 72 3.5 21 430 *********************
67 550 68 5.5 33 409 *********************************
66 541 63 3.2 19 376 *******************
65 533 59 5.0 30 657 ******************************
64 525 54 3.3 20 327 ********************
63 517 51 3.3 20 307 ********************
62 509 48 4.2 25 287 *************************
61 501 44 4.2 25 262 *************************
60 492 39 3.5 21 237 *********************
59 484 36 3.5 21 216 *********************
58 476 32 2.3 14 195 **************
57 468 30 2.7 16 181 ****************
56 460 27 2.7 16 165 ****************
55 452 25 2.3 14 149 **************
54 443 2 1.3 8 135 ********
53 435 21 1.8 11 127 ***********
52 427 19 2.7 16 116 ****************
51 419 17 1.3 8 100 ********
50 411 15 2.3 14 92 **************
49 403 13 1.2 7 78 *******
48 394 12 0.8 5 71 *****
47 386 11 1.0 6 66 ******
46 378 10 0.7 4 60 ****
45 370 9 0.5 3 56 ***
44 362 9 0.5 3 53 ***
43 354 8 1.0 6 50 ******
42 345 7 0.7 4 44 ****
41 337 7 0.7 4 40 ****
40 329 6 0.7 4 36 ****
39 321 5 0.2 1 32 *
38 313 5 0.2 1 31 *
37 305 5 0.3 2 30 **
36 296 5 0.2 1 28 *

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SAMPLE TOTAL TEST PROGRAM

      EXAM ESSAY 1 ESSAY 2 SHORT ANS SUMMED RAW  SCORE  SUMMED STD SCORE
ID  NAME   RAW STAND PCT RAW  STAND PCT  RAW STAND PCT RAW  STAND PCT RAW STAND PCT RAW STAND  PCT
357446186  ANDERSON    67 550 68 147 498  47  333 572 77 79 607 88 626  561 71 557     565 73
519689271 BROWN  O 62  509 48 171 585 81 307  528  58 77  590 81  617  552 67 553 560  71
335527876 CURKS R 57 468 30 120 400 16 210 365 9 59 438 28 446 381 11 418 406 17
349385232 DUNN S 70 574 79 165 563 75 312 537 60 82 632 93 629 564 72 577 587 81
777788888 FRANKS D 20 166 1 42 118 1 127 225 1 42 294 4 231 166 1 201 158 1
555544544 FULTON F 62 509 48 162 553 73 314 540 63 63 472 38 601 536 59 519 521 55
338527846 GOLDMANN S 68 558 72 135 455 30 256 442 26 74 565 73 533 468 34 505 505 48
320527430 HALL M 71 582 83 159 542 67 366 628 93 69 522 58 665 600 84 569 578 78
336525686 KLEEN J 60 492 39 126 422 21 267 461 31 50 362 9 503 438 24 434 424 20
330502083 LANN K 50 411 15 174 596 86 256 442 26 70 531 61 550 485 40 495 494 43
357387636 NEWMANN D 63 517 51 72 226 1 263 454 29 60 446 30 458 393 14 411 398 14
320525308 PAULS N 69 566 77 150 509 52 305 525 56 59 438 28 583 518 53 510 511 51
337526133 PETERS E 69 566 77 174 596 86 333 572 77 76 582 79 652 587 81 579 590 82
396465677 RAYMOND J 36 296 5 193 520 57 273 471 35 65 489 43 527 462 32 444 435 23
326504741 SMITH G 69 566 77 180 618 92 317 545 65 70 531 61 636 571 75 565 574 77
347507887 SMITH P 17 141 1 0 0 1 67 124 1 27 167 1 111 46 1 108 52 1

 

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