EDUCATIONAL TECHNOLOGY AND ASSESSMENT OF LEARNING

EDUCATIONAL
TECHNOLOGY AND
ASSESSMENT OF
LEARNING
ANDUS, ZILO VIN ROSE M. BEED III

Audiovisual aids are defined as any device used to aid in the
communication of an idea. As such, visually anything can be used
as an audiovisual aid provided it successfully communicates the
idea or information for which it is designed. An audiovisual aid
includes still photography, motion picture, audio or videotape,
slide or filmstrip, that is prepared individually or in combination to
communicate information or to elicit a desired audience response.
Even though early aids, such as maps and drawings, are still in
use, advances in the audiovisual field have opened up new
methods of presenting these aids, such as videotapes and
multimedia equipment which allow more professional and
entertaining presentations not only in the classrooms but also
anywhere in which ideas are to be conveyed to the audience.

DEVICE
Device is any means other than the subject-matter itself that is
employed by the teacher in presenting the subject matter to the
learner.
Purpose of Visual Aids
1.To challenge students’ attention
2.To stimulate the imagination and develop the mental imagery
of the pupils
3.To facilitate the understanding of the pupils
4.To provide motivation to the learners
5.To develop the ability to listen

Traditional Forms of Visual Aids
1.Demonstration
2.Field trips
3.Laboratory experiments
4.Pictures, films, stimulations, models
5.Real objects

Classification of Devices
1.Extrinsic-used to supplement a method used
•Ex. Picture, graph, film strips, slides, etc.
2. Intrinsic-used as a part of the method or teaching procedure
•Ex. Pictures accompanying an article.
3. Material Devices-device that have no bearing on the subject
matter
•Ex. blackboard, chalk, books, pencil, etc.
4. Mental Devices- a kind of device that is related in form and
meaning to the subject matter being presented
•Ex. questions, projects, drill, lesson plans, etc.

NONPROJECTED AUDIOVISUALS AIDS
Nonprojected aids are those that do not require the use of audiovisual
equipment such as a projector and screen. These include charts, graphs,
maps, illustrations, photographs, brochures, and handouts. Charts are
commonly used almost everywhere. A chart is a diagram which shows
relationships. An organizational chart is one of the most widely and
commonly used kind of chart.

-It focuses on the development and utilization of
assessment tools to improve the teaching -
learning process.
-It emphasizes on the use of testing for
measuring knowledge , comprehension and
other thinking skills.
-It allows the students to go through the standard
steps in test constitution for quality assessment.
-Students will experience how to develop rubrics
for performance-based and portfolio assessment.

Measurement refers to the quantitative aspect of evaluation. It involves outcomes
that can be quantified statistically. It also be defined d as the process in determining
and differentiating the information about the attributes or characteristics of things.
Evaluation is the qualitative aspect of determining the outcomes of learning. It
involves value judgment. Evaluation is more comprehensive than measurement.
in fact, measurement measurement is one of the aspect of evaluation.
Test consists of questions or exercises or other devices for measuring the
outcomes of learning.

Formative and summative are terms often used with evaluation, but they may also be used
with testing. Formative testing is done to monitor students' attainment of the instructional
objectives. Formative testing occurs over a period of time and monitors student progress.
Summative testing is done at the conclusion of instruction and measures the extent to which
students have attained the desired outcomes.
Standardized tests are already valid, reliable and objective. Standardized tests are tests for
which contents have been selected and for which norms or standards have been established.
Psychological tests and government national examinations are examples of standardized
tests.
Standards or norms are the goals to be achieved expressed in terms of the average
performance of the population tested.

Criterion-referenced measure is a measuring device with a predetermined level of
success or standard on the part of the first-takers. For example, a level of 75 percent
score in all the items could be considered a satisfactory performance.
Norm-referenced measure is aa test that is scored on the basis of the norm or standard
based on the normal curve of distribution.

CRITERIA OF A
GOOD
EXAMINATION

According to manner of response
a. oral
b. written
2. According to method of preparation
a. subjective /essay
b. objective
3. According to the nature of answer
a. personality tests
b. intelligence test
c. aptitude test
d. achievement or summative test
e. sociometric test
f. diagnostic or formative test
g. trade or vocational test

A good examination must pass the following criteria:
Validity
-refers to the degree to which a test measures what it is intended to measure. It is the
usefulness of the test of a given measure. A valid test is always reliable, To test the validity of
a test it is to pretested in order to determine of it really measures what it intends to measure
or what it purports to measure.
Reliability
-pertains to the degree to which a test measures what it suppose to measure. The test of
reliability is the consistency of the results when it is administered to different groups of
individuals with similar characteristics in different places at different times, Also, the results
are almost similar when the test is given to the same group of individuals at different days
and the coefficient of correlation is not less than 0.85.

