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Chapter - 5 Reliability, Validity & Norms
Chapter - 5 Reliability, Validity & Norms
5.1.0 Introduction
5.2.0 Concept of the Reliability
5.3.0 Methods of Estimation of reliability
5.3.1 Method of equivalent form
5.3.2 Test Retest Method
5.3.3 Split-half Method
5.3.4 Rulon Formula
5.3.5 Flanagan Formula
5.3.6 Method of Rational Equivalence (KR20)
5.3.7 Reliability by Cronbach’s α(alpha)
5.4.0 Validity
5.4.1 The Concept of validity
5.4.2 The Method of Determining validity
5.4.3 Face Validity
5.4.4 Congruent Validity
5.4.5 Concurrent Validity
5.4.6 Construct Validity
5.5.0 Norms
5.5.1 Norms for present test
5.6.0 Test Manual
5.6.1 Rules for the administration of the test
5.6.2 Conversion of raw scores into PR
5.6.3 Grade and level fixing
5.7.0 Conclusion
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Chapter – 5 Reliability, Validity & Norms
5.1.0 Introduction :
In the previous chapter, the process of finalization of the test has been
described in detail. The test constructor should present the evidences of reliability and
validity of the said test. Hence, it is obligatory on the part of the investigator to
establish the reliability and validity of the test. This chapter deals with reliability,
validity and norms.
5.2.0 Concept of the Reliability :
The main purpose of the measurement is to arrive at some standard
and precise judgment about an individual. The judgment would be of good value, if it
is based on dependable scores earned on dependable test. The dependable test means
nothing but a reliable test. The term reliability denotes truest worthiness, or
consistency Ebel(1972)1 has given an operational definition of a test reliability as
follows :
“The reliability co-efficient for a set of a scores from a group of examines is the co-efficient of co-relation between that set of scares and another set of scores on a equivalent test obtained independently from the members of the same group”
This definition implies that reliability is not a property of a test by
itself but rather of a test, when applied to a particular group of respondents. The more
appropriate, the test is to the level of abilities in the group, the higher is the reliability
of the scores it yields.
5.3.0 Methods of Estimation of Reliability :
There are different methods of estimating the reliability of the test and
they are :
1. Equivalent form
2. Test-retest method.
3. Split-half method
4. Rulon method
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5. Flanagan Method
6. Method of Rational Equivalence. (KR20)
7. Reliability by Cronbach’s α (Alpha)
5.3.1 Method of equivalent form :
This method is simple. From the very beginning, the
investigator has to prepare two equal form of the test. These two forms must
be very close in similarity i.e. number of items, matter of contents, traits to be
measured and procedure for responding the test item etc. Over and above the
items must have equal discriminative power, equal facility value, internal
consistency and unidimensional ability. The examinee, say subject, takes one
form of the test and then the other soon after first. In order to control some
error variance, the turns of the forms should be rotated. The agreement
between the two forms is determined by means of correlation co-efficient.
This method is rarely used because it is very difficult to prepare (Construct)
two absolute parallel forms of the same test construction of two equivalent
form needs a lots of time and energy on the part of the investigator. Therefore,
this method is rarely used for the purpose of determining the reliability of the
test. Due to these constrains, the investigator has not used this method.
5.3.2 Test Retest Method :
In this method, the test is given to the same individuals twice.
The agreement between the two sets of scores from the two administrations of
the same test is determined by means of a correlation of coefficient. There are
certain factors like practices, confidence, growth, physical conditions which
play certain role in these two different occasions of test administrations. To
minimize the effects of these variables, a fairly large sample would be needed.
Besides, the time interval should be adequate. The investigator, after studying
the pros and cons of this method, used it for estimating the reliability of the
present test. The scores obtained on two different administration of the same
test were used as two sets of scores for estimating the correlation of
coefficient. In this method the time interval for two successive administration
should not be too long or too short because it affects on the coefficient of
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correlation. The investigator had selected thirty-day time interval for two
successive administration which is supported by many researches.
After final run of the present test, a sub sample of 118 students
form main sample was drown (See. Chapter 3 para 3.4.5). After 30 days final
the test was administrated to the sample as per rules and regulations. After
scoring response of the respondents, true scores were entered in a excel
spreadsheet which is appended as appendix-VIII. The coefficient of
correlation was computed by using NRTVB-99 software. The said software
was developed by Navnit Rathod in year of 1999. (Prof. Bhavnagar
University, Bhavnagar, Gujarat State). The coefficient of correlation was
found 0.90 Hence, the reliability estimated by this method is satisfactory.
5.3.3 Split-half Method :
There are some practical difficulties which are associated with
the determination of reliability coefficient by the test-retest and equivalent
forms. These difficulties could be overcome by split-half method. One of the
practical alternative is to spilt up the entire form of the test into two reasonably
equivalent halves. For making two equivalent halves, usually pooling the odd
numbered items for one set of scores and pooling the even numbered items for
second set of scores. If controls such factors as practice, fatigue, distraction
and mental set. After the test has been given to a representative sample, two
scores are obtained for each subject, one of the odd numbered and the other on
the even numbered items. The agreement between these set of scores on the
same test as determined by a correlation of coefficient, reflects the reliability
of half the test. The reliability of the whole that could be obtained by
spearman – brown’s formula2 which is as under
2
1
The answer-sheet of retest were used for this purpose. Item
wise scores were entered in Excel spreadsheet there after score earned by the
respondent on odd number item and even number item were split into two
halves. The entire table is appended as appendix-IX The NRTVB-99 software
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was used to compute coefficient of correlation. The computed coefficient of
correlation was found 0.64. there after the coefficient of correlation for whole
test was computed by abovementioned formula by the said software.
2 0.641 0.64
1.281.64
0.78
It is observed from the value of r = 0.78. This value shows that the
present test is reliable.
5.3.4 Rulon Formula :
Rulon has developed a simple formula for establishing the
reliability of the total test Score using the basic definition of reliability.
Rulon equation expresses the complimentary statement that
reliability is equal to unity minus the proportion of error variance. Hence
computing error variance is a main thing in his work. The entire table is
appended as appendix-X the rulon formula3 is given below :
1
During the split-half reliability student wise score earned on
odd part and even part were computed from excel spread sheet there after
difference between these to scores (d) and (d2) were computed for the same
student and were computed. On that basis of and variance for
difference ( ) and variance for total ( ) were computed. They were as
under.
29.81, 140.66
129.81
140.66
1 0.21
= 0.79
The coefficient of correlation was found 0.79. The value shows
that correlation between two halves is high and reliable.
