adaptation of the otis-lennon mental ability test...

CHAPTER IV

Adaptation of the Otis-Lennon Mental Ability Test

(OLMAT)

As stated earlier, one of the objectives of this study is to ascertain whether or

not there would be a significant relationship between mental ability (intelligence)

scores of the Yemeni students and their age, sex, and school achievement. However,

before studying this aspect in detail, the present chapter aims at adapting Otis-Lennon

Mental Ability Test (OLMAT) on the Yemeni sample.

Therefore, in this chapter, the results of the adaptation of mental ability test

are presented in the following order:

1. Psychometric properties of the items, like difficulty and discrimination

indices.

2. The test reliability and validity indices.

3. The norms for the adapted version of the Yemeni culture.

The Arabic version of OLMAT advanced level form (K) was administered to

a random sample of 1561 students that included 801 males, and 760 females, from

government schools in Sana’a city from Yemen.

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4.I. PSYCHOMETRIC PROPERTIES OF THE ITEMS,

DIFFICULTY AND DISCRIMINATION, FOR THE TEST

ITEMS.

4.1.1. Item difficulty:

The item difficulty is defined in terms of the percentage of students who

answer it correctly. In this study the item difficulty was calculated according to

grades X, XI and XII for each subtest and for the total test. Table 4-1 presents the

frequency distribution for the items difficulty in each subtest and total test according

to grade levels. Appendix (5) shows the items difficulty for all the items according to

grade for each subtest and total test.

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Table 4-1:

Frequency Distribution of the items’ difficulty according to grade levels and total sample for each subtest.

Class

Interval

Verbal comprehension Verbal reasoning Figural reasoning Quantitative reasoning Total test

X XI XII tota

l

X XI XII Tot

al

X XI XII Tot

al

X XI XII tota

l

X XI XII Total

0.20 – 0.29 2 - - - 7 1 - - 5 1 - 1 2 2 - 2 16 4 - 3

0.30 – 0.39 6 5 - 4 9 7 2 6 3 4 3 4 8 2 2 1 26 18 7 15

0.40 – 0.49 5 5 4 6 5 5 4 9 5 3 1 2 2 3 - 6 17 16 9 23

0.50 – 0.59 5 4 5 5 2 7 6 6 2 5 1 6 2 6 5 3 11 22 17 20

0.60 – 0.69 3 5 4 3 2 4 5 4 - 1 8 1 - - 3 2 5 10 20 10

0.70 – 0.79 4 4 4 5 - 1 8 - - 1 - 1 1 1 2 1 5 7 14 7

0.80 – 0.89 - 2 7 2 - - - - - - 1 - - 1 3 1 1 3 11 2

0.90 – 0.99 - - 1 - - - - - - - 1 - - - - - - - 2 -

N. Items 25 25 25 25 25 25 25 25 15 15 15 15 15 15 15 15 80 80 80 80

Mean

difficulties

0.49 0.56 0.67 0.56 0.37 0.48 0.59 0.46 0.38 0.47 0.60 0.46 0.38 0.49 0.63 0.48 0.41 0.51 0.62 0.50

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The items’ difficulty in grade X ranged from 0.21 to 0.75 with a mean of 0.41,

in grade XI it ranged from 0.21 to 0.83 with a mean of 0.51, and in grade XII it ranged

from 0.32 to 0.92 with a mean of 0.62 and in the total sample it ranged from 0.25 to

0.81 with a mean of 0.50.

4.1.2. Item Discrimination

Item discrimination refers to the degree to which an item differentiates

correctly among test takers in the behavior that the test is designed to measure. In the

present study, the point biserial correlation (r pbs) between each item response and the

total test score were calculated according to grades (X, XI, XII) for each subtest and

for the total test. Table 4-2 presents the frequency distribution for the items’

discrimination in each subtest and total test according to grade levels. Appendix (6)

shows the items’ discrimination for all items, according to grades, for each subtest and

the total test.

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Table 4-2:

Frequency Distribution of the items’ discrimination according to grade level and total sample in each subtest

Class Interval

Verbal comprehension Verbal reasoning Figural reasoning Quantitative reasoning Total test

X XI XII Tot

al

X XI XII Tot

al

X XI XII Tot

al

X XI XII tota

l

X XI XII total

0.20 – 0.29 4 - - 2 2 - - 1 - - - 1 1 - - 1 7 - - 5

0.30 – 0.39 14 3 4 10 12 1 2 11 7 1 - 6 7 1 1 7 40 6 7 34

0.40 – 0.49 4 9 9 10 7 14 11 8 2 6 7 1 4 7 7 2 17 36 34 21

0.50 – 0.59 2 10 6 - 3 7 7 3 3 2 2 1 2 3 4 2 10 22 19 6

0.60 – 0.69 - 2 4 3 1 2 3 2 3 3 2 5 - 3 - 1 4 10 9 12

0.70 – 0.79 1 1 1 - - 1 2 - - 3 3 1 1 - 2 1 2 5 8 2

0.80 – 0.89 - - 1 - - - - - - - 1 - - 1 1 - - 1 3 -

N. Items 25 25 25 25 25 25 25 25 15 15 15 15 15 15 15 15 80 80 80 80

Mean

discrimination

0.38 0.49 0.52 0.41 0.40 0.49 0.51 0.42 0.45 0.55 0.58 0.48 0.42 0.53 0.53 0.46 0.41 0.51 0.53 0.44

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The item discriminations in grade X ranged from 0.24 to 0.75 with a mean of

0.41, in grade XI the range was from 0.35 to 0.83 with a mean of 0.51, in XII it

ranged from 0.34 to 0.88 with a mean of 0.53, and in the total test it ranged from 0.24

to 0.78 with a mean of 0.44.

4.2. THE TEST RELIABILITY AND VALIDITY INDICES.

4.2.1. The Test Reliability

Reliability is considered to be one of the very important psychometric

characteristics of the test. Reliability refers to the consistency of scores obtained by

the same persons, when they are reexamined with the same test on different

occasions, or with different sets of equivalent items, or under other variable

examining conditions (Anastasi & Urbina, 2003).

