PERFECT NA FINALS CUTIE!
REVIEWER IN ASL
students got the correct answer and more students
mastered the content measured by that item.
UNIT 3: ITEM ANALYSIS, RELIABILITY AND
VALIDITY
ITEM ANALYSIS
 Item analysis is a process of examining the
student’s response to individual item in the test. It
consists of different procedures for assessing the
quality of the test items given to the students.
Through the use of item analysis, we can identify
which of the given are good and defective test
items. Good items are to be retained and defective
items are to be improved, to be revised or to be
rejected.
USES OF ITEM ANALYSIS
1. Item analysis data provide a basis for efficient class
discussion of the test results.
2. Item analysis data provide a basis for remedial work.
3. Item analysis data provide a basis for general
improvement of classroom instruction.
4. Item analysis data provide a basis for increased skills
in test construction.
2. DISCRIMINATION INDEX
 It is the power of the item to discriminate the
students who know the lesson and those who do not
know the lesson. It also refers to the number of
students in the upper group who got an item
correctly minus the number of students in the lower
group who got an item correctly. Divide the
difference by either the number of the students in
the upper group or number of students in the lower
group or get the higher number if they are not equal.
Discrimination index is the basis of measuring the
validity of an item. This index can be interpreted as
an indication of the extent to which overall
knowledge of the content area or mastery of the
skills is related to the response on an item. The
formula used to compute for the discrimination
index is: where:
5. Item analysis procedures provide a basis for
constructing test bank.
DI = discrimination index value;
TYPES OF QUANTITATIVE ITEM ANALYSIS
CUG = number of the students selecting the correct
answer in the upper group;
1. DIFFICULTY INDEX
 It refers to the proportion of the number of students
in the upper and lower groups who answered an
item correctly. The larger the proportion, the more
students, who have learned the subject is measured
by the item. To compute the difficulty index of an
item, use the formula: where:
DF = difficulty index;
n = number of the students selecting item correctly in
the upper group and in the lower group; and
N = total number of students who answered the test.
LEVEL OF DIFFICULTY
 To determine the level of difficulty of an item, find
first the difficulty index using the formula and
identify the level of difficulty using the range given
below. The higher the value of the index of
difficulty, the easier the item is. Hence, more
CLG = number of students selecting the correct answer
in the lower group; and
D = the number of students in either the lower group or
upper group
TYPES OF DISCRIMINATION INDEX
1. Positive discrimination happens when more
students in the upper group got the item correctly
than those students in the lower group.
2. Negative discrimination occurs when more
students in the lower group got the item correctly
than the students in the upper group.
3. Zero discrimination happens when several
students in the upper group and lower group who
answer the test correctly are equal, hence, the test
item cannot distinguish the students who performed
in the overall test and the students whose
performance are very poor.
LEVEL OF DISCRIMINATION
 Ebel and Frisbie (1986) as cited by Hetzel (1997)
recommended the use of the Level of
Discrimination of an Item for easier interpretation.
not know the correct answer. The attractiveness of
the incorrect options is determined when more
students in the lower group than in the upper group
choose it. Analyzing the incorrect options allow the
teachers to improve the test items so that it can be
used again in the future.
DISTRACTER ANALYSIS
STEPS IN SOLVING DIFFICULTY INDEX AND
DISCRIMINATION INDEX
1. Arrange the scores from highest to lowest.
2. Separate the scores in the upper group and lower
group. There are different methods to do this:
(a) if a class consists of 30 students who takes an exam,
arrange their scores from highest to lowest, then divide
them into two groups. The highest score belongs to the
upper group. The lowest score belongs to the lower
group.
(b) Other literature suggested to use 27%, 30%, or 33%
of the students for the upper group and lower group.
(c)However, in the Licensure Examination for Teachers
(LET) the test developers always used 27% of the
students who participated in the examination for the
upper and lower groups.
3. Count the number of those who chose the
alternatives in the upper and lower group for each item
and record the information using the template.
Note: Put asterisk for the correct answer
4. Compute the value of the difficulty index and the
discrimination index and also the analysis of each
response in the distracters.
5. Make an analysis for each item.
3. ANALYSIS OF RESPONSE OPTIONS
 Aside from identifying the difficulty index and
discrimination index, another way to evaluate the
performance of the entire test item is through the
analysis of the response options. It is very important
to examine the performance of each option in a
multiple-choice item. Through this, you can
determine whether the distracters or incorrect
options are effective or attractive to those who do
1. Distracter. It is the term used for the incorrect
options in the multiple-choice type of test while the
correct answer represents the key.