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5.3.5 Flanagan Formula :
Flanagan’s formula for establishing reliability is very close to
Rulon’s formula. In Flanagan’s formula. The variance of two halves are
added, instead of difference of division of two sets. In other words it estimates
the error variance in a sense as the sum of the variance of the two halves. The
Flanagan formula4 is as under.
2 1
= Variance of Scores of odd numbered items.
= Variance of Score of even numbered items.
= Variance of total scores
During the computation of split-half reliability value for each
student for odd number item, even number item, d, d2, Xt and were
received. With the help of these data, , , were computed by using
excel – (spread sheet) program. The entire table is appended as appendix-XI
They ware as under
46.17, 41.20, 140.66
These values were used to compute coefficient of correlation
by using Flanagan formula. The computation is as under.
2 146.17 41.20
140.66
2 187.37 140.66
2 0.38 0.76
It is observed that the computed value of r was found 0.76.
This results also indicates that the test is reliable.
5.3.6 Method of Rational Equivalence (KR20) :
This method was developed by Kuder and Richardson, it is also
known as K.R. method. This method is useful for estimating the internal
consistency or homogeneity of a test. The Kuder Richardson formulas, was
developed because of dissatisfaction with Split-half method. A test can be split
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into two equal halves in great many way and such split might yield some what
different estimate of rtt. The use of items statistics set away from such basis as
may arise from arbitrary splitting into two halves. Finally the most accurate
and practical KR20 formula5 was developed as under.
1Σ .
n = number of items in the test p = Proportion of passing on items q = (1-P) proportion of the group answering
the item incorrectly = The variance of the entire test score. = reliability of the whole test
To compute reliability by using KR20. The responses of 118
student to whom the retest was administrated were used. The present test
carries 180 + 180 = 360 item. For each item total score, number of correct
items and number of incorrect items were worked out form the excel spread
sheet. The proportion of correct responses for each item and its proportion (p)
and proportion of incorrect responses (q = 100-p) were also computed for each
item. With the help of p and q, pxq for each item was also computed. The sum
of p x q i.e. Σpq and were also computed. The entire table is appended as
appendix-XII. The required statistic i.e. n, Σpq and are as under.
360, 20.41, Σ 13.11
These value were inserted in the formula and tt was computed. And
computation is as under.
360
360 120.41 13.11
20.41
= 1.003 x 0.97 = 0.97
The computed value of was found 0.97 and this value shows
that resent test is highly reliable.
5.3.7 Reliability by Cronbach’s (alpha) :
Cronbach’s α is the coefficient of reliability. It is commonly
used as measure of the internal consistency or reliability of a test. It was
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denoted as alpha by lee cronbach in 1951. According to him, he was intended
to continue with further coefficients. The measure can be viewed as an
extension of the Kunder-Rechardson formula (KR20). Which is an equivalent
measure of dichotomous items. Cronbach has given a formula to work out the
reliability by using variance of the scores not only on odd and even items but
also the total number of items. The software NRTVB-99 is based on the
following formula.
Cronbach’s α = 2[1 –( ) ]
The formula transformation is built in the NRTVB-99 software.
So that when we run the software, we get value of cronbach’s alpha directly.
Hence, after running these software the investigator got the value of
Cronbach’s alpha, which was 0.93.
A commonly accepted rule of thumb for describing internal
consistency using cronbach’s alpha is as follows :
Cronbach’s alpha Internal consistency α ≥ 0.9 Excellent 0.8 ≤ α ≥ 0.9 Good 0.7 ≤ α ≥ 0.8 Acceptable 0.6 ≤ α ≥ 0.7 Questionable 0.5 ≤ α ≥ 0.6 Poor α ≤ 0.5 Unacceptable
The cronbach's & value for present test was 0.93. As per norms
laid down by cronbach, the internal consistency say the reliability of the
present test is excellent.
Summary of the Reliablility :-
The investigator has used six methods of estimating reliability
of the present test. It is summarised in table 5.2.7
Summary of Reliability Sr No. Method Correlation Remark 1 Test-retest 0.90 Highly Reliable 2 Splif-half 0.78 Reliable 3 Rulon formula 0.79 Reliable 4 Flanagun Method 0.76 Reliable 5 Rational Equivalence (KR20) Method 0.97 Highly Reliable 6 Cronbach's & (alpha) Method 0.93 Highly Reliable
97
It is observed from the table 5.2.7 that the range of coefficient
of correlation worked out by five different methods of the present test is 0.76
to 0.97. Looking to different values one can dare to say that the speed and
Accuracy test is reliable. As per cronbach’s α the reliability of the said test is
trustable, reliable and no harm to used for the population.
5.4.0 Validity :
A test is expected to Prove its worth. If the test does not fullfill its
worth, it is not worth of anything. Ross and Stanley (1963)6 have rightly Pointed out :
“Although high reliability is no guarantee that the test is good, low reliability does not indicate that it is poor. Validity is always the first to be sought in a test, and granted that reliability is a valuable auxiliary”.
The test for measuring mental abilities, aptitude, attitude, etc., must
justify their Purpose. In the process of justification of purpose is known as the test
validation. Consequently, validation of a test score is the most important and
significant step in the process of standardization of any test. Most of the users, before
selecting the test for the use, looks carefully in to the values of validity. Therefore, the
constructor of the test should make clear the concept of the validity.
5.4.1 The Concept of validity :
The validity is an important characteristic of the test. It depends
upon the efficiency with which it measures that it attempts to measure. In
other words it is defined as the accuracy with which the test measures what it
claims to measure. The term validity and purpose are very closely associated
with each other. A test which fulfills the purpose for which it is designed is
called a valid test. This led to say that test of a Speed and Accuracy (SA)
measures the Speed and Accuracy and nothing else. Therefore, in the course of
valid Speed & Accuracy test the student reading for their grade XII in the
various higher secondary schools who have speed and accuracy should get
more scores than those who have less S.A.
Garrett (1965)7 has rightly put it as :
“The validity of the test or of any measuring instrument, depends upon the fidelity with which it measures what it proposes to measure”
98
In such situation the validity of the test must be established
even the test is highly reliable.
5.4.2 The Method of Determining validity :
Procedures for determining validity of tests are primarily
concerned with relationship between performance on the test and other
independently observable facts about the speed and accuracy characteristics
under consideration. There are numerous techniques that are employed for
investigating these relationships. They are described as various techniques.