The reliability of the test was obtained by two methods, Split – Half Method,

Test – Retest Method.

4.2.1.1. Split – Half Method

This type of reliability coefficient is sometimes called a coefficient of internal

consistency, for this only a single administration of a single form is required. To find

split-half reliability, the first problem is how to split the test in order to obtain the

most nearly equivalent halves. The test starts with the easiest items and then becomes

progressively more difficult. In splitting a test, the two halves would need to be as

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similar as possible. Therefore, the simplest method of approximating this goal is to

adopt an odd – even split, in which the odd – numbered items or one half of the test

and the even – numbered items form the other. This guarantees that each half will

contain an equal number of items from the beginning, middle, and end of the original

test. In this case the odd-even procedure was followed. The correlation between two

halves was calculated for each level and for the total test. The value was 0.86 for total

test and for different levels (X, XI, and XII), the values were 0.77, 0.75, and 0.83

respectively. These correlations would be a reasonable measure of the reliability of

one half of the test. The reliability of the entire test would be greater than the

reliability of either half taken alone. The Spearman – Brown formula can be used to

obtain the reliability of the whole test (Allen & Yen, 1979). The corrected reliability

coefficients obtained by Spearman – Brown formula, for the different levels (X, XI,

XII) and total test were as follows, 0.87, 0.86, 0.91, and 0.92 consecutively.

4.2.1.3. Test – Retest Method

The reliability coefficients found by this method is an index to the stability of

test results. After two weeks from the test administration the intelligence test was

administered again to 241 students, which included (106) X, (76) XI, and (59) XII std

students, and the Pearson’s correlation coefficients were calculated between the

scores of the students in first and second administrations. The obtained values of the

reliability were as follows: 0.83 for total test, and 0.74, 0.88, and 0.82 for X, XI, XII,

levels respectively.

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4.2.2. The Test Validity

The most crucial characteristic of intelligence tests is their validity. Validity

refers to how well a test measures what it is supposed to measure. There are different

types of validities for intelligence tests. In the present research three types of

validities were obtained viz. construct validity, concurrent validity, and discriminant

validity.

4.2.2.1. Construct validity:

The construct validity was obtained by computing the correlation coefficient

between the items with the total test, and between the subtests (dimensions). Besides,

the correlations of the subtests with each other and with the total test, the correlation

values between the items with subtests were positive at all levels, and the correlation

between the item with its subtests was higher than its correlation with the total test.

This is because the items included in the same subtest (dimension) have more

internal-consistency with each other.

Also the results revealed that the correlation coefficients between the items

and the total test were positive which indicate the construct validity. In addition

correlation coefficients between subtests and total test were higher than the

correlation coefficient values between subtests. This is because each subtest measures

one side of the general mental ability. Table 4-3 presents values of subtests

correlation coefficient with each other at different levels of grade and with total test.

All the values were positive and significant.

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Table 4-3: Correlation coefficients between subtests with each other and with total

test according to levels of grade.

Level of

grade

Subtest Total

test

Verbal

Compre

hension

Verbal

Reasoning

Figural

Reasoning

Tenth grade

(X)

(N = 682)

Verbal comprehension 0.82** --

Verbal reasoning 0.87** 0.60** --

Figural reasoning 0.80** 0.52** 0.61** --

Quantitative reasoning 0.77** 0.49** 0.57** 0.58**

Eleventh

grade1 (XI)

(N = 466)

Verbal comprehension 0.88** -

Verbal reasoning 0.90** 0.71** -

Figural reasoning 0.87** 0.65** 0.72**


Twelfth

grade (XII)

(N = 413)



Figural reasoning 0.89** 0.67** 0.74** -


Entire

Sample

(N = 1561)



Figural reasoning 0.88** 0.67** 0.74** -


A detailed analysis of Table (4-3) indicates that correlation coefficient values

between subtests and total test is higher than correlation coefficient values between

subtests with each other.

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4.2.2.2. Concurrent validity.

The concurrent validity was calculated by computing the correlation between

students’ scores on the intelligence test and their school achievement.

Table 4.4 presents the Pearson Correlation Coefficients between intelligence

scores and school achievement for each subtest and for the total test according to

grade levels, X, XI, and XII. All of these correlations are significant at the (0.01)

level. It is clear therefore, that the tests have high concurrent validity.

Table 4-4: Pearson’s correlations coefficients values between intelligence test

scores and school achievement scores.

Grade

Subtests

X grade XI grade XII grade Total

sample

Verbal Comprehension 0.68** 0.75** 0.74** 0.68**

Verbal Reasoning 0.71** 0.75** 0.71** 0.67**

Figural Reasoning 0.61** 0.67** 0.71** 0.62**

Quantitative Reasoning 0.62** 0.61** 0.67** 0.58**

Total Test 0.81** 0.81** 0.80** 0.73**

4.2.2.3. Discriminant validity:

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The discriminant validity was obtained by using one way analysis of variance,

ANOVA, for different levels of grade. This made sure of the capacity of the test to

distinguish between students in different levels of grade.

Table 4-5: Results of one way ANOVA for students’ scores according to

grade levels.

Source of

Variation

df Sum of Squares Mean Square F P

Between grade 2 71195.295 35597.648 250.492 0.000

Within grade 1558 221408.5 142.111

Total 1560 292603.8

Inspection of table 4-5 indicates that there are significant differences in grade

means at 0.000 level. Table 5-6 presents the results of post hoc tests to find out which

of the means were significantly different from others. The post hoc comparisons

indicated that there are significant differences between means of all grades at 0.000

level.

Table 4-6: Results of Sheffe’s post-hoc comparison between mean of students

scores according to grade.

85

Grade Means Sd X XI XII

X 33.09 10.16 -

XI 40.39 13.24 0.000 -

XII 49.69 13.00 0.000 0.000 -

4.3. THE NORMS FOR THE ADAPTED VERSION ON THE

YEMENI CULTURE

Scores on intelligence tests are most commonly interpreted by reference to

norms that represent the test performance of the standardization sample. The norms

are thus empirically established by determining what persons in a representative

group actually do on the test. Any individual’s raw score is then refereed to the

distribution of scores obtained by the standardization (Anastasi & Urbina, 1999).