Objectivity
-is the degree to which personal bias is eliminated in the scoring of the answers. When
we refer to the quality of measurement, essentially we mean the amount if information
contained in a score generated by the measurement. Measures of the student
instructional outcomes are rarely as precise as those of physical characteristics such as
height and weight. Student outcome are more difficult to defibe, and the units of
measurement are usually not physical units. The measures we take on students vary in
quality, which prompts the need for different scales of measurement. Terms that
describe the levels of measurement in these different scales are nominal, ordinal,
interval, and ratio.

Objective tests are tests which have definite answers and therefore are not subject to
personal bias.
Teacher-made tests or educational tests are constructed by the teachers based on the
contents of different subjects taught.
Diagnostic test are used to measure a student's strengths and weaknesses, usually to
identify deficiencies in skills or performance.

Measurements may differ in the amount of information the numbers contain. These
differences are distinguished by the terms nominal, ordinal, interval, and ratio scales of
measurement.
The terms nominal, ordinal, interval, and ratio actually a hierarchy. Nominal scales of
measurement are the sophisticated and contain the least information. Ordinal, interval and
ratio scales increase respectively in sophistication. The arrangement is a hierarchy in the
higher level, along with additional data. For example, numbers from an interval scale of
measurement contain all of the information that nominal and ordinal scales would provide,
plus some supplementary input. However, a ratio scale of the same attribute would contain
ever more information than the interval scale. This idea will become more clear as each
scale of measurement is described.

Ordinal Measurement
Ordinal scales classify, but they also assign work order. An example of ordinal
measurement is ranking individuals in a class according to their test scores. Student
scores could be ordered from first, second, third, and so forth to the lowest score. Such a
scale gives more information than nominal measurement, but it still has limitations. The
units of ordinal measurement are most likely unequal. The number separating the fifth
and sixth students. These unequal units of measurement are analogous to a ruler in
which some inches are longer than others. Addition and subtraction of such units yield
meaningless numbers.

Nominal Measurement
-Nominal scales are the least sophisticated; they merely classify objects or events by
assigning numbers to them. These numbers are arbitrary and imply no quantification,
but the categories must be mutually exclusive and exhaustive. For example, one could
nominally designate baseball positions by assigning the pitcher the numeral 1; the
catcher, 2; the first baseman, 3; the second baseman,4; and so on. These assignments
are arbitrary; no arithmetic of these numbers is meaningful. For example, 1 plus 2 does
not equal 3, because a pitcher plus a catcher does not equal a first baseman.

Interval Measurement
-In order to be able to add and subtract scores, we use Interval scales, sometimes called
equal interval or equal unit measurement. This measurement scale contains the nominal and
ordinal properties and is also characterized by equal units between score points. Examples
include thermometers and calendar years. For instance, the difference in temperature
between 10° and 20° is the same as that between 47° and 57°. Likewise, the difference in
length of time between 1946 and 1948 equals that between 1973 and 1975. These
measures are defines in terms of physical properties such that the intervals are equal. For
example, a year is the time it takes for the earth to orbit the sun. The advantage of equal
units of measurement is straightforward: Sums and differences now make sense, both
numerically and logically. Note, however the zero point in interval measurement is really an
arbitrary decision; for example 0° does not mean that there is no temperature.

r
Note that carefully designed tests over a specified domain of possible
items can approach ratio measurement. For example, consider an
objective concerning multiplication facts of pairs of numbers less than 10.
In all, there are 45 such combinations. However, the teacher might
randomly select 5 or 10 test problems to give to a particular student. The,
the proportion of items that the student has mastered. If the student
answers 4 or 5 such combinations. However, the teacher might randomly
select 5 or 10 test problems to give to a particular student. Then, the
proportion of items that the students get correct could be used to estimate
how many of the 45 possible items the students has mastered. If the
student answers 4 or 5 items correctly, it is legitimate to estimate that the
student would get 36 of the 45 items correct if all 45 items were
administered.

Ratio Measurement
- The most sophisticated type of measurement includes all the preceding properties, but
in a ratio scale, the zero point is not arbitrary; a score of zero includes the absence of
what is being measured. For example, if a person's wealth equaled zero, he or she
would have no wealth at all. This is unlike a social studies test, where missing item(i.e,
receiving a score of zero) may not indicate the complete absence of social studies
knowledge. Ratio measurement is rarely achieved in educational assessment, either in
cognitive or affective areas. The desirability of ratio measurement scales is they allow
comparisons, such as Ann is 1-1/2 times as tall as her little sister, Mary. We can seldom
say that one's intelligence or achievement is 1-1/2 times as great as that of another
person. An IQ of 120 may be 1-1/2 times as intelligent as a person with an IQ of 80.