They are as under :
1. Face Validity
2. Congruent Validity
3. Concurrent Validity
4. Construct Validity
The investigator has used all the four techniques for estimation
validity of the Speed & Accuracy test.
5.4.3 Face Validity :
This method is very simple and provides valid image of the test
which can be treated as validity. In this method, experts having long
experience to judge the test for which it has been constructed. The test was
given to experts and requested them to judge whether it has a capacity to
measure the Speed and Accuracy of the students of higher secondary school.
The investigator have selected 5 experts. Who have large
experience in test – construction. For the validation of item – content two
Teachers were also involved for judging item content. Over and above both
the expert – groups were requested to scale out level of difficulty of each item
by assigning 1, 2, and 3 for too easy, difficult and too difficult respectively.
The judges were also requested to make language correction if needed and if
he / she fills to add more items in the given list of items. The reactions of
experts were analysed and found that, there were no much more suggestions in
editing items. All the experts were opined that items have good power to
measure speed and Accuracy of the students under investigation. Hence, it was
concluded that the first draft of test carries good face validity.
99
5.4.4 Congruent Validity :
This type of validity is estimated by the means of a statistical
technique. For this, the set of scores on the present test is correlated with the
set of criteria of a similar measure. It means, it is correlated with some
available well known, fully valid and powerful test of the similar nature. The
correlation of the new test with the existing test would show to what extent the
two tests measure the same speed & Accuracy. For this purpose, the present
investigator has selected a speed and accuracy test constructed and
standardized by K. G. Desai.
The said test was based on Minesota claricde Apptitude test.
The said test was constructed and presently widely used by many researchers.
The reliability range of the said test was between 0.85 to 0.99. Its validation
was made by administering the test to criterian groups – like Accountants,
Clarks and persons busy with such work. More detail is given in chpt. 3 Para
3.5.0
After selection of valid criterion test, both tests were
administered to a representative randomized sample of 118 students and two
sets of scores were obtained for each student please see appendix – VII. The
agreement between these scores were determined by a correlation of co-
efficient. Both the set of scores were entered in a excel spread sheet. The
correlation of co-efficient was computed using the NRTVB – 99 soft-ware.
The value of coefficient of correlation was 0.60. Hence, the present test can be
treated as a valid test.
5.4.5 Concurrent Validity :
The evidence of the validity be obtained from the relationship
with other currently obtainable information about an individual. Anne
Anastasi (1976)8 has defined the concurrent validity as follows :
“The relationship between test scores and indices of criterion status obtained at approximately the same time is known as concurrent validity.”
Asking students to provide percentage of last annual
examination of the students included in the sample of re-test. For the students
100
of Std. XI, their board examination result of std X were taken into
consideration while for the students of XII, the annual examination of their std
XI were used. The stated results were verified by the investigator from school
record for its validation.
Two set of scores earned by each student on speed and
accuracy test and his /her percentage of annual examination (Educational
achievement) were entered in Excel - spread sheet please see appendix - VIII.
The coefficient of correlation between these two set of scores was computed
by using Excel program. The said values were 0.50.
The value of coefficient of correlation indicated that the
concurrent validity of the present test is satisfactory one.
5.4.6 Construct Validity :
There are different methods for examining construct validity.
The factor analysis is a well – known method of construct validity. In the
present investigation, the method of cliff’s consistency Indices ‘C’ was used
due to its strongness. In the present study cliff’s consistency Indices ‘C’ was
calculated using the computer program NRTVB – 99.
During computation of reliability by KR20 (See para : 5.3.6),
item wise correct and incorrect responses were entered in a Excel Spread
Sheet. The spread sheet prepared by data entry was directly supporting to
NRTVB-99. So that these soft-ware was run to get the value of cliff’s
consistency ‘C’. The computed cliff’s consistency ‘C’ was 0.36
As per criteria, if the value of ‘C’ is 0.36 or above it, then the
test is treated as valid one.
The computed value for different methods employed by the
investigator is present in table 5.3.6
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Table 5.4.6 Validity Summary
Method Values Remark 1) Face Validity - Good
2) Congruent Validity 0.60 Valid
3) Concurrent Validity 0.50 Satisfactory
4) Construct Validity 0.36 Valid
It is observed form table 5.3.6 that the present test is found
valid and useful to measure Speed and Accuracy of the higher secondary
school students.
5.5.0 Norms :
A norm represent a typical level of performance for a particular group.
A raw score on any Psychological test alone is meaningless unless we have additional
interpretive data. So the scores on psychological test are most commonly interpreted
by reference to norms that represent the test performance of the standardized sample.
Norms are empirically established by determining what parsons in a representative
group actually do on a test. In order to ascertain more precisely the individual’s exact
position with reference to the standardized sample, the raw score is converted into
some relative measure. These derived scores serve two purposes.
1. They indicate the individuals relative standing in the normative sample
and facilitate evaluation of performance.
2. They provide comparable measures that permit a direct comparison of
the individuals performance on different tests.
Fundamentally, derived scores are expressed in one of two major ways
(1) developmental Norms and (2) within group Norms.
• Developmental Norms :- These type of norms generally indicate the
normal developmental path the individual has progressed. They are very
helpful for descriptive purpose but they are not compatible to precise
statistical treatment. The types of developmental norms are –
• Mental age Norms • Grade Equivalent Norms. • Ordinal Scale Norms.
102
• Within Group Norms :-
Such type of norms help in comparing the individual’s
performance with the most nearly comparable standardised group’s
performance. Within group norms have a uniform and clearly defined
quantitative meaning and can be appropriately employed in most types of
statistical analyses.
• Percentiles :- Percentile scores represent the percentage of persons in
the standardised sample who fall below a given raw score. They
indicate an individual’s relative position in the standardized sample. In
case of percentiles, the counting begins from the bottom so lower the
percentile, poorer the standing / rank.
• Standard Score :- Standard score express the individual’s distance
from the mean in terms of the standard deviation of the distribution.
They are obtained by linear or nonlinear transformation of the original
raw scores.
• Age Norms :- To establish age norms, the mean of raw scores
obtained by all in the same age group within a standardized sample is
taken. So mean raw score of 12 year old students would represent the
12 years norm.
• Grade Norms :- Grade norms are found by computing the mean row
score obtained by students in particular grade.