There are age norms, grade norms, and group norms. The authors of OLMAT

recommended that the Otis-Lennon tests should provide normative data based upon

the performance of pupils in both age and grade reference groups.

Norms for performance by age: One meaningful frame of reference for

interpretation of scores earned on the Otis-Lennon tests is the pupil’s chronological

age group. When his/her test score is compared with the scores earned by pupils of

similar chronological age tested in the standardization sample, the Deviation IQ

(DIQ) and its associated Percentile-Rank and Stanine equivalent supplied to the

teacher, counselor, or administrator are an indication of his/her level of performance.

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Norms for performance by grade: A second general frame of reference for the

interpretation of scores earned on the Otis-Lennon tests is the pupil’s grade group.

The grade Percentile-Rank and Stanine scores indicate the level of pupil performance

when his/her test score is compared with the scores earned by pupils who were at the

same grade level in the standardization sample.

There are various types of scores that are used to report norms, for example,

Percentile-Ranks, Stanines, Grade Equivalents, and Standard scores. All of them are

types of score, derived from raw scores, to report normative performance.

4.3.1. Percentile - Rank

The percentile rank is one of the most widely used means of interpreting pupil

performance on standardized measures of ability and achievement. This particular

type of derived score shows, in effect, the relative rank of a given pupil when his/her

score is compared with those earned by pupils comprising a particular reference, or

norms, group. For example, if a pupil earned a DIQ score of 116 with its

corresponding percentile rank of 84, this means that 84 percent of the pupils in the

norming sample earned DIQs of 116 or less, while 16 percent earned DIQs higher

than 116. A DIQ score of 100 corresponds to a percentile rank of 50, representing the

middle, or average, DIQ for pupils of the same age in the normative group.

Percentile-rank norms have an appeal which stems from their ease of

interpretation. There are, however, certain cautions which warrant consideration in

the interpretation of these scores. The units of the percentile-rank score system are not

equal; for example, the difference in ability represented by the difference between

87

percentile ranks of 90 and 95 is much greater, than that represented by the difference

between percentile ranks of 50 and 55. This characteristic of the percentile-rank scale

results from the fact that most scores are concentrated near the middle of a given

score distribution, while relatively few fall at the extremes. Thus, percentile ranks are

useful for describing a pupil’s relative position within a particular reference group,

but they are not useful in expressing differences between the score of one pupil and

that of another pupil.

4.3.2. Standard scores ( z- score)

Standard scores have a mean of 0 and a standard deviation of 1. (A standard

score indicates how many standard deviations from the mean a score lies). For

example, if z = +1, the raw score lies one standard deviation above the mean; if z =

-2, the raw score is two standard deviations below the mean. One major disadvantage

of standard scores is that about half of the scores are negative. Most people prefer not

to deal with negative numbers, because transcription and mathematical errors are

more common (negative signs are easily lost) and because examinees dislike having

negative scores. For these reasons, standard scores generally are not used in reporting

scores.

4.3.3. Deviation IQs

The Otis-Lennon Deviation IQ (DIQ) is, in effect, a normalized standard score

with a mean of 100 and a standard deviation of 16 points. The DIQ is an index of the

88

pupil’s relative brightness when he is compared with pupils of similar chronological

age, regardless of grade placement. The Otis-Lennon DIQ reflects, at a given point in

time, the pupil’s ability to deal with abstract relationships involving the manipulation

of ideas expressed in verbal, numerical, figural, or symbolic form.

4.3.4. Standardized score (T- score)

Any set of standard scores can be transformed to have an arbitrary mean, µ,

and standard deviation, o, by applying the formula Y = oz + µ, where z is the standard

score and Y is the standardized score. T-score is a standardized score with a mean of

50 and a standard deviation of 10.

4.3.5. Stanine

Stanine is a normalized standard score having a mean of 5 and a standard

deviation of 2 points. These scores are expressed as single digits ranging from a low

of 1 to a high of 9, with the nine units of the stanine scale representing essentially

equal distances along the base line of the curve of normal distribution. This, in effect,

means that a stanine of 7 is much better than a stanine of 6 and a stanine 4 is better

than 3.

4.3.6. Mental-age equivalents

This represents the typical, or median, level of performance of pupils of a

given chronological age in the normative sample. For example, a mental-age

89

equivalent of 8- 0 for a certain raw score means that this raw score was the typical, or

median, score earned by 8- year-old pupils tested in the standardization sample.

The raw – scores transformations transform scores in order to make them

more meaningful. In most cases, this meaning is derived by comparing a student’s

performance with other students. Transformations of scores are of two basic types:

linear and nonlinear. A linear transformation can be defined by a linear equation of

the form Y= a X+ b where a and b are constants, X is the raw score, and Y is the

transformed score. In making this transformation, every examinee’s X is transformed

to a Y using linear rule. For example, if Y= 3X – 2, the transformed score

corresponding to a raw score of 12 is 3(12) – 2=34. When raw scores are linearly

transformed, the shape of the distribution of the transformed scores is the same as the

shape of the distribution of the raw scores (Allen & Yen, 1979).

A nonlinear transformation will change the shape of the raw scores’

distribution. The transformation by this way involves forcing the distribution of

transformed scores to be as close as possible to a normal distribution by smoothing

out, stretching or condensing irregularities and departures from normality in the raw

score distribution. This transformation can be reasonably applied if the test developer

believes that the underlying trait has a normal distribution and that the no normality

of the raw score distribution represents error due to sampling or test – construction

problems (Allen and Yen, 1979). A nonlinear transformation was used in this current

research. The normalization process involves several steps:

1. Transform the score to percentiles.

90

2. Find the grade score in the normal distribution corresponding to each

percentile.

3. (Optional) transform these standard scores to standardized scores with a

desired mean and standard deviation.

Tables 4-7 and 4-8 present the relationship between Percentile, Stanine, and

Deviation Intelligence Quotient (DIQ) for grade levels and age levels, and Tables 4-9

to 4-17, present the Raw-scores, Percentile Ranks, z-scores, T-scores, Deviation

Intelligence Quotient (DIQ), and Stanine for grades and, ages and total sample, which

were transformation by nonlinear transformation.