Norm-Referenced and Criterion Referenced Measurement
When we contrast norm-referenced measurement(or testing) with
criterion-referenced measurement, we are basically referring to two
different ways of interpreting information. However, Popham(1988, page
135) points out that certain characteristics tend to go with each type of
measurement, an it is unlikely that results of norm-referenced tests are
interpreted in criterion-referenced ways and vice versa.

r
This is possible because the set of possible items was specifically defined
in the objective, and the test items were a random, representative sample
from that set. Most educational measurements are better tha strictly
nominal or ordinal measures, but few can meet rigorous requirements of
interval measurement. Educational testing usually falls, somewhere
between ordinal and interval scales in sophistication. Fortunately,
empirical studies have shown arithmetic operations on these scales are
appropriate, and the scores do provide adequate information for most
decisions about the students and instruction. Also, as we will see later,
certain procedures can be applied to scores with reasonable confidence.

Nor-referenced interpretation historically has been used in education.
norm-referenced tests continue to comprise a substantial portion of the
measurement in today's schools. The terminology of criterion-referenced
measurement has existed for close to three decades, having been formally
introduced with Glaser's(1963) class article. Over the years, there has been
occasional confusion with the terminology and how criterion-referenced
measurement applies in the classroom. Do not infer that just
because a test is published, it will necessarily be norm-referenced, or of
teacher-constructed, criterion-referenced. Again, we emphasize that the
type of measurement or testing depends on how the scores are
interpreted. Both types can be used effectively by the teacher.

Norm-referenced interpretation stems from the desire to differentiate
among individuals or to discriminate among the individuals of some
defined group on whatever is being measured. In norm-referenced
measurement, an individual's score is interpreted by comparing it to the
scores of a defined group, often called the normative group. Norms
represent the scores earned by one or more groups of students who have
taken the test.
Norm-Referenced Interpretation

Norm-referenced interpretation is a relative interpretation based on an
individual's position with respect to some group, often called the normative
group. Norms consist of the scores, usually in some form of descriptive
statistics, of the normative group.
In norm-referenced interpretation, the individual's position in the normative
group is of concern; thus, this kind of positioning does not specify the
performance in absolute terms. The norm being used is the basis of
comparison and the individual score is designated by its position in the
normative group.

Most standardized achievement tests, especially those covering several
skills and academic areas, are primarily designed for norm-referenced
interpretations. However, the for of results and the interpretations of these
tests are somewhat complex and require concepts not yet introduced in
this text. Scores on teacher-constructed tests are often given norm-
referenced interpretations. Grading on the curve, for example, is a norm-
referenced interpretation of test scores on some type of performance
measure. Specified percentages of the scores are assigned the different
grades, and an individual's score is positioned in the distribution of scores.
(We mention this only as an example; we do not endorse this procedure).
Achievement Test as An Example

Suppose an algebra teacher has a total of 150 students in five classes,
and the classes have a common final examination. The teacher decides
that the distribution of the letter grades assigned to the final examination
performance will be 10 percent As, 20 percent Bs, 40 percent Cs, 20
percent Ds, and 10 percent Fs.(Note that the final examination grade is
not necessarily the course grade.) Since the grading is based on all 150
scores, do not assume that the 3 students in each class will receive As, on
the final examination.

James receives a score on the final exam such that 21 students have
higher scores and 128 students have lower scores. What will James's
letter grade be on the exam? The top 15 scores will receive As, and the
next 30 scores(20 percent of 150) will receive a B on the final examination.
Note that in this interpretation example, we did not specify James's actual
numerical score on the exam . That would have been necessary in order to
determine that his score positioned 22nd in the group of 150 scores. But in
terms of the interpretation of the score, it was based strictly on its position
in the total group of scores.

Criterion-Referenced interpretation
The concepts of criterion-referenced testing have developed with a dual
meaning for criterion-referenced. On one hand, it means referencing an
individual's performance to some criterion that id a defined performance
level. The individual's score is interpreted in absolute rather than relative
terms. The criterion, in this situation, means some level of specified
performance that has been determined independently of how other might
perform.
A second meaning for criterion-referenced involves the idea of a
defined behavioral domain-that is, a defined body of learner behaviors.
The criterion in this situation is the desired behaviors.

Criterion-referenced interpretation is an absolute rather than relative
interpretation, referenced to a defined body of learner behaviors, or, as is
commonly done, to some specified level of performance.
Criterion-referenced tests require the specification of learner behavios
prior to constructing the test. The behaviors should be redily identifiable
from instructional objectives. Criterion-referenced test tends to focus on
specific learner behaviors, and usually only a limited number are covered
on any one test.