5.5.1 Norms for the present test :-
To gage the performance of the testee, norms provide such
facility to its users. In the present study, Area, Gender, Stream of the study are
naturally divisible. The educational achievement levels and Occupation of the
parent father are not naturally divisible. As per chapter six levels of each
variable except standard has significant effect on Speed and Accuracy (SA) of
the students included in the sample. According to theory, one has to computed
norms for each variable – level wise. In such situation, one has to incorporate
all the rows for each raw-score. If we include all the variables than there will
be 144 rows (2 x 2 x 3 x 4 x 3) which may create complication for reading
103
equivalence for raw-score. To minimize the rows, it was decided to establish
norms for naturally divisible variables. i.e. Area, Gender and streams only.
To avoid confusions, again only norms were computed in form
of PR. PR will help to identify the position of the testee in the entire
population. It will also help the researchers, teachers and counsellors to decide
the level of speed & Accuracy in terms of letter grade and qualitative division
of the testees. e.g. Very Good (A), Good (B), Average (C) Below Average
(D) and Poor (E). For dividing into levels or letter grade following criteria
were used.
Table 5.5.1 Letter grade and qualitative division
Level Grade Coverage of PR Very Good A Above 80 PR Good B From 61 to 80 PR Average C From 41 to 60 PR Below Average D From 21 to 40 PR Poor E Below 21
Total true score earned by each student was classified
according to stratum. Area wise, Gender wise and Stratum wise frequency
distributions were prepared accordingly by using excel program. PR was
calculated for each raw score in the context of each variable with its levels.
The minimum score was 192 earn by the students, on present test. Hence, from
191 raw score, PR table was prepared : To make easy reading PR
corresponding to raw score stream wise, i.e. three tables were prepared. These
PRs are presented in table 5.4.2 say table - (A), table - (B) and table - (C) for
stream wise. They are as follow.
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Table 5.4.2 (A) Value of PR for each row score in the context of variable & its levels
Science Stream Row Score
Rural Urban Boys Girls Boys Girls
360 99.10 99.10 99.10 99.10 359 98.10 98.10 98.10 98.10 358 98.10 98.10 98.10 98.10 357 96.70 96.70 96.70 93.90 356 96.70 96.70 96.70 93.90 355 93.90 93.90 93.90 93.90 354 93.90 93.90 93.90 93.90 353 90.00 90.00 90.00 90.00 352 90.00 90.00 90.00 90.00 351 84.40 84.40 84.40 84.40 350 84.40 84.40 84.40 84.40 349 78.50 78.50 78.50 78.50 348 78.50 78.50 78.50 78.50 347 71.50 71.50 71.50 71.50 346 71.50 71.50 71.50 71.50 345 66.40 66.40 66.40 66.40 344 66.40 66.40 66.40 66.40 343 61.00 61.00 61.00 61.00 342 61.00 61.00 61.00 61.00 341 54.10 54.10 54.10 54.10 340 54.10 54.10 54.10 54.10 339 50.10 50.10 50.10 50.10 338 50.10 50.10 50.10 50.10 337 45.80 45.80 45.80 45.80 336 45.80 45.80 45.80 45.80 335 42.10 42.10 42.10 45.80 334 42.10 42.10 42.10 42.10 333 42.00 38.60 38.60 38.60 332 38.60 38.60 38.60 38.60 331 38.50 35.00 35.00 35.00 330 35.00 35.00 35.00 35.00 329 32.40 32.40 32.40 32.40 328 32.40 32.40 32.40 32.40 327 29.00 26.80 30.40 30.40 326 29.00 26.80 30.40 30.40 325 29.00 26.80 26.80 26.80 324 29.00 26.80 26.80 26.80 323 26.80 26.80 26.80 26.80 322 26.80 26.80 26.80 26.80 321 24.60 24.60 24.60 26.70
Row Score
Rural Urban Boys Girls Boys Girls
320 24.60 24.60 24.60 24.60 319 24.50 23.20 23.20 23.20 318 23.20 23.20 23.20 23.20 317 20.30 20.30 20.30 20.30 316 20.30 20.30 20.30 20.30 315 18.40 18.40 18.40 18.40 314 18.40 18.40 18.40 18.40 313 14.70 16.70 16.70 18.30 312 14.70 16.70 16.70 16.70 311 14.70 14.70 14.70 14.70 310 14.70 14.70 14.70 14.70 309 11.70 13.10 8.00 14.60 308 11.70 13.10 8.00 11.70 307 11.70 8.00 8.00 11.70 306 11.70 8.00 8.00 11.70 305 10.80 8.00 8.00 9.80 304 10.80 8.00 8.00 9.80 303 7.30 8.00 8.00 9.80 302 7.30 8.00 8.00 9.80 301 7.30 8.00 8.00 8.00 300 7.30 8.00 8.00 8.00 299 7.30 8.00 8.00 8.00 298 7.30 8.00 8.00 8.00 297 7.30 7.30 5.50 5.50 296 7.30 7.30 5.50 5.50 295 6.60 4.90 5.50 5.50 294 6.60 4.90 5.50 5.50 293 6.60 4.90 5.50 5.50 292 4.10 4.90 5.50 5.50 291 4.10 4.90 5.50 5.50 290 4.10 4.90 5.50 5.50 289 4.10 4.90 4.90 4.90 288 4.10 4.90 4.90 4.90 287 4.10 3.10 4.60 4.60 286 4.10 3.10 4.60 4.60 285 4.10 3.10 4.10 2.80 284 4.10 3.10 4.10 2.80 283 3.70 3.10 2.30 2.80 282 3.70 3.10 2.30 2.80 281 2.70 3.10 2.30 2.80