2. Mis keyed item. The test item is a potential miskey
if there are more students from the upper group who
choose the incorrect options than the key.
3. Guessing item. Students from the upper group have
equal spread of choices among the given
alternatives.
4. Ambiguous item. This happen when more
students from the upper group choose equally an
incorrect option and the keyed answer.
HOW TO IMPROVE THE TEST ITEM
Example 1. A class is composed of 40 students. Divide
the group into two. Option B is the correct answer.
Based from the given data on the table, as a teacher,
what would you do with the test item?
1. Compute the difficulty index.
N = 10 + 4 = 14
N = 40
2. Compute the discrimination index
CUG = 10
CLG = 4
D = 20
3. Make an analysis about the level of difficulty,
discrimination and distracters.
a. Only 35% of the examinees got the answer correctly,
hence, the item is difficult.
b. More students from the upper group got the answer
correctly, hence, it has positive discrimination.
c. Retain options A, C, and E because most of the
students who did not perform well in the overall
examination selected it. Those options attract most
students from the lower group
3. Conclusion: Retain the test item but change option
D, make it more realistic to make it effective for the
upper and lower groups. At least 5% of the
examinees choose the incorrect option.
Example 2. Below is the result of an item analysis for a
test item in Mathematics. Are you going to reject, revise
or retain the test item?
1. Compute the difficulty index.
N=4+3=7
N = 39
2. Compute the discrimination index
CUG = 4
CLG = 3
D = 20
3. Make an analysis about the level of difficulty,
discrimination and distracters.
a. Only 18% of the examinees got the answer
correctly, hence, the item is very difficult.
b. More students from the upper group got the answer
correctly, hence, it has a positive discrimination of
5%
c. Students respond about equally to all alternatives,
an indication that they are guessing.
d. If the test item is well-written but too difficult,
reteach the material to the class.
4. Conclusion: Reject the item because it is very
difficult and the discrimination index is very poor, and
option A and B are not effective distracters.
Example 3. A class is composed of 50 students. Use
27% to get the upper and the lower groups. Analyze the
item given the following results. Option D is the correct
answer. What will you do with the test item?
1. Compute the difficulty index.
N = 6 + 4 = 10
N = 28
2. Compute the discrimination index
CUG = 6
CLG = 4
D = 14
3. Make an analysis about the level of difficulty,
discrimination and distracters.
a. Only 36% of the examinees got the answer correctly,
hence, the item is difficult.
b. More students from the upper group got the answer
correctly, hence, it has a positive discrimination of 14%
c. Modify options B and E because more students from
the upper group chose them compare with the lower
group, hence, they are not effective distracters because
most of the students who performed well in the overall
examination selected them as their answers.
d. Retain options A and C because most of the students
who did not perform well in the overall examination
selected them as the correct answers. Hence, options A
and C are effective distracters.
4. Conclusion: Revised the item by modifying options
B and E. d. Retain options A and C because most of
the students who did not perform well in the overall
examination selected them as the correct answers.
Hence, options A and C are effective distracters.
5. Conclusion: Revised the item by modifying options
B and E.
TEST RELIABILITY
 Reliability refers to the consistency with which it
yields the same rank for individuals who take the
test more than once (Kubiszyn and Borich, 2007).
That is, how consistent test results or other
assessment results from one measurement to
another. A test is reliable when it can be used to
predict practically the same scores when test
administered twice to the same group of students
and with a reliability index of 0.60 or above. The
reliability of a test can be determined by means of
Pearson Product Moment of Correlation,
spearman-Brown Formula, Kuder-Richardson
Formulas, Cronbach’s Alpha, etc.
FACTORS AFFECTING RELIABILITY OF A
TEST
1. Length of the test
2. Moderate item difficulty
3. Objective scoring
4. Heterogeneity of the student group
5. Limited time
METHODS OF ESTABLISHING RELIABILITY
OF A TEST
1. TEST-RETEST METHOD
 A type of reliability determined by administering
the same test twice to the same group of students
with any time interval between the tests. The results
of the test scores are correlated using the Pearson
Product Correlation Coefficient (r) and this this
2.

3.

4.

correlation coefficient provides a measure of
stability. This indicated how stable the test result
over a period.
EQUIVALENT/PARALLEL/ALTERNATE
FORMS
A type of reliability determined by administering
two different but equivalent forms of the test to the
same group of students in close succession. The
equivalent forms are constructed to the same set of
specification that is similar in content, type of items
and difficulty. The results of the test scores are
correlated using the Pearson Product Correlation
Coefficient and this correlation coefficient provides
a measure of the degree to which generalization
about the performance of students from one
assessment to another assessment is justified. It
measures the equivalence of the tests.
