HMEF5053 Measurement and Evaluation in Education_vDec19

234  TOPIC 10 ANALYSIS OF TEST SCORES

However, there will be a few men who will be relatively shorter and an equal
number who are relatively taller. By plotting the heights of all Malaysian men
according to the frequency of occurrence, you can expect to obtain something
similar to a normal distribution curve.
Besides height, normal distribution curve can seen in terms of IQ. Figure 10.6
shows a normal distribution curve for IQ based on the Wechsler intelligence scale
for children.

Figure 10.6: The normal distribution curve
In a normal distribution, about two-thirds of individuals will have an IQ of
between 85 and 115 with a mean of 100. According to the American Association
on Intellectual and Developmental Disabilities, individuals who have an IQ of less
than 70 may be classified as mentally retarded or mentally challenged and those
who have an IQ of more than 130 may be considered as gifted.
Similarly, test scores that measure a particular characteristic such as language
proficiency, quantitative ability or scientific literacy of a specific population can be
expected to produce a normal curve. The normal curve is divided according to
standard deviations (i.e. -4s, -3s ⁄⁄ +3s and 4s) which are shown on the
horizontal axis. The area of the curve between standard deviations is indicated as
a percentage on the diagram. For example, the area between the mean and
standard deviation +1 is 34.13 per cent. Similarly, the area between the mean and

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TOPIC 10 ANALYSIS OF TEST SCORES  235

standard deviation -1 is also 34.13 per cent. Hence, the area between standard
deviation -1 and standard deviation +1 is 68.26 per cent. It means that in a normal
distribution, 68.26 per cent of individuals will score between standard deviations
-1 and +1.

In using the normal curve, it is important to make a distinction between standard
deviation values and standard deviation scores. A standard deviation value is a
constant and is shown on the horizontal axis in Figure 10.6.

On the other hand, the standard deviation score is the obtained score when we use
the standard deviation formula (which we discussed earlier). For example, if we
obtained a standard deviation of 5, then the score for one standard deviation is 5
and the score for two standard deviations is 10, the score for three standard
deviations is 15 and so forth. Standard deviation values of -1, -2 and -3 will have
corresponding negative scores of -5, -10 and -15.

Note, that in Figure 10.6, Z-scores are indicated from +1 to +4 and -1 to -4 with the
mean as 0. Each interval is equal to one standard deviation. Similarly, T-scores are
reported from 10 to 90 (interval of 10) with the mean set at 50. Each interval of 10
is equal to one standard deviation.

10.5 NORMS

In norm-referenced assessment, an individualÊs performance is evaluated in
relation to other peopleÊs performances. Norm-referenced tests are seldom used in
Malaysia but in the United States, standardised tests are widely used. Perhaps,
because of the decentralised education system in the United States, school-based
assessment is extensively practised. Unlike Malaysia, there are no national
examinations like the PMR and SPM in the United States. Hence, teachers there
who want to find out how their students are performing compared with other
students in the country rely on norm-referenced tests to compare the performances
of their students with the performances of other students in the norm group.

What are norms?

Norms are the characteristics of a population accurately estimated from the
characteristics of a representative subset of the population (called the sample
or norm sample).

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236  TOPIC 10 ANALYSIS OF TEST SCORES

Norms are produced based on the norm sample. For example, if you have norms
of reading ability for children of different age groups, you will be able to compare
the performance of a seven-year-old in your class on the reading ability test with
the rest of the population. In other words, you can determine whether your seven-
year-old is reading at the level of other seven-year-olds in the country. In
establishing these norms, you have to ensure that the norm sample is
representative of the population.

Representativeness
When you compare your students with the rest of the population, you want to
ensure that the norm sample is representative. In other words, the individuals
tested in the norm sample must consist of the appropriate age group, taking into
consideration gender differences, geographic location and cultural differences.

For example, the eight-year-olds selected for the norm sample should reflect eight-
year-olds in the rest of the country according to gender (male and female),
geographic location (urban or rural) and cultural differences. For example, the
norm sample consists of 3,000 Malaysian primary school children with 500
students for each age group (seven-year-olds = 500 students, eight-year-olds = 500
and so forth). The norm sample should consist of children in all the states of
Malaysia, including all the ethnic groups in the country and be drawn from
different socioeconomic backgrounds and geographic locations. Based on the
norm sample of 3,000 primary school children, the following hypothetical norms
on reading ability in Bahasa Melayu for Malaysian children were produced (refer
to Table 10.3).

Table 10.3: Norms for a Reading Ability Test

Reading Ability (Eight-year-olds)

Score Percentile

50 96

49 90

48 84

47 78

46 70

47 66

46 58

45 50

44 45

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TOPIC 10 ANALYSIS OF TEST SCORES  237

Percentile ranks (percentiles) are used in standardised tests which allow teachers
to compare the performance of their students with the norm group. An eight-year-
old student who obtained a score of 48 on the test has a percentile rank of 84. This
means that the student is reading at a level as well as, or better than,
84 per cent of other eight-year-old students in the test. Similarly, an eight-year-old
who obtains a percentile rank of 45 is reading as well as, or better than,
45 per cent of eight-year-olds in the norm sample.

To use norms effectively, you should be sure that the norm sample is appropriate,
both for the purpose of testing and for the person being tested. If you recognise
that the test norms are inadequate, you should be cautious because you may obtain
misleading information about the abilities of your students. The organisation
responsible for developing the norms should clearly state the groups tested
because you want to ensure that the norm sample is similar to your students. In
other words, the norm sample should consist of the same type of people in the
same proportion as is found in the population of reference. The norm sample
should be large enough to be stable over time.

SELF-CHECK 10.3

1. List some characteristics of the normal curve.
2. What are norms? How are norms used?
3. Do you think we should have standardised tests with norms for the

measurement of different kinds of abilities? Why?

 Statistics is a mathematical science pertaining to the analysis, interpretation
and presentation of data.

 Data collected about students can be subjected to statistical analysis, which
serves two related purposes: descriptive and inferential.

 The term „central tendency‰ refers to the „middle‰ value and is measured
using the mean, median and mode. It is an indication of the location of scores.

 The mean is simply the sum of all the values (marks) divided by the total
number of items (students) in the set.

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238  TOPIC 10 ANALYSIS OF TEST SCORES

 The range of scores in a test refers to the lowest and highest scores obtained in
the test.

 Standard deviation refers to how much the scores obtained by students deviate
or differ from the mean.

 Skew refers to the symmetry of a distribution.
 A negative skew has a longer tail in the negative direction. A positive skew has

a longer tail in the positive direction.
 The standard score refers to a raw score that has been converted from one scale

to another scale using the mean and standard deviation.
 Z-score tells how many standard deviations away from the mean the score is

located.
 The T-score is a standardised score with a mean of 50 and a standard deviation

of 10.
 The normal curve (also called the „bell curve‰) is a hypothetical curve that is

supposed to represent all natural occurring phenomena.
 In norm-referenced assessment, an individualÊs performance is evaluated in

relation to other peopleÊs performances.
 Norms are the characteristics of a population accurately estimated from the

characteristics of a representative subset of the population called the sample or
norm sample.

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TOPIC 10 ANALYSIS OF TEST SCORES  239

Central tendency Norms
Descriptive statistics Positive skew
Dispersion Range
Inferential statistics Standard deviation
Mean Standard score
Median T-scores
Negative skew Z-scores
Normal curve

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