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Row Score
Rural Urban Boys Girls Boys Girls
280 2.70 3.10 2.30 2.80 279 2.70 1.60 2.30 2.80 278 2.70 1.60 2.30 2.80 277 2.70 1.60 2.30 2.80 276 2.70 1.60 2.30 2.80 275 2.70 1.60 2.30 2.30 274 2.50 1.60 2.30 2.30 273 2.40 1.60 2.30 2.30 272 0.40 1.60 2.30 2.30 271 0.40 1.60 0.00 1.60 270 0.40 1.60 0.00 1.60 269 0.40 1.60 0.00 1.60 268 0.40 1.60 0.00 1.60 267 0.40 1.60 0.00 1.60 266 0.40 1.60 0.00 1.60 265 0.40 1.60 0.00 1.60 264 0.40 1.60 0.00 1.60 263 0.40 0.50 0.00 0.00 262 0.40 0.50 0.00 0.00 261 0.40 0.50 0.00 0.00 260 0.40 0.50 0.00 0.00 259 0.40 0.50 0.00 0.00 258 0.40 0.50 0.00 0.00 257 0.40 0.50 0.00 0.00 256 0.40 0.50 0.00 0.00 255 0.40 0.50 0.00 0.00 254 0.40 0.50 0.00 0.00 253 0.40 0.50 0.00 0.00 252 0.40 0.50 0.00 0.00 251 0.40 0.50 0.00 0.00 250 0.40 0.50 0.00 0.00 249 0.40 0.50 0.00 0.00 248 0.40 0.50 0.00 0.00 247 0.40 0.50 0.00 0.00 246 0.40 0.50 0.00 0.00 245 0.40 0.50 0.00 0.00 244 0.40 0.50 0.00 0.00 243 0.40 0.50 0.00 0.00 242 0.40 0.50 0.00 0.00 241 0.40 0.50 0.00 0.00 240 0.40 0.50 0.00 0.00 239 0.40 0.50 0.00 0.00
Row Score
Rural Urban Boys Girls Boys Girls
238 0.40 0.50 0.00 0.00 237 0.40 0.50 0.00 0.00 236 0.40 0.50 0.00 0.00 235 0.40 0.50 0.00 0.00 234 0.40 0.50 0.00 0.00 233 0.40 0.50 0.00 0.00 232 0.40 0.50 0.00 0.00 231 0.40 0.50 0.00 0.00 230 0.40 0.50 0.00 0.00 229 0.40 0.50 0.00 0.00 228 0.40 0.50 0.00 0.00 227 0.40 0.00 0.00 0.00 226 0.40 0.00 0.00 0.00 225 0.40 0.00 0.00 0.00 224 0.40 0.00 0.00 0.00 223 0.40 0.00 0.00 0.00 222 0.40 0.00 0.00 0.00 221 0.00 0.00 0.00 0.00 220 0.00 0.00 0.00 0.00 219 0.00 0.00 0.00 0.00 218 0.00 0.00 0.00 0.00 217 0.00 0.00 0.00 0.00 216 0.00 0.00 0.00 0.00 215 0.00 0.00 0.00 0.00 214 0.00 0.00 0.00 0.00 213 0.00 0.00 0.00 0.00 212 0.00 0.00 0.00 0.00 211 0.00 0.00 0.00 0.00 210 0.00 0.00 0.00 0.00 209 0.00 0.00 0.00 0.00 208 0.00 0.00 0.00 0.00 207 0.00 0.00 0.00 0.00 206 0.00 0.00 0.00 0.00 205 0.00 0.00 0.00 0.00 204 0.00 0.00 0.00 0.00 203 0.00 0.00 0.00 0.00 202 0.00 0.00 0.00 0.00 201 0.00 0.00 0.00 0.00 200 0.00 0.00 0.00 0.00 199 0.00 0.00 0.00 0.00 198 0.00 0.00 0.00 0.00 197 0.00 0.00 0.00 0.00
106
Row Score
Rural Urban Boys Girls Boys Girls
196 0.00 0.00 0.00 0.00 195 0.00 0.00 0.00 0.00 194 0.00 0.00 0.00 0.00 193 0.00 0.00 0.00 0.00 192 0.00 0.00 0.00 0.00 191 0.00 0.00 0.00 0.00 190 0.00 0.00 0.00 0.00 189 0.00 0.00 0.00 0.00 188 0.00 0.00 0.00 0.00 187 0.00 0.00 0.00 0.00 186 0.00 0.00 0.00 0.00 185 0.00 0.00 0.00 0.00 184 0.00 0.00 0.00 0.00
Row Score
Rural Urban Boys Girls Boys Girls
183 0.00 0.00 0.00 0.00 182 0.00 0.00 0.00 0.00 181 0.00 0.00 0.00 0.00 180 0.00 0.00 0.00 0.00 179 0.00 0.00 0.00 0.00 178 0.00 0.00 0.00 0.00 177 0.00 0.00 0.00 0.00 176 0.00 0.00 0.00 0.00 175 0.00 0.00 0.00 0.00 174 0.00 0.00 0.00 0.00 173 0.00 0.00 0.00 0.00 172 0.00 0.00 0.00 0.00 171 0.00 0.00 0.00 0.00
Table 5.4.2 (B)
Value of PR for each row score in the context of variable & its levels Commerce Stream
Row Score
Rural Urban Boys Girls Boys Girls
360 98.10 98.10 93.90 96.70 359 98.10 98.10 93.90 96.70 358 98.10 98.10 93.90 96.70 357 93.90 93.90 93.90 96.70 356 93.90 93.90 93.90 96.70 355 93.90 93.90 93.90 93.90 354 93.90 93.90 93.90 93.90 353 90.00 90.00 90.00 90.00 352 90.00 90.00 90.00 90.00 351 84.40 84.40 84.40 84.40 350 84.40 84.40 84.40 84.40 349 78.50 78.50 78.50 78.50 348 78.50 78.50 78.50 78.50 347 71.50 71.50 78.50 71.50 346 71.50 71.50 71.50 71.50 345 66.40 66.40 66.40 66.40 344 66.40 66.40 66.40 66.40 343 61.00 61.00 61.00 61.00 342 61.00 61.00 61.00 61.00 341 54.10 54.10 54.10 54.10 340 54.10 54.10 54.10 54.10 339 50.10 50.10 50.10 50.10 338 50.10 50.10 50.10 50.10 337 45.80 45.80 45.80 45.80
Row Score
Rural Urban Boys Girls Boys Girls
336 45.80 45.80 45.80 45.80 335 42.10 42.10 42.10 42.10 334 42.10 42.10 42.10 42.10 333 38.60 38.60 38.60 38.60 332 38.60 38.60 38.60 38.60 331 35.00 35.00 35.00 38.50 330 35.00 35.00 35.00 35.00 329 32.40 32.40 32.40 32.40 328 32.40 32.40 32.40 32.40 327 30.40 29.00 30.40 30.40 326 30.40 29.00 30.40 30.40 325 29.00 29.00 29.00 29.00 324 29.00 29.00 29.00 29.00 323 26.80 26.80 26.80 26.80 322 26.80 26.80 26.80 26.80 321 24.60 24.60 24.60 24.60 320 24.60 24.60 24.60 24.60 319 23.20 23.20 23.20 23.20 318 23.20 23.20 23.20 23.20 317 20.30 20.30 20.30 20.30 316 20.30 20.30 20.30 20.30 315 18.40 18.40 18.40 20.20 314 18.40 18.40 18.40 18.40 313 16.70 16.70 16.70 16.70