Suppose before the test is administered an 80-percent correct criterion is
established as the minimum performance required for mastery of each
objective. A student who does not attain the criterion has not mastered
the skills sufficiently to move ahead in the instructional sequence. To a
large extent, the criterion is based on teacher judgment. No magical,
iuniversal criterion for mastery lexists, although some curriculum
materials that contain criterion-referenced tests do suggest criteria for
mastery. Also, unless objectives are appropriate and the criterion for
achievement relevant, there is little meaning in the attainment of a
criterion, regardless of what it is.

Distinctions between Norm-Referenced and Criterion-Referenced Tests
Although interpretations, not characteristics, provide the distinction
between norm-reference and criterion-referenced tests, the two types do
tend to differ in some ways.
Norm-referenced tests are usually more general and comprehensive and
cover a large domain of content and learning tasks. They are used for
survey testing , although this is not their exclusive use.

Criterion-referenced tests focus on a specific group of learner behaviors.
To show the contrast, consider an example. Arithmetic skills represent a
general and broad category of student outcomes and would likely be
measured by a norm-referenced test. On the other hand, behaviors such
as solving addition problems with two five-digit number or determining
the multiplication products of three-and four digit numbers are much
more specific and may be measured by criterion-referenced tests.
A criterion-referenced test scores are transformed to positions within the
normative group. Criterion-referenced test scores are usually given in the
percentage of correct answers or another indicator of mastery or the
lack thereof.

Criterion-referenced tests tend to lend themselves more to
individualizing instruction than do norm-referenced tests. In
individualizing instruction, a student's performance is interpreted more
appropriately by comparison to the deisired behaviors for that particular
student, rather than by compasion with the performance of a group.
Norm -referenced test items tens to be of average difficulty. Criterion-
referenced tests have item difficulty matched to the learning tasks. The
distinction in item difficulty is necessary because norm-referenced tests
emphasize the discrimination among individuals and criterion-referenced
testes emphasize the description of performance. Easy items, for
example, do little for discriminationg among indicviduals, but they may
be necessary for describing performance.

Finally. when measuring attitudes, interests, and aptitudes, it is practicallt
impossible to interpret the results without comparing them to a reference
group. The reference groups in such cases are usually typical students or
students with high interests in certain areas. Teachers have no basis for
anticipating these kinds of scores; therefore, in order to ascribe meaning
to such a score, a referent group must bee used. For instance, a score of
80 on an interest inventory has no meaning in itslef. On the other hand, if
a score of 80 is the typical response by a group interested in mechanical
areas, the score ttakes on meaning.

I. Planning the test
A. Determining the Objectives
B. Preparing the Table of Specifications
C. Selecting the Appropriate Item Format
D. Writing the Test Items
E. Editing the Test Items
II. Trying Out the Test
A. Administering the First Tryout-then Item Analysis
B. Administering the Second Tryout-then Item
Analysis
C. Preparing the Final Form of the test
III. Establishing Test Validity
IV. Establishing the Test Reliability
V. Interpreting the Test Score
STAGES IN TEST
CONSTRUCTION

MAJOR CONSIDERATIONS IN TEST
CONSTRUCTION
The following are the major considerations in test consideration:
Type of Test
Our usual idea of testing is an in-class test that is administered by the
teacher. However, there are many variations on this theme: group tests,
individual tests, written tests, oral tests, speed tests, power tests,
pretests and post tests. Each of these has different characteristics that
must be considered when the tests are planned.

If it is a take-home test rather than an in-class test, how do you make
sure that students work independently, have equal access-to sources
and resources, or spend a suffiecient but not enormous amount of time
on the task? if it is an achievement test, should partial credit be
awarded, should there be penalties for guessing, or should points be
deducted for grammar and spelling errors?

Obviously, the test plan must include a wide array of issues. Anticipating
these potential problems allows the test contructor to develop positions
or policies that are consistent with his ior her testing philospohy. These
can then be communicated to students, administrations, parents, and
others who may be affected by the testing program. Make a list of the
objectives, the subject matter taught, and the activities undertaken.
These are contained in the daily lesson plans of the teacher and in the
references or textbook used. Such tests are usually very indirect
methods that only approximate real-word applications. The constraints
in classroom testing are often due to time and the developmental level of
students.

Test Length
A major decision in the test planning is how many items should be
included on the test. There should be enough to vcover the content
adequately, but the length of the class period or the attention span or
fatigue limits of the students usually restrict the test length. Decisions
about test length are usually based on practical constraints more than
on theoretical considerations.
Most teachers want test scores to be determined by how much the
student understands rather than by how quickly he or she answers the
questions. Thus, teachers prefer power tests, where at least 90 percent
of the students have timr to attempt 90 percent of the test through
experience with similar groups of students.