SPLIT-HALF METHOD
Administer test once and score two equivalent
halves of the test. To split the test into halves that
are equivalent, the usual procedure is to score the
even-numbered and the odd-numbered test item
separately. This provides two scores for each
student. The results of the test scores are correlated
using the Spearman-Brown formula and this
correlation coefficient provides a measure of
internal consistency. It indicates the degree to which
consistent results are obtained from two halves of
the test.
KUDER-RICHARDSON FORMULA
Administer the test once. Score the total test and
apply the Kuder Richardson (KR) formula. The
KR-20 formula is applicable only in situations
where
students’
responses
are
scored
dichotomously, and therefore, is most useful with
traditional test items that are scored as right or
wrong, true or false, and yes or no type. KR-20
formula estimates of reliability provide information
whether the degree to which the items in the test
measure is of the same characteristic, it is an
assumption that all items are of equal in difficulty.
Another formula for testing the internal consistency
of a test is the KR-21 formula, which is not limited
to test items that are scored dichotomously
RELIABILITY COEFFICIENT
 Reliability coefficient is a measure of the amount of
error associated with the test scores. Reliability
Coefficient has the following description:
(a) The range of the reliability coefficient is from 0 to
1.0;
(b) The acceptable range value is 0.60 or higher;
(c) The higher the value of the reliability coefficient,
the more reliable the overall test scores;
(d) Higher reliability indicates that the test items
measure the same thing.
INTERPRETING RELIABILITY COEFFICIENT
1. The group variability will affect the size of the
reliability coefficient. Higher coefficient results from
heterogeneous groups than from the homogeneous
groups. As group variability increases, reliability goes
up.
2. Scoring reliability limits test score reliability. If tests
are scored unreliable, error is introduced. This will limit
the reliability of the test scores.
3. Test length affects test score reliability. As the length
increases, the reliability tends to go up.
4. Item difficulty affects test score reliability. As test
items become very easy or very hard, the test’s
reliability goes down.
Using split-half method, is the test reliable? Show the
complete solution.
Example 1. Prof. Joel conducted a test to his 10
students in Elementary Statistics class twice after oneday interval. The test given after one day is exactly the
same test given the first time. Scores below were
gathered in the first test (FT) and second test (ST).
Using test-retest method, is the test reliable? Show the
complete solution.
Steps:
1. Use the Pearson Product Correlation Coefficient
Formula to solve for r
2. Find the reliability of the original test using the
formula:
3. Analysis:
The reliability coefficient using Brown formula is 0.50,
which is questionable reliability. Hence, the test items
should be revised.
Example 3. Ms. Tan administered a 40-item test in
English for her Grade VI pupils in UEPLES. Below are
the scores of 15 pupils, find the reliability using the
Kuder-Richardson formula.
Analysis: The reliability coefficient using the Pearson r
= 0.91 means that it has a very high reliability. The
scores of the 10 students conducted twice with one-day
interval are consistent. Hence, the test has a very high
reliability.
Example 2. Prof. Glenn conducted a test to his 10
students in his Chemistry class. The test was. given only
once. The scores of the students in odd and even items
below were gathered, (O) odd items and (E) even items.
Steps:
1. Solve the mean and the standard deviation of the
scores using the given table.
2. CONTENT VALIDITY.
 A type of validation that refers to the relationship
between test and the instructional objectives,
establishes content so that the test measures what is
supposed to. measure. Things to remember about
validity:
a. The evidence of the content validity of a test is found
in the Table of specification.
b. This is the most important type of validity for a
classroom teacher.
c. There is no coefficient for content validity. It is
determined by experts judgmentally, not empirically.
2. Solve for Standard Deviation using the formula:
3. Solve for the Mean using the formula:
4. Solve the reliability coefficient using the KuderRichardson formula
5. Analysis: The reliability coefficient using KR-21
formula is 0.90 which means that the test has a very
good reliability. Meaning, the test is very good for
a classroom test.
TEST VALIDITY
 Validity is concerned whether the information
obtained from an assessment permits the teacher to
make a correct decision about a student’s learning.
This means that the appropriateness of score-based
inferences or decisions made are based on the
students’ test results. Validity is the extent to which
a test measures what it is supposed to measure.
TYPES OF VALIDITY
1. FACE VALIDITY
 It is the extent to which a measurement method
appears “on its face” to measure the construct of
interest. Face validity is at best a very weak kind of
evidence that a measurement method is measuring
what it is supposed to. One reason is that it is based
on people’s intuitions about human behavior, which
are frequently wrong. It is also the case that many
established measures in psychology work quite well
despite lacking face validity.