Table 4- 7: Present the relationship between Percentile Rank, Stanine, DIQ for grade

levels, after nonlinear transformation.

Percentile

Rand

Stanine DIQ X DIQ XI DIQ XII Interpretation

0 – 4% 1 52 – 70 52 – 69 54 -72 Low

5% - 11% 2 70 – 77 69 – 80 72 – 79 Below

Average12% - 23% 3 77 – 85 80 – 88 79 – 88

24% - 40% 4 85 – 96 88 – 95 88 – 95

Average41% - 60% 5 96 – 103 95 – 103 95 – 104

61% - 77% 6 103 – 111 103 – 112 104 – 111

78% - 89% 7 111 – 119 112 – 120 111 – 120 Above

Average90% - 96% 8 119 – 128 120 – 127 120 – 126

97% - 100% 9 128 – 148 127 – 148 126 – 148 High

Table 4-8: Presented the relationship between Percentile Rank, Stanine, DIQ for age

levels after nonlinear transformation.

Percentile

Rank

Stanine DIQ 15

age

DIQ 16

age

DIQ 17

age

DIQ 18

age

DIQ

19 age

Interpreta-

ion

91

0 – 4% 1 60-71 56-71 56-71 60-68 67-70 Low

5% - 11% 2 71-79 71-78 71-79 68-78 70-79 Below

Average12% - 23 3 79-87 78-87 79-86 78-88 79-88

24% - 40% 4 87-96 87-95 86-95 88-96 88-96

Average 41% - 60% 5 96-104 95-103 95-103 96-104 96-103

61% - 77% 6 104-112 103-112 103-111 104-112 103-111

78% - 89% 7 112-118 112-120 112-119 112-120 111-119 Above

average90% - 96% 8 118-127 120-128 119-126 120-127 119-127

97%-100% 9 127-148 128-148 127-148 127-148 127-148 High

Table 4–9: Row scores and their equivalent, Percentile Rank, z- scores, T- scores,

Deviation Intelligence Quotient (DIQ), and Stanine for Total sample.

