1. Analyzing and Using
Test Item Data

2.  It refers to the process of examining
the students response to each item
in the test.

3. Purposes and Elements of Item Analysis
1. To select the best available items for the final form of the
test
2. To identify the structural defects in the items
3. To detect learning difficulties of the class as a whole; and
4. To identify the areas of weaknesses of the students in
need of remediation

4. Characteristics of an item
 Desirable characteristics can be
retain for subsequent use
 Undesirable characteristics is either
to revised or rejected

5. Three main Elements in an Item-
Analysis
1.Difficulty level of the items
2. Discrimination power of each item
3. Examination of the effectiveness of
distracters

6.  Difficulty index - refers to the
proportion of the number of students
in the upper and lower groups who
answered an item correctly.
Therefore it can be obtain by
adding the proportion in the upper
and lower groups who got the item
right and divide it by 2.

7.  Index of Discrimination- it is the
percentage of high-scoring
individuals responding correctly vs.
the number of low-scoring
individuals responding correctly to an
item.

8. • Maximum Positive Discriminating
Power of an item – it is indicated by an
index of 1.00 and is obtain when all the
groups answered correctly and no one in
the lower group did.
• Zero Discriminating power – is obtain
when an equal number of students in both
groups got the item right
• Negative Discriminating Power of an
item – it is obtain when more students in
the lower group got the item right than in
the upper group.



9. Measures of attractiveness.
 To measure the attractiveness of
the incorrect option in a multiple
choice test, we count the number of
the students who selected the
incorrect option in both the upper
and lower groups. The incorrect
options should attract less of the
upper group than the lower group.

10. PREPARING DATA FOR ITEM ANALYSIS
1. Arrange test scores from highest to lowest.
2. Get one-third of the papers from highest
scores and the other one-third from the
lowest scores.
3. Record separately the number of times each
alternative was chosen by the students in
both groups.
4. Add the number of correct answer to each
item made by the combined upper and
lower groups.

11. 5. Compute the index of difficulty for each item,
index of difficulty = No. of students responding correctly to an item x 100
Total no. of students in the upper and lower groups
6. Compute the index of discrimination
index of discrimination=Upperncr – Lowerncr
No. of students per group

12. Difficulty of a test item can be interpreted with the
use of...
Range Difficulty Level
20 & below very difficult
21-40 difficult
41-60 average
61-80 easy
81-above very easy

13. Discrimination Index
Range Verbal Description
0.40 and above very good item
0.30-0.39 good item
0.20-0.29 fair item
0.09-0.19 poor item

14. CORRELATING TEST SCORES
CORRELATION- the relationship
between two or more paired-factors
or two or more sets of tests scores
CORRELATION COEFFICIENT- a
numerical measure of the linear
relationship between two factors on
sets of scores

15. Obtained Correlation coefficient
can be interpreted with the use of….
Correlation Coefficient Degree of Relationship
0.00-0.20 negligible
0.21-0.40 low
0.41-0.60 moderate
0.61-0.80 substantial
0.81-1.00 high to very high

16. Pearson’s Product-Moment Correlation
1. Compute the sum of each set of scores (SX.SY).
2. Square each score and sum the squares (SX2
,SY2 ).
3. Count the number of scores in each group (N).
4. Multiply each X score by its corresponding Y
score.
5. Sum the cross product of X and Y (SXY).
6. Calculate the correlation, following the formula:

17. Spearman Rho
1. Rank the scores in distribution X,
giving the highest score a rank of 1.
2. Repeat the process for the scores in
distribution Y.
3. Obtain the difference between the
two sets of ranks (D).
4. Square each of these differences
and sum up squared differences
(SD2 )

18. 5. Solve for Rho following the formula:
Rho=1-{6 SD2 }
{N3 –N}
Where: rho= rank- order correlation
coefficient
D= difference between paired ranks
SD2 = sum of squared differences
between paired ranks
N= No. of paired ranks

19. Organizing Test Scores for
Statistical Analysis
1.Organizing test scores by ordering
2.Organizing test scores by ranking
3.Organizing test scores through a
stem- and leaf plot
4.Organizing data by means of a
frequency distribution

20. Preparing Single Value Frequency
Distribution
1. Arrange the scores in descending order.
List them in the X column of the table.
2. Tally each score in the tally column.
3. Add the tally marks at the end of each
row. Write the sum in the frequency
column.
4. Sum up all the row total tally marks
(N=___).