3. CRITERION-RELATED VALIDITY
 A type of validation that refers to the extent to
which scores from a test relate to theoretically
similar measures. It is a measure of how accurately
a student’s current test score can be used to estimate
a score on a criterion measure, like performance in
courses, classes, or another measurement
instrument. For example, the classroom reading
grades should indicate similar levels of
performance as Standardized Reading test scores.
a. Concurrent validity
 The criterion and the predictor data are collected at
the same time. This type of validity is appropriate
for tests designed to assess a student’s criterion
status or when you want to diagnose student’s
status; it is a good diagnostic screening test. It is
established by correlating the criterion and the
predictor using Pearson Product Correlation
Coefficient and other statistical tools correlations.
b. Predictive validity
 A type of validation that refers to a measure of the
extent to which student’s current test result can be
used to estimate accurately the outcome of the
student’s performance at later time. It is appropriate
for tests designed to assess students’ future status on
a criterion. Regression analysis can be sued to
predict the criterion of a single predictor or multiple
predictors.
4. CONSTRUCT VALIDITY
 A type of validation that refers to the measure of the
extent to which a test measures a theoretical and
unobservable variable qualities such as intelligence,
math achievement, performance anxiety, and the
like, over a period of time on the basis of gathering
evidence. It is established through intensive study
of the test or measurement instrument using
convergent/divergent validation and factor analysis.
There are other ways of assessing construct validity
like test’s internal consistency, developmental
change and experimental intervention.
a. Convergent validity is a type of construct validation
wherein a test has a high correlation with another test
that measures the same construct.
b. Divergent validity is type of construct validation
wherein a test has low correlation with a test that
measures a different construct. In this case, a high
validity occurs only when there is a low correlation
coefficient between the tests that measure different
traits.
c. Factor analysis assesses the construct validity of a
test using complex statistical procedures conducted
with different procedures.
IMPORTANT THINGS TO REMEMBER ABOUT
VALIDITY
1. Validity refers to the decisions we make, and not to
the test itself or to the measurement.
2. Like reliability, validity is not an all-or-nothing
concept; it is never totally absent or absolutely perfect.
3. A validity estimate, called a validity coefficient,
refers to specific type of validity. It ranges between 0
and 1.
4. Validity can never be finally determined; it is specific
to each administration of the test.
FACTORS AFFECTING THE VALIDITY OF A
TEST ITEM
1. The test itself.
2. The administration and scoring of a test.
3. Personal factors influencing how students’ response
to the test.
4. Validity is always specific to a particular group.
VALIDITY COEFFICIENT
 The validity coefficient is the computed value of the
rxy. In theory, the validity coefficient has values like
the correlation that ranges from 0 to 1. In practice,
most of the validity scores are usually small and
they range from 0.3 to 0.5, few exceed 0.6 to 0.7.
Hence, there is a lot of improvement in most of our
psychological measurement. Another way of
interpreting the findings is the squared correlation
coefficient (rxy)2, this is called coefficient of
determination. Coefficient of determination
indicates how much variation in the criterion can be
accounted for by the predictor
Coefficient of determination = (r)2 = (0.94)2=
88.36%
Interpretation: The correlation coefficient is 0.94, which
means that the validity of the test is high, or 88.36% of
the variance in the students’ performance can be
attributed to the test.
UNIT 4: ANALYSIS AND INTERPRETATION OF
ASSESSMENT RESULTS
NORMAL DISTRIBUTION OR BELL SHAPED
CURVE
METHODS OF THE PRESENTATION OF DATA
Presentation of Data is described as an organized of
information such as measurements, numbers, names,
observations, etc. in a certain way.
TEXTUAL PRESENTATION
 This is the technique in a graph form. In this
technique, it is does not necessary mean that the
presentation contains of words only but figures can
also be utilized as part of the presentation.
TABULAR PRESENTATION
 This is another way in presenting data. In this
technique, the data are summarized using tables. A
table usually used is on the Frequency and
Percentage Distribution. It is a table presenting the
frequency and percentage sharing of nominal data.
GRAPHICAL PRESENTATION
 There are many types of graphs such as line graph,
bar graph, pictograph, pie chart, etc.
DIFFERENT
KINDS
PRESENTATION
OF
GRAPHICAL
 LINE GRAPH. It shows associations between two
or more sets of quantities. In this technique, the
values are plotted using dots which are called
“markers” to be connected together by line
segments.
SKEWED DISTRIBUTION OF TEST SCORE
 Positively Skewed Distribution (mean>median>
mode)
 Negatively
Skewed
Distribution
(mode>median>mean)
 Skewness is the degree of asymmetry, or departure
from symmetry of a distribution.