Item Formats
Determining what kind of items to include on the test is a major decision.
Should they be objectively scored formats such as multiple choice or
matching type? Should they cause the students to organize their own
thoughts through short answer or essay formats? These are important
questions that csn be answered only by the teacher in terms of the local
context, his or her students, his or her classroom, and the specific
purpose of the test. Once the planning decisions are made, the item
writing begins. This tank is often the most feared by the beginning test
constructors. However, the procedures are more common sense than
formal rules.

POINTS TO BE CONSIDERED IN
PREPARING A TEST
• Are the instructional objectives clearly defined?
• What knowledge, skills and attitudes do you want to
measure?
• Did you prepare a table of specifications?
• Did you formulate well defined and clear test items?
• Did you employ correct English in writing test items?
• Did you avoid giving clues to the correct answer?
• Did you test the important ideas rather than the
trivial?
• Did you adapt the test's difficulty to your student's
ability?
• Did you avoid using textbook jargons?
• Did you cast the items in positive form?
• Did you prepare a scoring key?
• Does each item have a single correct answer?
• Did your review your items?

GENERAL PRINCIPLES IN CONSTRUCTING
DIFFERENT TYPES OF TEST
• The test items should be selected very carefully. Only important
facts should be included.
• The test should have extensive sampling of items.
• The tst items should be carefully expressed in simple, clear, definite,
and meaningful sentences.
• There should be only one possible correct response for each test
item.
• Each item should be independent. Leading clues to other items
should be avoided.

6. Lifting sentences from books should not be done to encourage
thinking and understanding.
7. The first person personal pronouns/ and we should not be used.
8. Various types of test items should be made to avoid monotony.
9 Majority of the test items should be of moderate difficulty. Few
difficulty and few easy items should be included.
10. The tests should be arranged in an ascending orfder of difficulty.
Easy items should be at the beginning to encourage the examine to
pursue the test and the most difficult items should be at the end.
11. Clear , concise, and complete directions should precede all the types
of test. Sample test items may be provided for expected responses.

12. Items which can be answered by previous experience alone without
knowledge of the suject matter should not be included.
13. Catchy words should not be used in the test items.
14. Test items must be based upon the objectives of the course and upon
the course content.
15. The test should measure the degree of achievement or determine the
difficulties of the learners.
16. The test should be of such length that it can be completed within the
time alloted by all or nearly all of the pupils. The teacher should perform
the test herself of facts.

17. The test should be of such length that it can be completed within the
time allotted by all or nearly all of the pupils. The teacher should perform
the test herself to determine is approximate time allotment.
18. Rules governing good language expression, grammar, spelling,
punctuation, and capitalization should be observed in all items.
19. Information on how scoring will be done should be provided.
20. Scoring Keys in correcting and scoring tests should be provided.

POINTERS TO BE OBSERVED IN
CONSTRUCTING ANS SCORING
THE DIFFRENT TYPES OF TESTS
A. RECALL TYPES
• Simple recall type
a. This type consists of questions calling for a single word or expression as an
answer.
b. Items usually begin with who, where, when, and what.
c. Score is the number of correct answers.
2. Completion type
a. Only important words or phrases should be omitted to avoid confusion.
b. Blanks should be equal lengths.
c. The blank, as much as possible, is placed near or at the end of the sentence.
d. Articles a, an, and the should not be provided before the omitted word or
phrase to avoid clues for answers.
e. Score is the number of correct answers.

3.Enumeration type
a. the exact number of expected answers should be stated.
b. Blanks should be of equal lengths.
4. Identification type
a. The items should make an examinee think of a word,
number, or group of words that would complete the statement or answer
the problem.
b. Score is the number of correct answers.

B. RECOGNITION TYPES
1. True-false or alternate-response type
a. Declarative sentences should be used.
b. The number of “true” and “false” items should be more or less equal.
c. The truth or falsity of the sentence should not be too evident.
d. Negative statements should be avoided.
e. The “modified true-false” is more preferable than the “plain true-false”.

f. In arranging the items, avoid the regular recurrence of “true” and
“false” statements.
g. Avoid using specific determiners like: all, always, never, none, nothing,
most, often, some, etc., and avoid weak statements as may, sometimes,
as a rule, in general etc.
h. Minimize the use of qualitative terms like few, great, many, more etc.
i. Avoid leading clues to answers in all items.
j. Score is the number of correct answers in” modified true-false” and
right answers minus wrong answers in “plain true-false”

2. Yes-No type
a. The items should be in interrogative sentences.
b. The same rules as in “true-false” are applied.
3. Multiple-response
type
a. There should be three to five choices. The number of
choices used in the first item should be the same number of choices in
all
items of this type of test.
b. The choices should be numbered or lettered so that only the number
or letter can be written on the blank provided.

c. If the choices are figured, they should be arranged in
ascending order.
d. Avoid the use of “a” or “an” as the last word prior to the listing of
the responses.
e. Random occurrence of responses should be employed.
f. The choices, as much as possible, should be at the end
of the statements.
g. The choices should be related in some way or should belong to the
same class.
h. Avoid the use of “none of these” as one of the choices.
i. Score is the number of correct answers.