21. Shapes of the frequency Polygons
1. Normal- bell- shaped curve.
2. Positive skewed- most scores are
below the mean and there are
extremely high scores. (mean is
greater than the mode)
3. Negatively skewed- most scores are
above the mean and there are
extremely low scores. (mean is
lower than the mode).

22. 4. Leptokurtic- highly peaked and the
tails are more elevated above the
baseline.
5. Mesokurtic- moderately peaked
6. Platykurtic- flattened peak
7. Bimodal curve- curve with two peaks
or mode.

23. 8. Polymodal curve- curve with three or
more modes
9. Rectangular Distribution- there is no
mode

24.  Skewness- degree of symmetry of
the scores
 kurtosis – degree of peakness or
flatness of the distribution curve

25.  Sk= 3( M –Md)
SD
K= Q
(P90 – P10)
• Normal distribution – 0.263
• Platykurtic - > 0.263
• Leptokurtic - < 0.263

26. Organizing Test Scores
for Statistical Analysis

27. Organizing Test Scores By
Ordering
 Ordering refers to the numerical
arrangement of numerical
observations or measurements.
There are two ways of ordering:
1. Ascending Order
2. Descending Order

28. the following are the scores obtained
by 10 students in their quizzes in
English for the first grading students.
A B C D E F G H I J
110 130 90 140 85 87 115 125 95 135

29. ASCENDING AND DESCENDING
ORDER respectively
85 87 90 95 110 115 125 130 135 140
140 135 130 135 125 110 95 90 87 85

30. Organizing test scores by
ranking
 Ranking is another way by which test
scores can be organized.
 It is process of determining the
relative position of scores, measures
of values based on magnitude,
worth, quality, or importance,

31. Steps in ranking test scores:
 Arrange the test scores from highest
to lowest
 Assign serial number for each score.
 Assign the rank of 1 to the highest
score and the lowest rank to the
lowest score.
 In case there are ties, get the
average of the serial numbers of the
tied scores.
R= ( SN1 + SN2 + SN3 .... SN N)

32. Example: Rank the following scores
obtained by 20 ist year high school
students in spelling.
15 the rank of 12, 8,7, and
Find 14 10 9 8
8 7 6 2 4
4 8 7 8 10
9 14 12 4 6

33. Organizing Test Scores Through A
stem and Leaf Plot
 It is a method of graphically sorting
and arranging data to reveal its
distribution.
 It is a method of organizing a scores,
a numerical score is separated into
two parts, usually the first one or
two digits and the other digits.
 The stem is the first leading digit of
the scores while the trailing digit is
the leaf

34. Score SN Rank Score SN Rank
s s
15 1 1 8 11 10.5
14 2 2.5 8 12 10.5
14 3 2.5 7 13 13.5
12 4 4 7 14 13.5
10 5 5.5 6 15 15.5
10 6 5.5 6 16 15.5
9 7 7.5 4 17 18
9 8 7.5 4 18 18
8 9 9.5 4 19 18
8 10 9.5 2 20 20

35. Procedures:
 Split each numerical score or value into
two sets of digit. The first or leading set
of digits is the stem, and the second or
trailing set of digits is the leaf
 List all possible stem digits from lowest
to highest.
 For each score in the mass of data,
write down the leaf numbers on the line
labelled by the appropriate stem
number

36. Illustrate the stem and leaf plot on
the following periodical test results
in biology.
30 74 80 57 32
31 77 82 59 90
33 46 65 49 92
42 50 68 48 57

37. Organizing Data by means of
frequency distribution
 Preparing Single value Frequency
Distribution
1. Arrange the scores in descending
order. List them in the x column of
the table.
2. Tally each score in the tally column.
3. Add the tally marks at the end of
each row. Write down the sum in the
frequency column.
4. Sum up all the row total tally marks

38. Prepare a single value frequency
distribution for the spelling test
scores of grade 3 pupils
14 2 6 8 8 6 6 9 8 6
4 2 14 9 4 6 2 4 14 4
5 6 3 6 6 10 10 4 3 8

39. Preparing Group Frequency
Distribution
 Steps
 Find the lowest and the highest score.
 Compute the range.
 Determine the class interval
 Determine the score at which the
lowest interval should begin.
 Record the limits of all class interval
 Tally the raw scores in the appropriate
class interval
 Convert each tally to frequency.