Raw-

scores

Percentile

Ranks

z- scores T- scores DIQ Stanine

12 0.1 -3.0 20 52 -0.1

15 0.4 -2.65 23.5 57.6 -0.3

16 1.0 2.40 26 61.6 0.2

17 1.4 -2.20 28 64.8 0.6

18 2.4 -1.98 30.2 68.32 1.04

19 3.8 -1.77 32.3 71.68 1.46

20 5.9 -1.65 33.5 73.6 1.7

21 8.2 -1.39 36.1 77.76 2.22

Table 4–9: Continued

Raw-

scores

Percentile

Ranks


22 10.0 -1.29 37.1 79.36 2.42

23 11.0 -1.23 37.7 80.32 2.54

92

24 12.2 -1.17 38.3 81.28 2.66

25 15.1 -1.03 39.7 83.52 2.94

26 18.2 -0.91 40.9 85.44 3.18

27 21.1 -0.81 41.9 87.04 3.38

28 22.8 -0.74 42.6 88.16 3.52

29 24.2 -0.70 43 88.8 3.60

30 25.0 -0.65 43.5 89.6 3.76

31 30.0 -0.53 44.7 91.52 3.94

32 33.8 -0.42 45.8 93.28 4.16

33 39.0 -0.28 47.2 95.52 4.44

34 40.2 -0.25 57.5 96 4.50

35 44.3 -0.14 48.6 97.76 4.72

36 49.1 -0.03 49.97 99.52 4.94

37 51.4 0.04 50.4 100.64 5.08

38 53.8 0.10 51 101.6 5.20

39 56.8 0.17 51.7 102.72 5.34

40 59.6 0.24 52.4 103.84 5.48

41 61.6 0.29 52.9 104.64 5.58

42 63.2 0.34 53.4 105.44 5.68

43 65.8 0.41 54.1 106.56 5.82

44 67.8 0.47 54.7 107.25 5.94

45 70.2 0.53 55.3 108.48 6.06

46 71.2 0.56 55.6 108.96 6.12

47 72.8 0.61 56.1 109.76 6.22

48 74.2 0.65 56.5 110.40 6.30


Raw-

scores

Percentile

ranks


49 75.4 0.69 56.9 111.04 6.38

93

50 76.9 0.74 57.4 111.84 6.48

51 78.4 0.79 57.9 112.64 6.58

52 80.0 0.85 58.5 113.6 6.70

53 81.0 0.88 58.8 114.08 6.76

54 82.3 0.93 59.3 114.88 6.86

55 83.2 0.96 59.6 115.36 6.92

56 84.5 1.02 60.2 116.32 7.04

57 85.3 1.05 60.5 116.68 7.10

58 86.5 1.1 61.00 117.6 7.20

59 88.1 1.18 61.8 118.88 7.36

60 88.9 1.22 62.2 119.52 7.44

61 90.3 1.30 62.3 120.8 7.60

62 91.7 1.38 63.8 122.08 7.76

63 93.1 1.48 64.8 123.68 7.96

64 94.7 1.62 66.2 125.92 8.24

65 95.6 1.69 66.9 127.04 83.8

66 96.7 1.84 68.4 129.44 8.68

67 97.8 2.02 70.2 132.32 9.04

68 98.4 2.15 71.50 134.40 9.30

69 98.8 2.26 72.60 136.16 9.52

70 99.0 2.33 73.30 137.28 9.66

71 99.4 2.51 75.10 140.16 10.02

72 99.7 2.75 77.50 144.00 10.50

73 99.8 2.88 78.8 146.08 10.76

75 99.9 2.96 79.6 147.36 10.92

77 100 3.00 80.0 148 11


Deviation Intelligence Quotient (DIQ), and Stanine for Tenth (X) grade

Raw- Percentile z- scores T- scores DIQ Stanine

94

scores Ranks

12 0.1 -3.0 20 52 -1

15 1.0 -2.33 26.7 62.72 0.34

16 2.2 -2.02 29.8 67.68 0.96

17 3.1 -1.87 31.30 70.08 1.26

18 5.0 -1.64 33.6 73.76 1.72

19 7.6 -1.43 35.7 77.12 2.14

20 11.4 -1.21 37.9 80.64 2.58

21 14.2 -1.07 39.3 82.88 2.86

22 16.7 -0.96 40.40 84.64 3.00

23 18.2 -0.91 40.9 85.44 3.81

24 20.1 -0.84 41.6 86.56 3.32

25 24.5 -0.69 43.1 88.96 3.62

26 29.3 -0.55 44.5 91.2 3.90

27 34.2 -0.41 45.9 93.44 4.18

28 36.7 -0.34 46.6 94.56 4.32

29 38.3 -0.30 47 95.20 4.40

30 39.7 -0.26 47.40 95.84 4.48

31 44.9 -0.13 48.7 97.92 4.74

32 49.7 -0.01 49.99 99.84 4.98

33 56.0 0.14 51.4 102.24 5.28

34 57.6 0.20 52 103.2 5.40

35 63.8 0.35 53.5 105.6 5.70

36 69.5 0.51 55.10 108.16 6.02

37 71.7 0.57 55.7 109.12 6.14

38 73.2 0.62 56.2 109.92 6.24

Table: 4–10 Continued.

Raw-

scores

Percentile

ranks


95

39 75.8 0.70 57 111.2 6.40

40 78.6 0.79 57.9 112.64 6.58

41 80.5 0.86 58.6 113.76 6.72

42 82.0 0.92 59.2 114.72 6.84

43 83.9 0.99 59.9 115.84 6.98

44 85.5 1.06 60.6 116.96 7.12

45 87.4 1.15 61.5 118.4 7.30

46 88.1 1.18 61.8 118.88 7.36

47 89.9 1.28 62.8 120.48 7.56

48 91.1 1.35 63.50 121.16 7.70

49 92.4 1.43 64.3 122.88 7.86

50 93.5 1.51 65.1 124.16 8.02

51 94.7 1.62 66.2 125.92 8.24

52 95.7 1.72 67.2 127.52 8.44

53 96.0 1.76 67.6 128.16 8.52

54 96.9 1.87 68.7 129.92 8.74

55 97.4 1.95 69.50 131.2 8.90

56 98.1 2.07 70.7 133.12 9.14

57 98.4 2.15 71.5 134.4 9.30

58 99.0 2.32 73.2 137.12 9.64.

59 99.1 2.37 73.70 137.92 9.74

61 99.4 2.51 75.10 140.16 10.02

62 99.7 2.75 77.50 144 10.50

63 99.9 2.96 79.6 147.36 10.92

69 100 3.00 80 148 11

Table 4–11: Raw scores and their equivalent, Percentile Rank, Z- scores, T- scores,

Deviation Intelligence Quotient (DIQ), and Stanine for Eleventh (XI) Grade.

Raw- Percentile z- scores T- scores DIQ Stanine

96

scores Ranks

17 0.2 -3.0 20 52 -1

18 0.6 -2.51 24.9 59.84 -0.02

19 1.5 -2.17 28.3 65.28 .66

20 2.8 -1.91 30.9 69.44 1.18

21 6.2 -1.54 34.6 75.36 1.92

22 8.2 -1.39 36.1 77.76 2.22

23 9.0 -1.35 36.5 78.4 2.30

24 10.1 -1.28 37.2 79.52 2.44

25 12.7 -1.14 38.6 81.76 2.72

26 14.6 -1.05 39.5 83.20 2.90

27 16.5 -0.97 40.3 84.48 3.06

28 18.2 -0.91 40.9 85.44 3.18

29 19.7 -0.86 41.4 86.24 3.28

30 21.7 -0.78 42.2 87.52 3.44

31 26.2 -0.64 43.6 89.76 3.72

32 30.7 -0.50 45 92.00 4.00

33 35.8 -0.36 46.4 94.24 4.28

34 37.1 -0.33 46.7 94.72 4.34

35 40.1 -0.25 48.5 96 4.50

36 45.5 -0.12 48.8 98.08 4.76

37 49.1 -0.03 49.7 99.52 4.94

38 53.6 +0.16 51.6 102.56 5.32

39 57.1 +0.18 51.8 102.88 5.36

40 60.1 0.26 52.6 104.16 5.52

41 61.2 0.29 52.9 104.64 5.58

Table 4–11: Continued.

Raw-

scores

Percentile

Ranks


97

42 63.3 0.34 53.4 105.44 5.68

43 65.9 0.41 54.1 106.56 5.82

44 67.6 0.46 54.6 407.36 5.92

45 70.2 0.53 55.3 108.48 6.06

46 71.2 0.56 55.6 108.96 6.12

47 72.7 0.60 56.0 109.6 6.20

48 74.0 0.65 56.5 110.4 6.30

49 74.7 0.67 56.7 110.72 6.34

50 76.6 0.73 57.3 111.68 6.46

51 78.3 0.79 57.9 112.64 6.58

52 79.8 0.83 58.3 113.28 6.66

53 80.7 0.87 58.7 113.92 6.74

54 81.8 0.91 59.1 114.56 6.82

55 82.8 0.95 59.5 115.2 6.90

56 83.3 0.97 59.7 115.52 6.64

57 84.3 1.01 60.1 116.16 7.02

58 85.6 1.07 60.7 117.12 7.14

59 88.2 1.19 61.9 119.04 7.38

60 88.6 1.21 62.1 119.36 7.42

61 89.9 1.27 62.7 120.32 7.54

62 91.0 1.34 63.4 121.44 7.68

63 92.3 1.43 64.3 122.88 7.86

64 94.2 1.57 65.7 125.12 8.14

65 95.3 1.67 66.7 126.72 8.34

66 96.1 1.76 67.6 128.16 8.52

67 97.6 1.97 69.7 131.52 8.94


98

Raw-

scores

Percentile

Ranks


68 98.3 2.12 71.2 133.92 9.24

69 98.9 2.29 72.9 136.64 9.58

70 99.1 2.35 73.5 137.6 9.70

71 99.8 2.88 78.8 146.08 10.76

72 100 3.00 80.0 148 11

Table 4–12: Row scores and their equivalent, Percentile Rank, z- scores, T-

scores, Deviation Intelligence Quotient (DIQ), and Stanine for Twelfth (XII) Grade