 Skewed to the right: (positive skewness): if the
frequency curve of a distribution has a longer “tail”
to the left of the central maximum than to the right.
Most scores are below the mean.
 Skewed to the left: (negative skewness): if the
frequency curve of a distribution has a longer “tail”
to the right of the central maximum than to the left.
Most scores are above the mean and there are
extremely low scores.
 BAR GRAPH. It is graphical method in which
each value in the data is represented by rectangular
bars. The length if the bars show the measure of a
certain value which its width has a fixed size.
 PICTOGRAPH. This is a graphical technique that
express its meaning through its pictorial similarity
to a physical object. Each object used in pictograph
stands for corresponding measure.
 PIE CHART. This is the type of graphical
presentation in which a circle (or sometimes a
cylinder) is divided into several parts with each
parts typifying the categories of the data.
KURTOSIS
 Kurtosis: is the degree of peakedness of a
distribution, usually taken relative to a normal
distribution.
 Leptokurtic: distribution having a relatively high
peak.
 Platykurtic: a distribution having flat-topped
 Mesokurtic: a distribution which is moderately
peaked.
Examples of continuous variables are: Height, Mass,
Distance, Weight, Temperature
Continuous variables can be further categorized as
either INTERVAL or RATIO variables
 INTERVAL VARIABLES: are variables for which
their central characteristic is that they can be
measured along a continuum and they have a
numerical value.
 RATIO VARIABLES: are interval variables, but
with the added condition that 0 (zero) of the
measurement indicates that there is none of that
variable.
MEASURE OF CENTRAL TENDENCY
MEAN
 The most commonly used measure of central
tendency is the mean.
B.
QUANTITATIVE
INTERPRETATION
ANALYSIS
AND
1. LEVELS OF MEASUREMENT
2. MEASURES OF CENTRAL TENDENCY
3. MEASURES OF VARIABILITY
4. MEASURES OF RELATIVE POSITION
DEFINITION OF TERMS
 CATEGORICAL VARIABLES are also known as
qualitative variables.
Examples of categorical variables:
 GENDER (2 categories: male and female);
 MARITAL STATUS (3 categories: Single, married,
separated);
 PHYSICAL ACTIVITY LEVEL (e.g., 4 categories:
sedentary, low, moderate, and high).
A categorial variable can be further categorized as
NORMAL, DICHOTOMOUS, OR ORDINAL.
 NORMALVARIABLE: if the categories cannot be
ordered or ranked.
 DICHOTOMOUS VARIABLES: are nominal
variables with only two categories.
 ORDINAL VARIABLE: if the categories can be
ranked or ordered.
CONTINUOUS VARIABLES are also known as
quantitative variables.
 The arithmetic mean, or simply the mean is the
sum of all the given values or items in a
distribution divided by the number of
observations.
 The mean is commonly called the average. It is
̅ (reads "x bar").
denoted by 𝑿
 There are some cases when values are given more
importance than others. The mean derived in this
case is known as the weighted arithmetic mean or
weighted mean.
MEDIAN
 The median is the middle value in the distribution
after arranging the data either in ascending or
descending order.
 Half of the observations belong to the higher 50%
of the group, while the other half belongs to the
lower 50% of the group.
 It is denoted by "md" (reads "median"). Or 𝑥̃
 Midpoint of a distribution;
 Used when the distribution is skewed/ most stable
MODE
 The mode is the simplest measure of central
tendency. It can be easily identified by inspection
by getting the score or item which occurs most
frequently.
 A set of data with only one mode is called
unimodal. A set of data with two modes is bimodal,
with three is trimodal, and with many modes,
multimodal.
 In some instances, the mode may not even exist at
all.

MEASURES OF VARIABILITY
 Indicate or describe how spread the scores are.
 The larger the measure of variability the more
spread the score are and the group is said to be
heterogeneous; the smaller the less spread the
scores are and the group is said to be homogeneous.
Opposite of the mean, unreliable/unstable;
 Used as quick description in term of average/typical
performance of the group.
COMPUTATION OF
UNGROUPED DATA
THE
MEAN
FOR
ARITHMETIC MEAN
̅ =
Formula: 𝑿
𝜮𝑿
𝒏
Example: The following are the ages of six senior
citizens: 67, 72, 63, 65, 70, 68
INTERPRETATION
 The two sets of scores have the same mean, median,
and mode. But if you will look closely at the scores,
you will notice that the values in set A are less
spread compared to the values in set B.