40. Setting the class boundaries and
class limits
 Class boundary is the integral limit of
a class. These integral limit should
be apparent or real.
• The apparent limits of a class are
comprised of an upper and lower limit
 Class mark is the midpoint of a class
in a grouped frequency distribution.
• It is used when the potential score is to
be represented by one value if other
measures are to be calculated

41. Derived Frequencies From
Grouped Frequency Distribution
 Relative frequency distribution
indicates what percent of scores falls
within each of the classes.
RF = ( F/N) 100
.

42. Computation of relative
frequency
Class frequenc Relative
interval y Frequen
cy
75-77 1 2.5
72-74 3 7.5
69-71 5 27.5
66-68 12 30
63-65 11 25.5
60-62 8 20
40 100

43. Cumulative Frequency distribution indicates the
number of scores that lie above or below a class
boundary
Types:
1. <cf- are obtained by adding the
successive frequencies from the bottom
to the top of the distribution
2. >cf- are obtained by adding the
frequencies from top to bottom

44. Computation of <cf and >cf
Class frequen <cf >cf
interval cy
75-77 1 40 1
72-74 3 39 4
69-71 5 36 9
66-68 12 31 21
63-65 11 19 32
60-62 8 8 40
40

45. Measures of Central
Tendency

46. 1. MEAN
 It is often called arithmetic average.

47. 2. Median
 It is the score that occurs at a point
on the scale below which 50 % of the
scores fall and above which the other
50 % of the scores occur.

48. 3. Mode
 It is the most recurring score in a set
of test scores

49. Measure of Dispersion
To determine the size of the
distribution of the test scores
or the portion of it.

50. Range
 It is the simplest and the easiest
measure of dispersion.
 It simply measure how far the
highest score from the lowest score
 It is considered as the least
satisfactory measure of dispersion
 For ungrouped data we have:
R= Hs - Ls

51. Example
 Determine the range of the test
score of nine students in a
community development course test.
Sol: R = 43-19 = 24

52. For Grouped Data
R= Hmdpt – Lmdpt

53. Compute the range of the following
frequency distribution of the test
scores in Math
Class interval Frequency
60-64 1
55-59 5
50-54 4
45-49 5
40-44 7
35-39 8
30-34 4
25-29 3
20-24 2
15-19 1

54. R = 62- 17
= 45

55. Interquartile range
 It is the range of the score of
specified group usually the middle
50% of the cases lying between Q1
and Q3
 IQR = Q3-Q1

56. Example
 Determine the interquartile range of
the test score of nine students in a
community development course test.
Sol: R = 38-23 = 15

57. For Grouped Data:
 IQR = Q3-Q1

58. Compute the inter quartile range of
the following frequency distribution
of the test scores in Math
Class interval Frequency
60-64 1
55-59 5
50-54 4
45-49 5
40-44 7
35-39 8
30-34 4
25-29 3
20-24 2
15-19 1

59.  IQR = 49.5 – 34.5
= 15

60. The quartile Deviation
 It devides the difference of the 3rd
and 1st quartile into two.
 It is the average distance from the
median to the two quartiles
 QD = Q3- Q2
2

61. Example
 Determine the quartile deviation of
the test score of nine students in a
community development course test.
Sol: 15 / 2 = 7.5

62. Compute the quartile deviation of
the following frequency distribution
of the test scores in Math
Class interval Frequency
60-64 1
55-59 5
50-54 4
45-49 5
40-44 7
35-39 8
30-34 4
25-29 3
20-24 2
15-19 1