Raw-

scores

Percentile

ranks


19 0.2 -2.88 21.2 53.92 -0.76

21 0.5 -2.60 24 58.40 0.20

22 1.5 -2.33 26.7 62.72 .34

23 1.2 -2.26 27.4 63.84 0.48

24 1.7 -2.12 28.8 66.08 0.76

25 2.2 -2.01 29.9 67.84 0.98

26 3.9 -1.76 32.4 71.84 1.48

27 4.8 -1.66 33.4 73.44 1.68

28 5.1 -1.64 33.6 73.76 1.72

29 5.8 -1.57 34.3 74.88 1.86

30 6.5 -1.50 35.0 76.00 2.00

31 9.7 -1.30 37.0 79.2 2.40

32 11.1 -1.22 37.8 80.48 2.56

33 14.5 -1.06 39.4 83.04 2.88


99

Raw-

scores

Percentile

Ranks


34 15.0 -1.03 39.7 83.52 2.94

35 16.7 -0.97 40.3 84.48 3.06

36 19.4 -0.86 41.4 86.24 3.28

37 20.6 -0.82 41.8 86.88 3.36

38 22.0 -0.76 42.4 87.84 3.42

39 25.2 -0.67 43.4 89.28 3.66

40 27.8 -0.59 44.1 90.56 3.82

41 31.0 -0.49 45.1 92.16 4.02

42 32.2 -0.47 45.3 92.48 4.06

43 35.8 -0.37 46.3 94.08 4.26

44 38.7 -0.29 47.1 95.36 4.42

45 41.9 -0.21 47.9 96.64 4.58

46 43.1 -0.18 48.2 97.12 4.64

47 44.6 -0.14 48.6 97.76 4.72

48 46.7 -0.08 49.2 98.72 4.84

49 48.2 -0.05 49.5 99.2 4.90

50 49.6 -0.01 49.9 99.84 4.98

51 51.6 0.04 50.40 100.64 5.08

52 54.2 0.10 51.0 101.6 5.20

53 56.7 0.17 51.7 102.72 5.34

54 58.8 0.22 52.2 103.52 5.44

55 60.3 0.26 52.6 104.16 5.52

56 63.4 0.34 53.4 105.44 5.68

57 64.6 0.38 53.8 106.08 5.76

58 67.1 0.45 54.5 107.2 5.90


100

Raw-

scores

Percentile

Ranks


59 69.7 0.52 55.2 108.32 6.04

60 72.2 0.59 55.9 109.44 6.18

61 75.8 0.70 57.0 111.2 6.40

62 79.4 0.82 58.2 113.12 6.64

63 82.8 0.95 59.5 115.2 6.90

64 86.7 1.16 61.6 118.56 7.32

65 89.1 1.23 62.3 119.68 7.46

66 92.0 1.40 64.0 122.4 7.80

67 94.7 1.62 66.2 125.92 8.24

68 96.1 1.76 67.6 128.16 8.52

69 96.6 1.82 68.2 129.12 8.64

70 97.3 1.92 69.2 130.72 8.84

71 98.1 2.07 70.7 133.12 9.14

72 98.8 2.25 72.5 136.00 9.50

73 99.3 2.45 74.5 139.2 9.90

75 99.5 2.57 75.7 141.12 10.14

77 100 3.00 80.0 148 11

101


Deviation Intelligence Quotient (DIQ), and Stanine for Age 15.

