UNIVERSITY OF PRETORIA B.Ed (Hons) Computer Integrated Studies CIA 722
TEST AND ITEM ANALYSIS REPORT
BY A.M.C. NOLAN 96006758
TEST AND ITEM ANALYSIS REPORT
TABLE OF CONTENTS
1. 2. 3. 3.1. 3.2. 3.3. 4. 4.1. 4.2. 5. 6. 7.
List of tables List of figures Introduction Purpose of the report Test analysis Descriptive statistics Frequency graph Test reliability Item analysis Difficulty indices Discrimination indices Conclusion Bibliography Appendix
Test & Item Analysis Report A.M.C. Nolan 96006758
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LIST OF TABLES
Table 1 Table 2 Table 3 Table 4 Table 5 Table 6 Table 7
Simple Frequency Distribution Frequency Data Grouped Frequency Distribution Measures of Central tendency Reliability data Item difficulty index Discrimination index
Test & Item Analysis Report A.M.C. Nolan 96006758
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LIST OF FIGURES
Figure 1 Figure 2 Figure 3
Frequency Histogram Frequency Polygon Cumulative Frequency Ogive Curve
Test & Item Analysis Report A.M.C. Nolan 96006758
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1.
INTRODUCTION
A test was given to 25 students to complete. After completion the data was captured and analysed. The test was analysed to measure the reliability of the test. The different responses was also analysed to measure the discrimination and difficulty. After the analysis the test will be improved by using the different indices.
2.
PURPOSE OF THE REPORT
The purpose of this report is to disseminate information on the test analysis of a test given to 25 students. The test consisted of 20 questions, each with 3 distracters and one answer. The responses of the test was also analysed and the information is given in part 4 of this report.
3.
TEST ANALYSIS
For the purpose of this analysis all the final test values of the students were rounded off, to eliminate the decimals. The rest of the values ware rounded to the second decimal. This made all the calculations easier and the interpretation much better. All the students’ marks were used to calculate the central tendency. Please note that 4 of the students did not complete all the questions. Their marks were calculated using only the number of questions answered.
3.1
DESCRIPTIVE STATISTICS
When the data was tabulated in a simple frequency distribution (Table 1) the large amount of variation in test scores it became clear that the interpretation of the data would be difficult. The data was then tabulated in a grouped frequency distribution (Table 2).
Test & Item Analysis Report A.M.C. Nolan 96006758
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Table 1 – Simple Frequency Distribution Score f 100 90 85 75 70 65 60 55 50 45 40 30 15
2 3 3 1 2 4 1 2 2 1 1 2 1 25
The raw scores were categorized into 8 intervals. The intervals were calculated by using the range of scores. See Table 2 for the values.
Table 2 – Frequency Data H L Range No intervals Interval
100 15 85* 8.5 10
*R (range of scores) = H (highest score) – L (lowest scores) Each interval consists of 3 values LV (lower value of the interval), UV (upper value of the interval) and MV (middle value of the interval). The intervals with their different values and frequency are summarized in Table 3.
Test & Item Analysis Report A.M.C. Nolan 96006758
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Table 3 – Grouped Frequency Distribution Interval 15 – 25 26 – 36 37 – 47 48 – 58 59 – 69 70 – 80 81 – 91 92 – 102
LV 15 26 37 48 59 70 81 92
UV 25 36 47 58 69 80 91 102
MV 20 31 42 53 64 75 86 97
f 1 2 2 4 5 3 6 2
Cum f 1 3 5 9 14 17 23 25
The three measures of central tendency was calculated, see Table 4 for the values. The mean, mode and median is almost the same, this indicates a small negative skewed distribution.
Table 4 – Measures of Central tendency Mean Mode Median
65.8 65 65
FREQUENCY GRAPH
3.2
A graphic representation of the data was made to form a Frequency histogram (Figure 1), Frequency polygon (Figure 2) and a Cumulative Frequency ogive curve (Figure 3).
Frequency Histogram 7 6 5
f
4 3 2 1 0 15 -25
26 - 36
37 - 47
48 - 58
59 - 69
70 - 80
81 - 91
92 - 100
Intervals
Figure 1 – Frequency Histogram
Test & Item Analysis Report A.M.C. Nolan 96006758
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Frequency Polygon 7 6 5
f
4 3 2 1 0 20
31
42
53
64
75
86
97
Middle value of interval
Figure 2 – Frequency Polygon The asymmetrical distribution of the graph shows a small negative skewed distribution. The interpretation for a negative skewed graph is that the students did well in the test. There is majority of high score with only some low ones.
