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Optimum time for an objective test
5,wrem, Vol. 15, No. 3. pp. 335-338, Printed in Great Britain
OPTIMUM
1987 0
TIME FOR AN OBJECTIVE
0346-251X/87 S3.00+0.00 1987 Pergamoo Journals Ltd.
TEST
K. VISWANATHAM
Southern Regional Language Centre (Central Institute of Indian Languages), Mysore- 70006, India This paper is the outcome of an experiment conducted on 34 students the optimum time to be fixed for objective tests. As a result of the a formula for deciding the optimum time necessary for completing is evolved. It also discusses the need for such a formula and its limitations.
to find out experiment a given test merits and
1. INTRODUCTION In most cases in India the time for a test is arbitrarily fixed. The written papers of High School examinations are given 2 hours and 30 minutes; above High School it is 3 hours. In muhiple choice tests most institutions in India fix 60 minutes for IOO-item tests. In some cases it goes beyond this limit, reaching to 90 or even to 120 minutes in rare cases. This appears to be more arbitrary and unscientific. After many years of experimentation by me with many batches of trainees learning Telugu (a Dravidian language) in the Southern Regional Language Centre at Mysore, a procedure to fix the optimum time for objective tests meant for large populations has been evolved which can also be extended to well prepared question papers with open-ended answers.
2. PROCEDURE The procedure is based on the principles outlined below. Objective tests for Entrance Examinations for professional colleges, Bank Recruitment Boards, Public Service Commissions are meant for large populations. Such tests are generally prepared by teams of experts and are standardised. Those tests are also to be administered first to representative samples of the corresponding populations. Exactly at this point our procedure starts. When the test is administered each testee is asked to note down the time of the starting of the test at the top of the paper. He is also asked to attempt each and every item whether he knows the answer or not in the same serial order without skipping. He is also asked to note down the closing time of the test. With this the collection of the necessary data will be over. 335
K. VISWX4ATHA?4
336
The ne.xt step is to analyse the data. For each sampling unit, i.e. for each testee, the time taken for answering the test is determined. This can be done by subtracting the “starting time” from the “closing time”. Arrange these data in the form of a table and compute the arithmetic mean. Also compute the standard deviation. Now, the suggested formula for the optimum time required for the test is T, = x-t S,, approximated to the nearest multiple of 10 (or 5 in the case of more precise tests); where To = the optimum time required for the test, ??= the arithmetic mean and S, = the standard deviation. This formula appears to be the most appropriate to decide the required time for an objective test.
3. ILLUSTRATION As an illustration consider the following data. A batch of 34 students learning Telugu as a second language are given a lOO-item multiple choice test, each item having four alternatives. The time consumed by them to complete the test without omitting or skipping the items is presented in the following frequency distribution (Table 1). Table 1. Computation
of mean and standard deviation for scores obtained on a language test
Frequency
Class interval
f
96 - 100 91 - 95 86 - 90 81 -85 76 - 80 71-75 66 - 70 61 - 65 56 - 60 51 - 55 46 - 50 41 -45 Total:
1 0 2
1 4 3 2 6 4 1 6 4
mean ??
x’ = x-2
98 0 176 83 312 219 136 378 232 53 288 172
34.85 29.85 24.85 19.85 14.85 9.85 4.85 -0.15 -5.15 - 10.15 - 15.15 -20.15
2147
88.70
98 93 88 83 78 73 68 63 58 53 48 43
34(=N)
The arithmetic
J-X
Slid-value X
X’l
fX’?
1214.52 891.02 617.52 394.02 220.52 97.02 23.52 0.02 26.52 103.02 229.52 406.02
1214.52 0000.00 1235.04 394.02 882.08 291.06 47.04 0.12 106.08 103.02 1377.12 1624.08 7274.16
EfX
= -
N
= 5~63.15
The standard
deviation
S, =
Ix
,2
4- N-l
=dF_
T,=js+S, = 63.15 + 14.85 = 78.90 - 80.
dw
from 34 students
= 14.85.
OPTI.MUMTIME FOR AN OBJECTIVE TEST
337
Thus the optimum time required to answer the above mentioned loo-item multiple choice test is 80 minutes.