107
Row Score
Rural Urban Boys Girls Boys Girls
312 16.70 16.70 16.70 16.70 311 14.70 14.70 14.70 14.70 310 14.70 14.70 14.70 14.70 309 13.10 13.10 14.60 13.10 308 13.10 13.10 13.10 13.10 307 11.70 10.80 11.70 10.80 306 11.70 10.80 11.70 10.80 305 10.80 10.80 10.80 10.80 304 10.80 10.80 10.80 10.80 303 9.80 9.80 9.80 9.80 302 9.80 9.80 9.80 9.80 301 9.00 9.00 9.00 9.00 300 9.00 9.00 9.00 9.00 299 8.00 8.00 8.00 8.00 298 8.00 8.00 8.00 8.00 297 7.30 7.30 7.30 4.90 296 7.30 7.30 7.30 4.90 295 6.70 6.10 6.70 4.90 294 6.70 6.10 6.70 4.90 293 6.10 6.10 6.60 4.90 292 6.10 6.10 6.10 4.90 291 5.50 5.50 5.50 4.90 290 5.50 5.50 5.50 4.90 289 3.00 4.10 4.80 4.90 288 3.00 4.10 4.80 4.90 287 3.00 4.10 4.80 4.10 286 3.00 4.10 4.60 4.10 285 3.00 4.10 4.10 4.10 284 3.00 4.10 4.10 4.10 283 3.00 3.10 3.70 3.70 282 3.00 3.10 3.70 3.70 281 3.00 3.10 3.10 2.00 280 3.00 3.10 3.10 2.00 279 3.00 0.60 2.80 2.00 278 3.00 0.60 2.80 2.00 277 0.70 0.60 2.80 2.00 276 0.70 0.60 2.80 2.00 275 0.70 0.60 1.60 2.00 274 0.70 0.60 1.60 2.00 273 0.70 0.60 1.60 2.00 272 0.70 0.60 1.60 2.00 271 0.70 0.60 1.60 2.00
Row Score
Rural Urban Boys Girls Boys Girls
270 0.70 0.60 1.60 2.00 269 0.70 0.60 1.60 1.60 268 0.70 0.60 1.60 1.60 267 0.70 0.60 1.60 1.60 266 0.70 0.60 1.60 1.60 265 0.70 0.60 1.60 1.60 264 0.70 0.60 1.60 1.60 263 0.70 0.60 0.70 1.60 262 0.70 0.60 0.70 1.10 261 0.70 0.60 0.70 1.10 260 0.70 0.60 0.70 1.10 259 0.70 0.60 0.70 1.10 258 0.70 0.60 0.70 1.10 257 0.70 0.60 0.70 1.10 256 0.70 0.60 0.70 1.10 255 0.70 0.60 0.70 1.10 254 0.70 0.60 0.70 1.10 253 0.70 0.60 0.70 0.00 252 0.70 0.60 0.70 0.00 251 0.70 0.60 0.70 0.00 250 0.70 0.60 0.70 0.00 249 0.70 0.60 0.70 0.00 248 0.70 0.60 0.70 0.00 247 0.70 0.60 0.70 0.00 246 0.70 0.60 0.70 0.00 245 0.70 0.60 0.70 0.00 244 0.70 0.60 0.70 0.00 243 0.70 0.60 0.70 0.00 242 0.70 0.60 0.70 0.00 241 0.70 0.60 0.70 0.00 240 0.70 0.60 0.70 0.00 239 0.00 0.60 0.30 0.00 238 0.00 0.60 0.30 0.00 237 0.00 0.60 0.30 0.00 236 0.00 0.60 0.30 0.00 235 0.00 0.60 0.30 0.00 234 0.00 0.60 0.30 0.00 233 0.00 0.60 0.30 0.00 232 0.00 0.60 0.30 0.00 231 0.00 0.60 0.30 0.00 230 0.00 0.60 0.30 0.00 229 0.00 0.00 0.30 0.00
108
Row Score
Rural Urban Boys Girls Boys Girls
228 0.00 0.00 0.30 0.00 227 0.00 0.00 0.30 0.00 226 0.00 0.00 0.30 0.00 225 0.00 0.00 0.30 0.00 224 0.00 0.00 0.30 0.00 223 0.00 0.00 0.30 0.00 222 0.00 0.00 0.30 0.00 221 0.00 0.00 0.30 0.00 220 0.00 0.00 0.30 0.00 219 0.00 0.00 0.00 0.00 218 0.00 0.00 0.00 0.00 217 0.00 0.00 0.00 0.00 216 0.00 0.00 0.00 0.00 215 0.00 0.00 0.00 0.00 214 0.00 0.00 0.00 0.00 213 0.00 0.00 0.00 0.00 212 0.00 0.00 0.00 0.00 211 0.00 0.00 0.00 0.00 210 0.00 0.00 0.00 0.00 209 0.00 0.00 0.00 0.00 208 0.00 0.00 0.00 0.00 207 0.00 0.00 0.00 0.00 206 0.00 0.00 0.00 0.00 205 0.00 0.00 0.00 0.00 204 0.00 0.00 0.00 0.00 203 0.00 0.00 0.00 0.00 202 0.00 0.00 0.00 0.00 201 0.00 0.00 0.00 0.00 200 0.00 0.00 0.00 0.00
Row Score
Rural Urban Boys Girls Boys Girls
199 0.00 0.00 0.00 0.00 198 0.00 0.00 0.00 0.00 197 0.00 0.00 0.00 0.00 196 0.00 0.00 0.00 0.00 195 0.00 0.00 0.00 0.00 194 0.00 0.00 0.00 0.00 193 0.00 0.00 0.00 0.00 192 0.00 0.00 0.00 0.00 191 0.00 0.00 0.00 0.00 190 0.00 0.00 0.00 0.00 189 0.00 0.00 0.00 0.00 188 0.00 0.00 0.00 0.00 187 0.00 0.00 0.00 0.00 186 0.00 0.00 0.00 0.00 185 0.00 0.00 0.00 0.00 184 0.00 0.00 0.00 0.00 183 0.00 0.00 0.00 0.00 182 0.00 0.00 0.00 0.00 181 0.00 0.00 0.00 0.00 180 0.00 0.00 0.00 0.00 179 0.00 0.00 0.00 0.00 178 0.00 0.00 0.00 0.00 177 0.00 0.00 0.00 0.00 176 0.00 0.00 0.00 0.00 175 0.00 0.00 0.00 0.00 174 0.00 0.00 0.00 0.00 173 0.00 0.00 0.00 0.00 172 0.00 0.00 0.00 0.00 171 0.00 0.00 0.00 0.00
Table 5.4.2 (C)
Value of PR for each row score in the context of variable & its levels Arts Stream
Row Score
Arts Urban Boys Girls Boys Girls
360 99.10 99.10 93.90 99.10 359 96.70 96.70 93.90 84.40 358 96.70 96.70 93.90 84.40 357 96.70 96.70 93.90 84.40 356 96.70 96.70 93.90 84.40 355 93.90 93.90 93.90 84.40 354 93.90 93.90 93.90 84.40 353 90.00 90.00 84.40 84.40
Row Score
Arts Urban Boys Girls Boys Girls