WEIGHTED MEAN
The formula is:
ΣwX
X = Σw
where: X = represents each of the item values
w = represents the weight of each item value
Compute the weighted mean grade
 This shows that computing the measures of central
tendency will not give us all the features or
characteristics of a given set of data.
 Other measures can provide other information
about the data, and these are the measures of
variability.
 The measures of variability tell us how the data are
spread out or dispersed around the center.
 The values are more clustered around the center if
the computed measure of variability is small.
COMPUTATION OF
UNGROUPED DATA
THE
MEAN
FOR
WEIGHTED MEAN
𝑥̅ =
Σ𝑤𝑋 3(1.5) + 5(1.25) + 3(1.75) + 3.(2.0) 22
=
=
∑𝑤
14
3+5+3+3
= 1.57
Interpretation: The average grade of the student for the
four subjects is 1.57.
 On the other hand, a high measure of variability
indicates that the values fall farther from the center.
 Measures of variability are also called measures of
variation and measures of dispersion.
 The most common measures of variability are the
following:
1.
2.
3.
4.
5.
Range
Quartile deviation or semi-interquartile range,
Mean or average deviation,
Variance, and
Standard deviation.
RANGE
 The range is the simplest measure of variability but
the most unstable because its value quickly
fluctuates when there is a change in either the
lowest or highest value. It is easily affected by
outliers (extremely small or extremely large
values).
 It does not give the dispersion or the spread of the
values between the highest and the lowest value.
 The range is the difference between the highest and
the lowest value.
The formula is: H-L =R
INTERQUARTILE RANGE
 A measure of variability that is not influenced by
the presence of outliers in the data is the
interquartile range. This measure considers the
spread of the middle 50 percent of data points
falling between Q1 and Q3. It gives the spread of
the scores around the median (Q2). The
interquartile range (IQR) is simply the difference
between the third and first quartiles corresponding
to
the
75th
and
25th
percentiles.
The formula is:
MEAN DEVIATION (MD)
Interquartile Range = 3rd Quartile − 1st Quartile
IQR = Q3 − Q1 or IQR = P75 − P25
 A Z-score expresses this value in standard deviation
units.
 The mean deviation (MD) or the average
deviation (AD) is the sum of the absolute
deviations of each value from the mean divided by
the
total
number
of
observations in the distribution.
 This measure shows the spread of the distribution
around the mean.
STANDARD SCORE
 A measure of relative position which is appropriate
when the data represent an interval or ratio scale; a
z score express how far a score is from the mean in
terms of standard deviation units; allows all scores
from different tests to be compared; In cases of
negative values transform z scores to T scores
(multiply z score by to plus 50)
Z-VALUE
 A raw score by itself is rather meaningless.
 What gives the score meaning is its deviation from
the mean
𝑧=
𝑋−𝑋̅
𝜎
𝑋 = Score
𝑋̅ = Mean
𝜎 = SD = Standard Deviation
EXAMPLE
QUARTILE DEVIATION
 The quartile deviation is also called the semiinterquartile
range.
It
is
the
dispersion of the middle 50% of the data. It tells
something
about
how
data
is
dispersed
around
the
median.
It is computed as one half the difference between
the
third
and
first
quartiles.
In
the formula, we have
Quartile Deviation:
𝑃 −𝑃
𝐼𝑄𝑅
QD: 75 2 25 = 2
𝑄3 −𝑄1
𝐼𝑄𝑅
= 2
2
 A correlation coefficient tells us the size
(magnitude) and direction (positive or negative) of
the relationship between two variables. It can range
form −1.0 𝑡𝑜 + 1.0. The closer a coefficient to
−1.0 𝑡𝑜 + 1.0 the higher or stronger the
relationship.
Positive correlation means.
1. High scores in Test A are associated with high
scores in Test B.
2. Low score in Test A is associated with low score in
Test B.
Negative correlation means:
1. High scores in Test A are associated with low scores
in Test B.
2. Low scores in Test A are associated with high scores
in Test B.
Below shows the coefficients of correlation between
two variables as indicated by numerical values and their
corresponding interpretation
The student who got a score of 76 is -1.5SD below the
mean. And there are 6.68% students got a score below
76.
T-SCORES
 Tells the location of a score in a normal distribution
having a mean of 50 and a standard deviation of 10.
𝑇 = 50 + 10𝑧
Example:
A z score of 1.27 =
𝑇 = 50 + 10(1.27) = 50 + 12.70 = 62.70 = 63
CORRELATING TWO VARIABLES
 There are times that we want to know if a student
who got score in reading will also obtain high score
in mathematics. When we are concerned with the
relationship between two measures, we are talking
about correlation. To determine the extent of such
relationship we use a correlation coefficient
(symbolized by 𝑟)
KUDER-RICHARDSON FORMULA 20
 One way to determine whether the test items are
homogenous or heterogenous is through the use of
Kuder-Richardson Formula 20(KR20)
The formula in computing data through KuderRichardson Formula 20 is given below.