4. Best answer type
a. There should be three to five choices all of which are right but vary in
their degree of merit, importance or desirability.
b. The other rules for multiple-response items are applied here.
5. Matching type
a. There should be two columns. Under “A” are the stimuli which should
be longer and more descriptive than the responses under column “B”. The
response may be a word, a phase, number, or a formula.

b. Their stimuli under column “A” should be numbered and the responses
under column “B” should be lettered. Answers will be indicated by letters
only on lines provided in column “A”.
c. The number of pairs usually should not exceed twenty
items. Less than ten introduced chance elements. Twenty pairs may be
used but more than twenty is decidedly wasteful of time.
d. The number of responses in column “B” should be two or
more than the number of items in Column “A” to avoid guessing.

e. Only one correct matching for each item should be
possible.
f. Matching sets should neither be too long nor too
short.
g. All items should be on the same page to avoid turning of
pages in the process of the matching pairs.
h. Score is the number of correct answers.

C.ESSAY TYPE EXAMINATIONS
Common types of essay questions. (The types are related
to purposes of
which the essay examinations are to be used.)
1. Comparison of two things
2. Explanation of the use or meaning of a statement or
passage.
3. Analysis
4. Decisions for or against
5. Discussion.

How to construct examinations.
1. Determine the objectives or essentials for each question to be
evaluated.
2. Phrase questions in simple, clear and concise language.
3. Suit the length of the questions to the time available for answering the
essay examination. The teacher should try to answer the test herself.
4. Scoring
a. Have a model answer in advance.
b. Indicate the number of points for each question.
c. Score a point for each essential.

ADVANTAGES AND DISADVANTAGES OF THE OBJECTIVE TYPE OF
TESTS
Advantages
a. The objective test is free from personal bias in
scoring.
b. It is easy to score. With a scoring key, the test be
corrected by different individuals without affecting the accuracy of the
grades
given.
c. It has high validity because it is comprehensive with
wide sampling of essentials.

d. It is less time- consuming since many items can be answered in a
given time.
e. It is fair to students since the slow writers can be accomplish the
test as fast as the fast writers.
Disadvantages
a. It is difficult to construct and requires more time to
prepare.
b. It does not afford the students the opportunity in training for self-
and thought organization.
c. It cannot be used to test ability in theme writing or
journalistic writing.

ADVANTAGES AND DISADVANTAGES OF THE ESSAY TYPE OF TESTS
Advantages
a. The essay examination can be used in practically all subjects of the
school curriculum.
b. It trains students for thought organization and self-expression.
c. It affords opportunities to express their originality and independence
of thinking.
d. Only the essay test can be used in some subjects like composition
writing and journalistic writing which cannot be tested by the objective
type test.

e. Essay examination measures higher mental abilities like comparison,
interpretation, criticism, defense of opinion and decision.
f. The essay test is easily prepared.
g. It is inexpensive.
Disadvantages
a. The limited sampling of items makes the test unreliable
measure of achievements or abilities.
b. Questions usually are not well prepared.
c. Scoring is highly subjective due to the influence of the
corrector’s personal judgment.
d. Grading of the essay is inaccurate measure of pupils’ achievements
due to subjectivity of scoring.

STATISTICAL MEASURES OR
TOOLS USED IN INTERPRETING
NUMERICAL DATA
Frequency Distributions
A simple, common sense technique for describing a set of test scores is through
the use of a frequency distribution. A frequency distribution is merely a listing of
the possible score values and the number of persons who achieved each score.
Such an arrangement presents the scores in a more -simple and understandable
manner than merely listing all of the separate scores.

Consider a specific set of scored to clarify these ideas. A set scores for a group of
25 students who took a 50- item test is listed in Table 1. It is easier to analyze the
scores if they are arranged in a simple frequency distribution. (The frequency
distribution for the same set of scores is given in Table 2). The steps that are
involved in creating the frequency distribution are: First, list the possible score
values in rank order, from highest to lowest. Then, a second column indicates the
frequency or number of persons who received each score. For example, three
students received a score of 47, tow received 40, and so forth. There is no need to
list score values below the lowest score that anyone received.