352 90.00 90.00 84.40 84.40 351 84.40 84.40 84.40 84.40 350 84.40 84.40 84.40 84.40 349 78.50 78.50 78.50 78.50 348 78.50 78.50 78.50 78.50 347 71.50 71.50 71.50 71.50 346 71.50 71.50 71.50 71.50 345 66.40 66.40 66.40 66.40
109
Row Score
Arts Urban Boys Girls Boys Girls
344 66.40 66.40 66.40 66.40 343 61.00 66.30 61.00 61.00 342 61.00 61.00 61.00 61.00 341 54.10 54.10 54.10 54.10 340 54.10 54.10 54.10 54.10 339 50.10 50.10 50.10 50.10 338 50.10 50.10 50.10 50.10 337 45.80 45.80 45.80 45.80 336 45.80 45.80 45.80 45.80 335 42.10 42.10 42.10 42.10 334 42.10 42.10 42.10 42.10 333 42.00 38.60 38.60 38.60 332 38.60 38.60 38.60 38.60 331 35.00 35.00 35.00 35.00 330 35.00 35.00 35.00 35.00 329 32.40 32.40 35.00 32.40 328 32.40 32.40 32.40 32.40 327 30.40 30.40 30.40 30.40 326 30.40 30.40 30.40 30.40 325 29.00 29.00 29.00 29.00 324 29.00 29.00 29.00 29.00 323 26.80 26.80 26.80 26.80 322 26.80 26.80 26.80 26.80 321 24.60 24.60 24.60 24.60 320 24.60 24.60 24.60 24.60 319 23.20 23.20 23.20 24.50 318 23.20 23.20 23.20 23.20 317 20.30 20.30 20.30 20.30 316 20.30 20.30 20.30 20.30 315 18.40 18.40 18.40 18.40 314 18.40 18.40 18.40 18.40 313 16.70 16.70 16.70 18.30 312 16.70 16.70 16.70 16.70 311 14.70 14.70 14.70 16.60 310 14.70 14.70 14.70 14.70 309 13.10 13.10 13.10 13.10 308 13.10 13.10 13.10 13.10 307 11.70 11.70 11.70 11.70 306 11.70 11.70 11.70 11.70 305 10.80 10.80 10.80 10.80 304 10.80 10.80 10.80 10.80 303 9.80 9.80 9.80 9.80
Row Score
Arts Urban Boys Girls Boys Girls
302 9.80 9.80 9.80 9.80 301 8.00 9.00 9.00 9.00 300 8.00 9.00 9.00 9.00 299 8.00 8.00 8.00 8.00 298 8.00 8.00 8.00 8.00 297 6.70 6.70 7.30 7.30 296 6.70 6.70 7.30 7.30 295 6.70 6.70 6.70 6.10 294 6.70 6.70 6.70 6.10 293 4.90 5.50 6.10 6.10 292 4.90 5.50 6.10 6.10 291 4.90 5.50 5.50 4.90 290 4.90 5.50 5.50 4.90 289 4.90 4.80 4.90 4.90 288 4.90 4.80 4.90 4.90 287 4.10 4.80 4.60 3.70 286 4.10 4.10 4.60 3.70 285 4.10 4.10 4.10 3.70 284 4.10 4.10 4.10 3.70 283 3.70 2.00 3.70 3.70 282 3.70 2.00 3.70 3.70 281 3.10 2.00 3.10 3.00 280 3.10 2.00 3.10 3.00 279 2.50 2.00 2.50 3.00 278 2.50 2.00 2.50 3.00 277 2.50 2.00 2.50 2.50 276 2.50 2.00 2.50 2.50 275 2.50 2.00 2.50 2.50 274 2.50 2.00 2.50 2.50 273 1.60 2.00 2.00 2.00 272 1.60 2.00 2.00 2.00 271 1.60 2.00 2.00 2.00 270 1.60 2.00 2.00 2.00 269 1.60 1.50 2.00 1.30 268 1.60 1.50 2.00 1.30 267 1.60 1.50 1.80 1.30 266 1.60 1.50 1.80 1.30 265 1.60 1.50 1.30 1.30 264 1.60 1.50 1.30 1.30 263 1.50 1.50 1.30 1.30 262 1.50 1.50 1.30 1.30 261 1.20 1.50 1.30 1.30
110
Row Score
Arts Urban Boys Girls Boys Girls
260 1.20 0.50 1.30 1.30 259 1.20 0.50 1.30 1.00 258 1.20 0.50 1.30 1.00 257 1.20 0.50 1.00 1.00 256 1.20 0.50 1.00 1.00 255 0.70 0.50 1.00 1.00 254 0.70 0.50 1.00 1.00 253 0.70 0.50 1.00 1.00 252 0.70 0.50 1.00 1.00 251 0.70 0.50 1.00 1.00 250 0.70 0.50 1.00 1.00 249 0.70 0.50 1.00 1.00 248 0.70 0.50 1.00 1.00 247 0.70 0.50 0.90 0.70 246 0.70 0.50 0.90 0.70 245 0.70 0.50 0.90 0.70 244 0.70 0.50 0.90 0.70 243 0.70 0.50 0.20 0.70 242 0.70 0.50 0.20 0.70 241 0.70 0.50 0.20 0.70 240 0.70 0.50 0.20 0.70 239 0.20 0.50 0.20 0.70 238 0.20 0.50 0.20 0.70 237 0.20 0.50 0.20 0.70 236 0.20 0.50 0.20 0.70 235 0.20 0.50 0.20 0.70 234 0.20 0.50 0.20 0.70 233 0.20 0.50 0.20 0.60 232 0.20 0.50 0.20 0.60 231 0.20 0.50 0.20 0.00 230 0.20 0.50 0.20 0.00 229 0.20 0.50 0.20 0.00 228 0.20 0.50 0.20 0.00 227 0.20 0.50 0.20 0.00 226 0.20 0.10 0.20 0.00 225 0.20 0.10 0.20 0.00 224 0.20 0.10 0.20 0.00 223 0.20 0.10 0.20 0.00 222 0.20 0.10 0.20 0.00 221 0.20 0.10 0.20 0.00 220 0.20 0.10 0.20 0.00 219 0.20 0.10 0.20 0.00
Row Score
Arts Urban Boys Girls Boys Girls
218 0.20 0.10 0.20 0.00 217 0.20 0.10 0.20 0.00 216 0.20 0.10 0.20 0.00 215 0.20 0.10 0.20 0.00 214 0.20 0.10 0.20 0.00 213 0.20 0.10 0.20 0.00 212 0.20 0.10 0.20 0.00 211 0.20 0.10 0.20 0.00 210 0.20 0.10 0.20 0.00 209 0.20 0.10 0.00 0.00 208 0.20 0.10 0.00 0.00 207 0.20 0.10 0.00 0.00 206 0.20 0.10 0.00 0.00 205 0.20 0.10 0.00 0.00 204 0.20 0.10 0.00 0.00 203 0.20 0.10 0.00 0.00 202 0.20 0.10 0.00 0.00 201 0.20 0.10 0.00 0.00 200 0.20 0.10 0.00 0.00 199 0.10 0.10 0.00 0.00 198 0.10 0.00 0.00 0.00 197 0.10 0.00 0.00 0.00 196 0.10 0.00 0.00 0.00 195 0.10 0.00 0.00 0.00 194 0.10 0.00 0.00 0.00 193 0.10 0.00 0.00 0.00 192 0.10 0.00 0.00 0.00 191 0.00 0.00 0.00 0.00 190 0.00 0.00 0.00 0.00 189 0.00 0.00 0.00 0.00 188 0.00 0.00 0.00 0.00 187 0.00 0.00 0.00 0.00 186 0.00 0.00 0.00 0.00 185 0.00 0.00 0.00 0.00 184 0.00 0.00 0.00 0.00 183 0.00 0.00 0.00 0.00 182 0.00 0.00 0.00 0.00 181 0.00 0.00 0.00 0.00 180 0.00 0.00 0.00 0.00 179 0.00 0.00 0.00 0.00 178 0.00 0.00 0.00 0.00 177 0.00 0.00 0.00 0.00