∑ 𝑝𝑞
𝑛
𝑟𝑡𝑡 =
(1 −
)
𝑛−1
𝑆𝐷 2
𝑟𝑡𝑡 = reliability of the total test
𝑛 = number of items
𝑝 = proportions/percentage of passing an item
𝑞 = proportions/percentage of failing an item
∑ 𝑝𝑞 = sum of the product of 𝑝 and 𝑞
𝑆𝐷 = Standard deviation of the total scores.
EXAMPLE
𝑟𝑡𝑡 =
∑ 𝑝𝑞
𝑛
(1 −
)
𝑛−1
𝑆𝐷 2
𝑆𝐷 = 2.8
10
1.9117
𝑟𝑡𝑡 = 10−1 (1 − 2.82 )
1.9117
𝑟𝑡𝑡 = 1.11 (1 − 7.84 )
𝑟𝑡𝑡 = 1.11 (1 − 0.24)
𝑟𝑡𝑡 = 1.11 (0.76)
𝑟𝑡𝑡 = 0.84
very high correlation
The coefficient of correlation using KR20 suggests that
the test items are homogenous.
POINTS TO REMEMBER
1. Correlation is the relationship between two
variables characterized by its magnitude and
direction.
2. A correlation coefficient is a numerical value which
gives the size and direction of the relationship
between two variables.
3. The direction of the correlation may either be
positive or negative.
4. The magnitude (or size) of correlation may range
from negligible to perfect relationship.
5. Two statistical tools used to compute the coefficient
of correlation are the Pearson Product Moment
Correlation Coefficient and Kuder-Richard
Formula 20.
FEEDBACKING
AND
ASSESSMENT RESULTS
A. Qualitative Evaluation
B. Constructive Feedbacking
1. Principles and characteristics
2. Strategies
- Written feedback
- Oral feedback
C. Self-assessment
D. Peer assessment
COMMUNICATING
A. QUALITATIVE EVALUATION
 Qualitative evaluation provides you with the ability
to gain an in-depth understanding of a program or
process.
 It involves the “why” and the “how” and allows a
deeper look at issues of interest and to explore
nuances.
 Collecting qualitative evaluation data requires the
use of different tools than if you were focused only
on gathering quantitative data.
 Some commonly used data collection methods for
qualitative data include interviews, focus groups,
document/material review, and ethnographic
participation/observation.
B. CONSTRUCTIVE FEEDBACKING
 Provide positive and constructive feedback to guide
students’ learning and behavior: The purpose of
feedback is to guide student learning and behavior
and increase student motivation, engagement, and
independence, leading to improved student learning
and behavior.
 Effective feedback must be strategically delivered
and goal directed; feedback is most effective when
the learner has a goal and the feedback informs the
learner regarding areas needing improvement and
ways to improve performance.
 Feedback may be verbal, nonverbal, or written, and
should be timely, contingent, genuine, meaningful,
age appropriate, and at rates commensurate with the
task and phase of learning (i.e., acquisition, fluency,
maintenance). Teachers should provide ongoing
feedback until learners reach their established
learning goals
PEER AND SELF-ASSESSMENT
 Peer and self-assessment, where students assess
each other and themselves, can encourage students
to take greater responsibility for their learning, for
example, by encouraging engagement with
assessment criteria and reflection of their own
performance and that of their peers. Through this,
students can learn from their previous mistakes,
identify their strengths and weaknesses and learn to
target their learning accordingly.
 Getting students to become more active in their
learning in this way can help to alter the perception
of learning as being a passive process whereby
students listen to you and absorb the information in
order to regurgitate during a subsequent
assignment.
 If students are participants rather than 'spectators',
they are more likely to engage with their learning
IMPROVING TEST ITEMS: ITEM ANALYSIS
ASSESSMENT DEVELOPMENT CYCLE
ITEM ANALYSIS
 Once scores of students/test takers are obtained, the
items are now ready for item analysis.
 Item analysis is a procedure used to identify good
items by determining the index of difficulty and the
index discrimination.
 Index of difficulty is the portion of students/test
takers who answered the item correctly.
 Index of discrimination is the extent of which a test
item can differentiate between good performers and
poor performers
 One method that can be employed for item analysis
is the U-L Index Method.
 The most commonly used U-L Index Method is the
Upper and Lower 27%.