When there is a wide range of scores in a frequency distribution, the distribution
can be quite long, with a lot of zeroes in the column of frequencies. Such a
frequency distribution can make interpretation of the scores difficult and
confusing. A grouped frequency distribution would be more appropriate in this
kind of situation. Groups of score values are listed rather than each separate
possible score value.
If we were to change the frequency distribution in Table 2 into a grouped
frequency distribution, we might choose intervals such as 48-50, 45-47, and so
forth. The frequency corresponding to interval 48-50 would be 9(1+3+5). The
choice of the width of the interval is arbitrary, but it must be the same for all
intervals. In addition, it is a good idea to have an odd-numbered interval width
(we used 3 above) so that the midpoint of the interval is a whole number. This
strategy will simplify subsequent graphs and description of the data. The grouped
frequency distribution is presented in

Frequency distributions
summarize sets of test scores
by listing the number of people
who received each test score.
All of the test scores can be
listed separately, or the scores
can be grouped in a frequency
distribution.

MEASURES OF CENTRAL TENDENCY
Frequency distributions are helpful for indicating the shape go describe a
distribution of scores, but we need more information than the shape to
describe a distribution adequately. We need to know where on the scale of
measurement a distribution is located and how the scores are dispersed in the
distribution. For the former, we compute measures of central tendency, and for
the later, we compute measures of dispersion. Measures of central tendency
are points on the scale of measurement, and they are representative of how
the scores tend to average. There are three commonly used measures of
central tendency: the mean, the median, and the mode, but the mean is by far
the most widely used.

The Mean
The mean of a set of scored is the arithmetic mean. It is found by
summing the scores and diving the sum by the number of scores.
The mean is the most commonly used measure of central tendency
because it is easily understood and is based on all of the scores in
the set; hence, it summarizes a lot of information. The formula for the
mean is as follows:

X=
X
N
where
X̄ is the mean,
X is the symbol for a score, the summation operator (it tells us to
add all Xs)
N is the number of scores.
For the set of score in Table 1,
X= 1100
N= 25,
so then
X̄ =
1100
25
=44

The mean of the set of scores in Table 1 is 44. The mean does not
have equal an observed score; it is usually not even a whole number.
When the scores are arranged in a frequency distribution, the
formula is:
X̄ =
𝑓𝑋 𝑚𝑑𝑝𝑡,
𝑁
Where fX mdpt means that the midpoint of the interval is multiplied
by the frequency for the interval. In computing the mean for the
scores in Table 3, using formula we obtain:
X̄ =
9(49)+4(46)+4(43)+3(37)+ 2(34)
25
= 43.84
Note that this mean is slightly different than the meaning using
ungrouped data. This difference is due to the midpoint representing
the scores in the interval rather than using the actual scores.

The Median
Another measure of central tendency is the median which is the
point that divided the distribution in half, that is, half of the scores
fall above the median and half of the scores fall below the median.
When there are only a few scores, the median can often be found
inspection. If there is an odd number of scores, the score is the
median. Where there is an even number of scores, the median is
halfway between the two middle scores. However, when there are
tied scored in the middle of the distribution, or when the scores are in
a frequency distribution, the median may be so obvious.

Consider again the frequency distribution in Table 2. There were 25
scores in the distribution, so middle score should be the median. A
straightforward way to find this median is to augment the frequency
distribution with a column of cumulative frequencies.
Cumulative frequencies indicate the number of scores at or below
each score. Table 4 indicates the cumulative frequencies for the data
in Table 2.

For example, 7 persons scored at or below a score of 40, and 21
persons scored at or below a score of 48.
To find the median, we need to locate the middle score in the
cumulative frequency column, because this score is the median.
Since there are 25 scores in the distribution, the middle one is the
13th, a score of 46. Thus, 46 is the median of this distribution, half of
the people scored about 46 and half scored.
When there are ties in the middle of the distribution, there may be a
need to interpolate between scores to get the exact median.
However, such precision is not needed for most classroom tests. The
whole number closest to the median is usually sufficient.

The Mode
•The measure of central tendency that is the easiest to find is the
mode. The mode is the most frequently occurring score in the
distribution. The mode of the scores in Table 1 is 48. Five persons
has score of 48 and no other score
occurred as often.
• Each of these three measured of central tendency-the mean, the
median, and the mode means a legitimate definition of “average”
performance on this test. However, each does provide different
information. The arithmetic average was 44; half the people scored
at or below 46 and more people received 48 than any other score.

There are some distributions in which all three measured of central
tendency are equal, but more often than not they will be different.
The choice of which measure of central tendency is best will differ
from situation to situation. The mean is used most often, perhaps
because it includes information from all of the scores.
When a distribution has a small number of very extreme scores,
though, the median may be a better definition of central tendency.
The mode provides the least information and is used infrequently as
an “average”.