111
Row Score
Arts Urban Boys Girls Boys Girls
176 0.00 0.00 0.00 0.00 175 0.00 0.00 0.00 0.00 174 0.00 0.00 0.00 0.00
Row Score
Arts Urban Boys Girls Boys Girls
173 0.00 0.00 0.00 0.00 172 0.00 0.00 0.00 0.00 171 0.00 0.00 0.00 0.00
5.6.0 Test Manual :-
Test manual provides guide line about how to use the present test
scientifically. The present test is a speed test so that proper administrative rules are
needed. The manual also provides guide line to evaluate testee's score in terms of his /
her PR and also how to categories PR into different levels – say assigning letter grade
to the Speed and Accuracy of the testee. The manual also provides important hints to
counsellor for student's counselling.
5.6.1 Rules for the administration of the test :
• Population :
This test would be used for the students studying in the higher
secondary schools having all the three streams : Science, Commerce and
Arts situated in the Gujarat state such as Ahmedabad, Gandhinagar,
Mehsana, Surendranagar and Vadodara districts having Gujarati Medium.
• Administration of the test :
o Proper sitting arrangement should be made. For that distance
between to testees must be 3 feet.
o For Section I and Section II, the time limit must be eight-eight
minutes, so everyone has to finish the work in that time. To
maintain the said time one has to use stop-watch for that.
o Be sure that every student must fill up necessary primary
information before starting the test.
o Give detailed explanation with example how student has to register
their response in the test-booklet. Check personally for illustrative
items.
o Clarify if the pair is not proper then one has not to put any sign in
the space given between them.
112
o Calculate true scores by subtracting numbers of incorrect responses
from correct numbers of responses for each section and there after
for the whole test.
5.6.2 Conversion of raw scores into PR :
• Identify the Stream, Area and Gender of the respondent. if
o Science stream than use Norm table No. 5.4.2.(A).
o Commerce stream than table no. 5.4.2.(B).
o Arts stream than table no. 5.4.2.(C)
• Decide the Area and Gender of the student and select appropriate
column.
• Traced-out the position of True-score say row scores of the testee and
read PR from the norm-table for corresponding true score.
• Obtained PR suggests the position of the testee in that particular
variable group. e.g. If the student having PR 70, he/she is superior than
69% of the students in that particular group.
5.6.3 Letter grade and level fixing :
To decide letter grade or level of Speed and Accuracy follow
the is to be used.
Table No. 5.6.3 Letter grade and Level of SA
Sr. No. Range of PR Letter Grade Level of Speed
and Accuracy 1 80 & above A Excellent 2 60 – 79 B Good 3 50 – 59 C Average 4 40 – 49 D Poor 5 below 40 E Very Poor
5.7.0 Conclusion :
The present chapter dealt with the Reliability, Validity and Norms. The
reliability was measured by using Test-retest, split-half and Cronebatch α which was
running between 0.85 to 0.99.
A Congruent validity was estimated and was high one. A guide line for
users along with norms were discussed at length in this chapter. The next chapter is
based on data analysis in the light of objectives stated for phase II.
113
References
1. Robert L. Ebel, (1972); Measuring Educational Achievement, New Delhi :
Prentice Hall. P. 311
2. Kothari R. C. (2009), Research Methodology, Method and Techniques, (New
Delhi : New Age International (P) ltd.), pp. 139-140.
3. Rulon, P. J. A. (1939), Simplified procedure for determining the reliability of a
test by split-halves theory, Edu. Pr. 9, pp. 99-103
4. Garrelt, J. H. E. (1985), Statistics in Psychology and Education; Vakils, (Bombay
: Feffer and Simons Pvt. Ltd.), p.354.
5. Freeman, S.F.(1968), Theory and Practice of Psychological Testing, (New York :
Holt, Rinehart and Winston. Inc. No.4), p.26
6. Ross and Stanley, (1963), Measurement in today's school, New York, Prentice
Hall, P. 122
7. H.E. Garrtl, (1965); 'Statistical in Psychology and Education, Bombay; Vakils,
Feffer and Simoson Pvt. Ltd. P. 354
8. Anne Anastasi (1976); Psychological Testing, Fourth edition, London, The
McMillan Co. Colliar MacMillan Ltd. P. 135