Raw-

scores

Percentile

Ranks


15 0.6 -2.51 24.9 59.84 -0.02

16 3.5 -1.81 31.9 71.04 1.38

17 4.2 -1.73 32.7 72.32 1.54

18 6.1 -1.55 34.5 75.2 1.9

19 9.3 -1.32 36.8 78.88 2.36

20 14.1 -1.08 39.2 82.22 2.84

21 17.9 -0.85 41.5 86.4 3.3

22 21.5 -0.79 42.1 87.36 3.42

23 23.4 -0.73 42.7 88.32 3.54

24 25.6 -0.66 43.4 89.44 3.68

25 30.1 -0.52 44.8 91.68 3.96

26 34.9 -0.39 46.10 93.76 4.22

27 39.7 -0.29 47.40 95.84 4.48

28 42.0 -0.20 48 96.8 4.6

29 42.6 -0.19 48.1 96.96 4.62

30 43.6 -0.16 48.40 97.44 4.68

31 49.7 -0.01 49.9 99.84 4.98

32 55.8 +0.15 51.5 102.4 5.3

33 59.6 0.24 52.40 103.84 5.48

34 60.3 0.26 52.60 104.16 5.52

35 64.4 0.37 53.7 105.92 5.74

36 70.5 0.54 55.4 108.64 6.08

37 72.1 0.59 55.9 109.44 6.18

38 73.7 0.64 56.40 110.24 6.28

39 76.3 0.72 57.2 111.52 6.44

102


Raw-

scores

Percentile

ranks


40 81.4 0.90 59.0 114.4 6.8

41 82.4 0.93 59.3 114.88 6.86

42 84.0 1.00 60.0 116 7.00

43 87.2 1.14 61.40 118.24 7.28

44 88.1 1.18 61.80 118.88 7.36

45 90.4 1.31 63.10 120.96 7.62

47 92.9 1.47 64.7 123.52 7.94

48 94.2 1.58 65.8 125.28 8.16

49 95.5 1.70 67.0 127.2 8.4

50 97.4 1.95 69.5 131.2 8.9

52 98.1 2.08 70.8 133.28 9.16

54 98.4 2.12 71.2 133.92 9.24

57 98.7 2.23 72.30 135.68 9.46

58 99.0 2.33 73.30 137.28 9.66

59 99.4 2.51 75.10 140.16 10.02

62 99.7 2.75 77.5 144 10.50

71 100 3.00 80.00 148 11



103

Raw-

scores

Percentile

Ranks


12 0.3 -2.75 22.5 56 0.5

15 0.5 -2.58 24.2 58.72 0.16

17 1.8 -2.1 29 66.40 0.80

18 3.4 -1.83 31.70 70.72 1.34

19 6.5 -1.51 34.90 75.84 1.98

20 8.8 -1.35 36.50 78.40 2.30

21 11.4 -0.1.21 37.90 80.64 2.58

22 12.5 -1.15 38.50 81.60 2.70

23 13.5 -1.1 39.00 82.40 2.80

24 16.1 -0.99 40.1 84.16 3.02

25 20.0 -0.84 41.6 86.56 3.32

26 23.9 -0.71 42.90 88.64 3.58

27 27.3 -0.60 44 90.4 3.80

28 29.4 -0.55 44.5 91.2 3.90

29 30.9 -0.49 45.1 92.16 4.02

30 33.0 -0.44 45.6 92.96 4.12

31 37.1 -0.33 46.7 94.72 4.34

32 40.8 -0.24 47.6 96.16 4.52

33 48.3 -0.04 49.6 99.36 4.92

34 50.1 +0.01 50.1 100.10 5.02

35 56.1 +0.16 51.6 102.56 5.32

36 62.1 0.31 53.1 104.96 5.62

37 64.7 0.38 53.8 106.08 5.76

38 67.3 0.45 54.5 107.20 5.90

39 70.9 0.55 55.5 108.80 6.10


104

Raw-

scores

Percentile

Ranks


40 72.5 0.60 56.00 109.60 6.20

41 74.8 0.67 56.70 110.72 6.34

42 75.1 0.68 56.80 110.88 6.36

43 76.9 0.73 57.30 111.68 6.46

44 79.2 0.82 58.20 113.12 6.64

45 80.8 0.87 58.70 113.92 6.74

46 81.6 0.90 59.00 114.4 6.80

47 82.9 0.95 59.50 115.2 6.90

48 84.4 1.01 60.10 116.16 7.02

49 85.5 1.06 60.60 116.96 7.12

50 86.8 1.12 61.2 117.92 7.24

51 88.8 1.22 62.2 119.52 7.44

52 90.9 1.34 63.4 121.44 7.68

53 91.7 1.39 63.9 122.24 7.78

54 93.2 1.49 64.9 123.84 7.98

55 93.8 1.54 65.4 124.64 8.08

56 95.1 1.65 66.50 126.4 8.30

57 95.3 1.67 66.70 126.72 8.34

58 95.8 1.73 67.30 127.68 8.46

59 96.4 1.80 68.00 128.8 8.60

60 96.9 1.87 68.70 129.92 8.74

61 97.9 2.04 70.40 132.64 9.08

62 98.4 2.15 71.50 134.4 9.30

64 99.2 2.41 74.10 138.55 9.82

67 99.5 1.58 65.80 125.28 8.16

68 99.7 2.75 77.50 144 10.50

69 100 3.00 80.00 148 11

105



Raw- scores Percentile ranks z- scores T- scores DIQ Stanine

18 0.3 -2.75 22.5 56 -0.5

20 0.8 -2.41 25.9 61.44 0.18

21 2.3 -2.00 30.0 68.0 1

22 3.4 -1.83 31.7 70.72 1.34

23 3.7 -1.79 32.1 71.36 1.42

24 4.2 -1.73 32.7 72.32 1.54

25 6.5 -1.52 34.8 75.68 1.96

26 9.3 -1.32 36.8 78.88 2.36

27 11.3 -1.21 37.9 80.64 2.58

28 13.6 -1.10 39.00 82.4 2.8

29 16.4 -0.98 40.2 84.32 3.04

30 18.9 -0.88 41.2 85.92 3.24

31 23.4 -0.73 42.7 88.32 3.54

32 26.3 -0.64 43.6 89.76 3.72

33 31.1 -0.52 44.8 91.68 3.96

34 32.5 -0.45 45.5 92.8 4.1

35 37.3 -0.33 46.7 94.72 4.34

36 41.0 -0.23 47.7 96.32 4.54

37 44.4 -0.14 48.6 97.79 4.72

38 47.5 -0.06 49.4 99.04 4.88

39 51.7 +0.04 50.4 100.64 5.08

40 54.2 +0.11 51.1 101.76 5.22

41 57.6 0.19 51.9 103.04 5.38

42 61.3 0.29 52.9 104.64 5.58

43 63.3 0.33 53.3 105.28 5.66

106



44 65.8 0.41 54.1 106.56 5.82

45 69.2 0.50 55.0 108.0 6.00

46 71.5 0.57 55.7 109.12 6.14

47 73.4 0.63 56.3 110.08 6.26

48 74.9 0.68 56.8 110.88 6.36

49 76.0 0.71 57.1 111.36 6.42

50 77.7 0.76 57.6 112.16 6.52

51 79.7 0.83 58.3 113.28 6.66

52 81.6 0.90 59.0 114.4 6.8

53 82.9 0.91 59.10 114.56 6.82