The mode can be used with normal scale data, just as an indicator
of the most frequently appearing category. The mean, median, and
the mode all describe central tendency:
• The mean is the arithmetic average.
• The median divided the distribution in half.
• The mode is the most frequent score.

MEASURES OF DISPERSION
•Measures of central tendency are useful for summarizing average
performance,
but they tell us nothing about how the scores are distributed or
“spread out” around the averages. Two sets of test scores may
have equal measures of central tendency, but they might differ in
other ways. One of distributions may have the scored tightly
clustered around the average, and the other distribution may have
scored that are widely separated. As you may have anticipated,
there are descriptive statistics that measure dispersion, which also
are called measured of variability. These measures indicate how
spread out the scores tend to be.

The Range
The range indicates the difference between the highest and lowest
scores in the distribution. It is simple to calculate, but it provides
limited information. We subtract the lowest from the highest score
and add 1 so that we include both scores in the spread between
them. For the scores of Table 2, the range is 50-34+1=17.
A problem with using range is that only two most extreme scores
are used in the computation. There is no indication of the spread of
scores between the highest and lowest. Measures of dispersion
that take into consideration every score in the distribution are the
variance and standard deviation. The standard deviation is used a
great deal in interpreting scores from standardized tests.

The Variance
The variance measures how widely the scores in the distribution
are spread about the mean. In other words, the variance is the
average squared between the scores and the mean. As a formula,
it looks like this:
S²=
(X̄ − X)²
𝑁
•An equivalent formula, easier to compute is:
S²=
X²
𝑁
X̄ ²
The computation of the variance for the scores of Table 1
illustrated in the Table 5. The data for students K
through V are omitted to save space, but these values are included
in the column totals and in the computation.

The Standard Deviation
The standard deviation also indicates how spread out the scores
are, but it is expressed in the same units as the original scores. The
standard deviation is computed by finding the square root of the
variance.
S= S²
For the data in Table 1, the variance is 22.8. The standard
deviation is 22.8, or 4.77. The scored of most norm group have the
shape of a "normal" distribution-a symmetrical, bell-shaped
distribution with which most people are familiar. With a normal
distribution, about 95 percent of the scores are within two
standard deviations of the mean.

Even when scores are not normally distributed, most of the scores
will be within two standard deviations of the mean. In the example,
the mean minus two standard deviations is 34, 46, and the mean
plus two standard deviations is 53.54. Therefore, only one score is
outside of this interval; the lowest score, 34, is slightly more than
two standard deviations from the mean.

To determine the mean:
X̄ =
1100
25
= 44.
Then, to determine the
variance:
S²=
(X−X̄ )²
𝑁
=
570
25
=22.8

The usefulness of the standard deviation becomes apparent when
scores from different tests are compared. Suppose that the two
tests are given to the same class-- one on fraction and the other on
the reading comprehension. The fractions test has a mean of 30
and a standard deviation of 8; the reading comprehension test has
a mean of 60 and a standard deviation of 10.
If Ann scored 38 on the fractions test and 55 on the reading
comprehension test, it appears from the raw scored that she did
better in reading than in fractions, because 55 is greater than
38.But, relative to the performance of the others in the class, the
opposite is true.
X̄

A score of 38 on the fraction test is one standard deviation about
the mean a score that is lower than average. Clearly, when
comparison is made relative to the class mean, Ann's performance
on the fractions test is better than her performance on the reading
comprehension test.
In fine, descriptive statistics that indicate dispersion are the range,
the variance, the standard deviation. The range is the difference
between the highest and lowest scores in the distribution plus one.
The standard deviation is a unit of measurement that shows by
how much the separate scores tend to differ from the mean. The
variance is the square of the standard deviation. Most scores are
within two standard deviations from the mean.

Graphing Distributions
A graph of a distribution of test scores is often better understood
than is the frequency distribution or a mere table of numbers. The
general pattern of scores, as well as any unique characteristics of
the distribution, can be seen easily in simple graphs. There are
several kinds of graphs that can be used, but a simple bar graph,
or histogram, is as used as any.

The general shape of the distribution is clear from the graph. Most
of the scores in this distribution are high, at the upper end of the
graph. Such a shape is quite common for the score of classroom
tests. That is, test scores will be grouped toward the right end of
the measurement scale.
A normal distribution has most of the test scores in the middle of
the distribution and progressively fewer scores toward the
extremes. The scores of norm group are seldom graphed but they
could be if we were concerned about seeing the specific shape of
the distribution of scores. Usually, we know or assume that the
scores are normally distributed.

EDUCATIONAL TECHNOLOGY AND ASSESSMENT OF LEARNING

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