4. INTERPRETATION
OF To
The formula To = x + S, has two constituents, x, the mean of the time consumed by the testees and S, the standard deviation of the X values. 3 is the most appropriate and accurate measure of the central tendency which can be exposed to mathematical operations unlike the other measures, viz. the median and the mode. Similarly, S, the standard deviation is the most appropriate and accurate measure of the variability. While the arithmetical mean gives the average of the data, the standard deviation shows the average variability of the data. Now, To = x+ S,, the sum of the average score and the average of the deviations becomes the most appropriate measure of the optimum time to be given for a test. Though x is the most accurate measure of central tendency it fluctuates to the extreme values. Also this covers only 50% of the total cases. This is checked by adding the standard deviation in order to achieve a more accurate and better measure.
5. MERITS OF To If any data available are normally distributed, 68.3% of the cases fall within one standard deviation on either side of the mean. In any type of distribution, either normal or nonnormal (skewed), about 50% of the cases fall below the mean value. The distribution of time consumed by different individuals for a test is in most cases positively skewed because very few cases will be in the top extreme (high end of the curve) and it will not have extreme cases in the low end. If a curve is drawn for such a distribution the right till will be longer and the left end will abruptly cut the base line. In such a distribution most of the cases are concentrated below the mean or within one standard deviation to the right of the mean, (See Fig. 1.) _-
455
50.5
55.5 60.5
6S.S
70.5 75.5
805
65.5
SO.3
W.5
100.5
X
Fig. 1. Free hand curve joining the points plotted on the graph taking the real upper limits of the class intervals on the X axis and the frequency on the Y axis from the data in Table 1.
338
K. VISWANATHx4kl
Only few extreme cases fall beyond this limit. For instance, in the above distribution 18 out of 34 cases, i.e. 52.9070, fall below x = 63.15 and 28.5 cases, i.e. 83.8% of the cases, fall below x+ 1s. Only 5.5 cases, i.e. 16.2% (roughly) fall beyond this. In other words, only 16.2 cases in 100 are extreme and fall beyond this. In situations like this, i.e. time taken by individuals in answering a test, this is a negotiable percentage. Hence, To = x+ S, proves to be a better measure for alloting an optimum time for an objective test. Though this is basically meant to measure the optimum time for objective tests its use can be extended even to tests with open-ended answers on the same lines of objective tests. Once the design of the question paper is decided and once the optimum time is computed with this procedure, at any time later, for tests of similar design, the same optimum time can be given without again going through all these procedures of administering the tests to representative samples and computations. This is because in tests with open-ended answers giving a few minutes more or less will not make much difference.
OPTIMUM
1987 0
TIME FOR AN OBJECTIVE
0346-251X/87 S3.00+0.00 1987 Pergamoo Journals Ltd.
TEST
K. VISWANATHAM
Southern Regional Language Centre (Central Institute of Indian Languages), Mysore- 70006, India This paper is the outcome of an experiment conducted on 34 students the optimum time to be fixed for objective tests. As a result of the a formula for deciding the optimum time necessary for completing is evolved. It also discusses the need for such a formula and its limitations.
to find out experiment a given test merits and
1. INTRODUCTION In most cases in India the time for a test is arbitrarily fixed. The written papers of High School examinations are given 2 hours and 30 minutes; above High School it is 3 hours. In muhiple choice tests most institutions in India fix 60 minutes for IOO-item tests. In some cases it goes beyond this limit, reaching to 90 or even to 120 minutes in rare cases. This appears to be more arbitrary and unscientific. After many years of experimentation by me with many batches of trainees learning Telugu (a Dravidian language) in the Southern Regional Language Centre at Mysore, a procedure to fix the optimum time for objective tests meant for large populations has been evolved which can also be extended to well prepared question papers with open-ended answers.
2. PROCEDURE The procedure is based on the principles outlined below. Objective tests for Entrance Examinations for professional colleges, Bank Recruitment Boards, Public Service Commissions are meant for large populations. Such tests are generally prepared by teams of experts and are standardised. Those tests are also to be administered first to representative samples of the corresponding populations. Exactly at this point our procedure starts. When the test is administered each testee is asked to note down the time of the starting of the test at the top of the paper. He is also asked to attempt each and every item whether he knows the answer or not in the same serial order without skipping. He is also asked to note down the closing time of the test. With this the collection of the necessary data will be over. 335
K. VISWX4ATHA?4
336
The ne.xt step is to analyse the data. For each sampling unit, i.e. for each testee, the time taken for answering the test is determined. This can be done by subtracting the “starting time” from the “closing time”. Arrange these data in the form of a table and compute the arithmetic mean. Also compute the standard deviation. Now, the suggested formula for the optimum time required for the test is T, = x-t S,, approximated to the nearest multiple of 10 (or 5 in the case of more precise tests); where To = the optimum time required for the test, ??= the arithmetic mean and S, = the standard deviation. This formula appears to be the most appropriate to decide the required time for an objective test.