54 83.6 0.98 59.8 115.68 6.96

55 84.7 1.03 60.3 116.48 7.06

56 85.3 1.05 60.5 116.8 7.10

57 86.7 1.11 61.1 117.76 7.22

58 88.1 1.18 61.8 118.88 7.36

59 90.1 1.29 62.9 120.64 7.58

60 91.2 1.35 63.5 121.6 7.75

61 92.4 1.43 64.3 122.88 7.86

62 93.8 1.54 65.4 124.64 8.08

63 94.9 1.64 66.4 126.24 8.28

64 96.3 1.79 67.9 128.64 8.58

65 97.5 1.96 69.6 131.36 8.92

66 97.7 2.00 70.0 132 9.0

67 98.9 2.29 72.9 136.64 9.58

68 99.4 2.54 75.1 140.16 10.02

69 99.7 2.75 77.5 144 10.5

72 100 3.00 80.00 148 11

107




16 0.6 -2.51 24.9 59.84 0.02

18 1.3 -2.23 27.7 64.32 0.54

19 1.6 -2.15 28.5 65.69 0.70

20 2.2 -2.02 29.8 67.68 0.96

21 4.4 -1.71 32.9 72.64 1.58

22 5.9 -1.57 34.3 74.88 1.86

23 6.9 -1.48 35.2 76.32 2.04

25 8.8 -1.35 36.5 78.4 2.3

26 10.9 -1.23 37.7 80.32 2.54

27 13.1 -1.12 38.8 82.8 2.70

28 13.4 -1.11 38.9 82.24 2.78

29 14.4 -1.07 39.3 82.88 2.86

30 15.0 -1.04 39.6 83.36 2.92

31 19.4 -0.87 41.3 86.08 3.26

32 22.2 -0.77 42.3 87.68 3.46

33 27.2 -0.60 44.0 90.40 3.80

34 28.1 -0.55 44.5 91.2 3.90

35 30.3 -0.52 44.8 91.68 3.96

36 34.1 -0.41 45.9 93.44 4.18

37 35.9 -0.36 46.4 97.24 4.28

38 38.1 -0.30 47.00 95.20 4.40

39 40.0 -0.26 47.40 95.84 4.48

40 41.9 -0.22 47.80 96.48 4.56

41 42.8 -0.20 48.00 96.80 4.60

42 43.8 -0.16 48.40 97.44 4.68

43 47.8 -0.06 49.40 99.04 4.88

108



44 49.4 -0.02 49.80 99.68 4.96

45 51.6 +0.04 50.40 100.64 5.08

46 52.5 0.07 50.70 101.12 5.14

47 53.8 0.10 51.0 101.6 5.20

48 55.6 0.14 51.40 102.14 5.28

49 56.6 0.17 51.70 102.72 5.34

50 57.8 0.20 52.0 103.20 5.40

51 59.4 0.24 52.4 103.68 5.48

52 60.9 0.28 52.80 104.48 5.56

53 63.1 0.34 53.40 105.44 5.68

54 64.4 0.37 53.70 105.92 5.74

55 65.9 0.41 54.10 106.56 5.82

56 68.4 0.48 54.80 107.68 5.96

57 69.4 0.51 55.10 108.16 6.02

58 71.9 0.58 55.8 109.28 6.16

59 73.4 0.63 56.30 110.08 6.26

60 74.4 0.66 56.60 110.56 6.32

61 76.9 0.74 57.40 111.84 6.48

62 79.7 0.83 58.30 113.28 6.66

63 83.4 0.97 59.70 115.52 6.94

64 86.6 1.11 61.1 117.76 7.22

65 89.1 1.23 62.3 119.68 7.46

66 92.2 1.42 64.2 122.72 7.84

109



67 95.6 1.71 67.1 127.36 8.42

68 96.3 1.79 67.9 128.64 8.58

69 97.5 1.96 69.6 131.36 8.92

70 98.1 2.08 70.8 133.28 9.16

71 98.4 2.15 71.50 134.4 9.30

72 98.8 2.26 72.60 136.16 9.52

73 99.4 2.51 75.10 140.16 10.02

75 99.7 2.75 77.5 144 10.5

77 100 3.00 80.00 148 11

Table 4–17: Row scores and their equivalent, Percentile Rank, z- scores, T-

scores, Deviation Intelligence Quotient (DIQ), and Stanine for Age 19.


20 2.1 -2.04 29.6 67.36 0.92

21 3.2 -1.86 31.4 70.24 1.28

22 5.3 -1.62 33.8 74.08 1.76

23 5.8 -1.57 34.30 74.88 1.86

24 6.3 -1.53 34.70 75.52 1.94

25 6.8 -1.49 35.10 76.16 2.02

26 7.9 -1.41 35.90 77.44 2.18

27 10.0 -1.29 37.10 79.36 2.42

28 11.1 -1.22 37.80 80.48 2.56

31 13.2 -1.07 39.30 82.88 2.86

32 17.4 -0.94 40.6 84.96 3.12

33 21.1 -0.81 41.9 87.04 3.38

34 22.1 -0.77 42.30 87.68 3.46

110


Raw- scores Percentile

Ranks


35 23.7 -0.72 42.8 88.48 3.56

36 27.9 -0.56 44.4 91.04 3.88

38 32.1 -0.44 45.6 92.96 4.12

39 34.2 -0.39 46.1 94.24 4.22

40 37.9 -0.31 46.9 95.04 4.38

41 40.0 -0.26 47.4 95.84 4.48

42 41.6 -0.22 48.8 96.48 4.56

43 43.2 -0.18 48.2 97.12 4.64

44 45.8 -0.11 48.9 98.24 4.78

45 48.9 -0.03 49.7 99.52 4.94

46 49.5 -0.02 49.8 99.68 4.96

47 50.0 .000 50 100 5

48 51.1 +0.03 50.3 100.48 5.06

49 52.6 0.07 50.3 100.48 5.06

50 53.7 0.10 51.0 101.16 5.20

51 55.6 0.14 51.40 102.24 5.28

52 57.4 0.19 51.90 103.04 5.38

53 60.0 0.27 52.7 104.32 5.54

54 61.6 0.30 53.0 104.8 5.60

55 63.2 0.34 53.4 105.44 5.68

56 65.8 0.41 54.10 106.56 5.82

57 66.8 0.44 54.4 107.04 5.88

58 68.9 0.52 55.2 108.32 6.04

59 73.7 0.64 56.4 110.24 6.28

60 75.3 0.69 56.9 111.04 6.38

111


Raw- scores Percentile

Ranks


61 78.9 0.80 58.0 112.80 6.60

62 81.6 0.90 59.0 114.4 6.80

63 84.2 1.01 60.1 116.16 7.02

64 87.9 1.17 61.7 118.72 7.34

65 89.5 1.26 62.6 120.16 7.52

66 92.1 1.41 64.1 122.56 7.82

67 63.2 1.50 65.0 124 8.00

68 95.3 1.67 66.7 126.72 8.34

70 96.3 1.79 67.9 128.64 8.58

71 98.4 2.15 71.5 134.4 9.30

72 99.5 2.58 75.8 141.28 10.16

77 100 3.00 80.00 148 11

112

adaptation of the otis-lennon mental ability test...

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