The steps are as follows:
1. Score the test papers and arrange the total scores from
highest to lowest.
2. Segregate the top and bottom 27% of the papers.
3. Tally the correct answers to each item by each
student/test takers in the upper 27% group.
4. Repeat Step 3 but this time consider the lower 27%
5. Get the percentage of the upper group that obtained
the correct answer and call this U.
6. Repeat Step 5 but this time consider the lower group
and call this L.
7. Get the average percentage of U and L percentages.
8. Get the difference between U and L percentages.
 A good or retained item must have not acceptable
index of difficult and discrimination index. The
acceptable index of difficulty ranges from 0.41 .60
while the acceptable index of discrimination ranges
from +.20 to 1.00
 A fair or revised item contains either unacceptable
difficulty or discrimination index.
 A poor or rejected item must possess both
unacceptable difficulty and discrimination indices.
It has to be discarded right away.
The table below shows the result of a tryout test in
Reading 6. Study the data presented in the table and
answer the questions that follow. N=50
The table below shows the result of a tryout test in
Reading 6. Study the data presented in the table and
answer the questions that follow. N=50
The table below shows some fair items that need
revision
Table of Nonplausible of Distracters on the result of a
tryout test in Reading 6
It shows that option D in item number 4 was chosen by
7 percent of the students in the lower group but none (0)
in the upper group. If less than 3 percent of both/either
group did not select that particular option, then that
alternative must be revised because it is not attractive or
plausible
MODIFIED ITEM ANALYSIS FOR CRITERIONREFERENCED TEST
 There is another way to analyze test items. This is
by comparing the percentage answering each item
correctly on both pretest and posttest. It is assumed
that most of students should obtain a low score on a
pretest and a high score on a post test. If this
happens, we can say that there is an improvement in
the performance of students in a certain subject of
learning area.
The steps in comparing the percentage answering
each item correctly on both pretest and posttest are
as follows:
1. Get the percentage of the students passing on a
pretest and the percentage of students passing each item
on a posttest. Use the formula given below.
𝑝�𝑒�𝑟�𝑐�𝑒�𝑛�𝑡�𝑎�𝑔�𝑒� = 𝑁�𝑜�.� 𝑜�𝑓� 𝑠�𝑡�𝑢�𝑑�𝑒�𝑛�𝑡�𝑠� 𝑤�ℎ𝑜�
𝑎�𝑛�𝑠�𝑤�𝑒�𝑟�𝑒�𝑑� 𝑡�ℎ𝑒� 𝑖�𝑡�𝑒�𝑚� 𝑐�𝑜�𝑟�𝑟�𝑒�𝑡�𝑙�𝑦� 𝑇�𝑜�𝑡�𝑎�𝑙�
𝑛�𝑢�𝑚�𝑏�𝑒�𝑟� 𝑜�𝑓� 𝑠�𝑡�𝑢�𝑑�𝑒�𝑛�𝑡�𝑠� 𝑤�ℎ𝑜� 𝑡�𝑜�𝑜�𝑘� 𝑡�ℎ𝑒�
𝑡�𝑒�𝑠�𝑡�
2. Subtract the percentage obtained on a pretest from
that on a posttest. The more positive the difference is
obtained; the more effective instruction is on that
particular objective being answered
Take note that Item 2 shows no change in performance
of students before and after instruction. Even without
instruction, the students already mastered the particular
objective.
 Item 4 has the highest percentage of difference
(87%). It registered that a very marked
improvement has taken place among the students in
that particular objective before and after instruction.
Item 1 and 3 also register marked improvement in
the performance of the students before and after
instruction. Item 5 shows that only a little
improvement is noted in the performance of the
students
 Another approach in modified item analysis is to
determine the percentage of item answered in both
pretest and posttest. This is finding the number of
items each student failed on the pretest but passes
on the posttest.
The steps in using this approach are as follows:
1. Determine the number of items each student
answered incorrectly on the pretest but answered
correctly on posttest.
2. Get the sum of the counts in Step 1 for all
examinees. Then divide by the number of
examinees.
3. Divide the result from Step 2 by the number of the
test.
4. Multiply the quotient obtained from Step 3 by 100.
POINTS TO REMEMBER
1. Item analysis is one way to improve test items.
2. Item analysis is the process of determining good
test items.
3. The U-L method employing 27 percent is the
common way to analyze items quantitatively
4. Moderately difficult items are those with
acceptable index of difficulty and discrimination
index.
5. Moderately difficult items tend to increase the
test validity and reliability.
6. A modified item analysis determines the
percentage of items answered by examinees in
both pretest and posttest
T-TEST FOR PRETEST AND POSTTEST