3. ILLUSTRATION As an illustration consider the following data. A batch of 34 students learning Telugu as a second language are given a lOO-item multiple choice test, each item having four alternatives. The time consumed by them to complete the test without omitting or skipping the items is presented in the following frequency distribution (Table 1). Table 1. Computation
of mean and standard deviation for scores obtained on a language test
Frequency
Class interval
f
96 - 100 91 - 95 86 - 90 81 -85 76 - 80 71-75 66 - 70 61 - 65 56 - 60 51 - 55 46 - 50 41 -45 Total:
1 0 2
1 4 3 2 6 4 1 6 4
mean ??
x’ = x-2
98 0 176 83 312 219 136 378 232 53 288 172
34.85 29.85 24.85 19.85 14.85 9.85 4.85 -0.15 -5.15 - 10.15 - 15.15 -20.15
2147
88.70
98 93 88 83 78 73 68 63 58 53 48 43
34(=N)
The arithmetic
J-X
Slid-value X
X’l
fX’?
1214.52 891.02 617.52 394.02 220.52 97.02 23.52 0.02 26.52 103.02 229.52 406.02
1214.52 0000.00 1235.04 394.02 882.08 291.06 47.04 0.12 106.08 103.02 1377.12 1624.08 7274.16
EfX
= -
N
= 5~63.15
The standard
deviation
S, =
Ix
,2
4- N-l
=dF_
T,=js+S, = 63.15 + 14.85 = 78.90 - 80.
dw
from 34 students
= 14.85.
OPTI.MUMTIME FOR AN OBJECTIVE TEST
337
Thus the optimum time required to answer the above mentioned loo-item multiple choice test is 80 minutes.
4. INTERPRETATION
OF To
The formula To = x + S, has two constituents, x, the mean of the time consumed by the testees and S, the standard deviation of the X values. 3 is the most appropriate and accurate measure of the central tendency which can be exposed to mathematical operations unlike the other measures, viz. the median and the mode. Similarly, S, the standard deviation is the most appropriate and accurate measure of the variability. While the arithmetical mean gives the average of the data, the standard deviation shows the average variability of the data. Now, To = x+ S,, the sum of the average score and the average of the deviations becomes the most appropriate measure of the optimum time to be given for a test. Though x is the most accurate measure of central tendency it fluctuates to the extreme values. Also this covers only 50% of the total cases. This is checked by adding the standard deviation in order to achieve a more accurate and better measure.
5. MERITS OF To If any data available are normally distributed, 68.3% of the cases fall within one standard deviation on either side of the mean. In any type of distribution, either normal or nonnormal (skewed), about 50% of the cases fall below the mean value. The distribution of time consumed by different individuals for a test is in most cases positively skewed because very few cases will be in the top extreme (high end of the curve) and it will not have extreme cases in the low end. If a curve is drawn for such a distribution the right till will be longer and the left end will abruptly cut the base line. In such a distribution most of the cases are concentrated below the mean or within one standard deviation to the right of the mean, (See Fig. 1.) _-
455
50.5
55.5 60.5
6S.S
70.5 75.5
805
65.5
SO.3
W.5
100.5
X
Fig. 1. Free hand curve joining the points plotted on the graph taking the real upper limits of the class intervals on the X axis and the frequency on the Y axis from the data in Table 1.
338
K. VISWANATHx4kl
Only few extreme cases fall beyond this limit. For instance, in the above distribution 18 out of 34 cases, i.e. 52.9070, fall below x = 63.15 and 28.5 cases, i.e. 83.8% of the cases, fall below x+ 1s. Only 5.5 cases, i.e. 16.2% (roughly) fall beyond this. In other words, only 16.2 cases in 100 are extreme and fall beyond this. In situations like this, i.e. time taken by individuals in answering a test, this is a negotiable percentage. Hence, To = x+ S, proves to be a better measure for alloting an optimum time for an objective test. Though this is basically meant to measure the optimum time for objective tests its use can be extended even to tests with open-ended answers on the same lines of objective tests. Once the design of the question paper is decided and once the optimum time is computed with this procedure, at any time later, for tests of similar design, the same optimum time can be given without again going through all these procedures of administering the tests to representative samples and computations. This is because in tests with open-ended answers giving a few minutes more or less will not make much difference.