Cumulative Frequency Ogive Curve 30 25 20
Cum. f 15 10 5 0 25
36
47
58
69
80
91
102
Top value of interval
Figure 3 – Cumulative Frequency Ogive Curve 3.3
TEST RELIABILITY
The Kuder-Richardson coefficient (KR20) was used to calculate the reliability coefficient. See Table 5 for the reliability data.
Test & Item Analysis Report A.M.C. Nolan 96006758
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Table 5 – Reliability data STDEV2 Total PQ # Questions (k) k-1 KR20
499.55 3.83 25.00 24.00 1.03
Because the KR20 value is greater than 0.6 we may conclude that the test is reliable.
ITEM ANALYSIS
4.
The item analysis was done to assess the quality and utility of each item. The multiple choice test consisted of 20 questions, each with 3 distracters. All the values in this part of the report were rounded off to the second decimal. This was done because the values used were very small.
DIFFICULTY INDICES
4.1
The difficulty index of each question was calculated and is represented in Table 6. According to the calculations, 8 of 20 questions (40%) were unacceptable. The reason for the unacceptability is the fact that the questions were to easy. The rest of the questions, 60% fall in the acceptable range.
Table 6 – Item Difficulty Index Question Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10
p-value 0.84 0.88 0.68 0.48 0.84 0.68 0.44 0.52 0.52 0.33
Interpretation Unacceptable Unacceptable Acceptable Acceptable
Reason To easy To easy
Unacceptable Acceptable Acceptable Acceptable Acceptable Acceptable
To easy
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Table 6 – Item Difficulty Index (continuing) Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20
0.92 0.76 0.60 0.84 0.80 0.92 0.63 0.33 0.52 0.64
Unacceptable Unacceptable Acceptable Unacceptable Unacceptable Unacceptable Acceptable Acceptable Acceptable Acceptable
To easy To easy To easy To easy To easy
DISCRIMINATION INDICES
4.2
In order for the discrimination index to be acceptable the value must be positive. All the discrimination indices were calculated and tabulated in Table 7. All the values are positive and therefore acceptable.
Table 7 – Discrimination Index Question Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20
5.
d-value 0.60 0.53 0.73 0.27 0.60 0.47 0.47 0.53 0.47 0.53 0.33 0.60 0.60 0.60 0.53 0.53 0.60 0.13 0.73 0.40
Interpretation Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable
CONCLUSION
Test & Item Analysis Report A.M.C. Nolan 96006758
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The test data was analysed to establish reliability. The graphs drawn from the data showed an asymmetrical distribution, a small negative skewed distribution. A negative skewed graph indicates that the students did well in the test. There is majority of high score with only some low ones. The Kuder-Richardson coefficient (KR20) was used to calculate the reliability coefficient. The KR20 for this test is 1.03. Because the KR20 value is greater than 0.6 it is concluded that the test is reliable. The test items were analysed to establish difficulty and discrimination. The difficulty indices shows that 60% of the questions is acceptable and only 40% is unacceptable. The reason for the unacceptability is the fact that the questions were to easy. The discrimination values were all positive, which indicates acceptability. According to the analysis this is a good test. The test can be improved by altering some of the question to make it more difficult.
6.
BIBLIOGRAPHY
Kubizyn T. and Borich G.(2003). Educational testing and measurement: Classroom application and practice. Seventh Edition. USA: Wiley/JosseyBass Education.
Test & Item Analysis Report A.M.C. Nolan 96006758
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APPENDIX
7.
TEST DATA
#A 20 20 20 20 20 19 20 20 20 20 20 20 20 20 20 20 20 20 20 20 17 20 19 19 20
% 100 100 90 90 90 89 85 85 75 70 70 65 65 65 65 60 55 55 50 50 47 45 32 32 15
3.83
0.36 0.23
5.00
11.0
0.64
25
9
16
#C 20 20 18 18 18 17 17 17 15 14 14 13 13 13 13 12 11 11 10 10 8 9 6 6 3
0.40
13 12 25 0.52 12.0 1.00 0.48 0.25
0.73
8 16 24 0.33 5.0 3.00 0.67 0.22
0.13
15 9 24 0.63 12.0 3.00 0.38 0.23
0.60
22 2 24 0.92 15.0 7.00 0.08 0.08
0.53
20 5 25 0.80 14.0 6.00 0.20 0.16
0.53
21 4 25 0.84 15.0 6.00 0.16 0.13
0.60
15 10 25 0.60 12.0 3.00 0.40 0.24
0.60
19 6 25 0.76 14.0 5.00 0.24 0.18
0.60
23 2 25 0.92 14.0 9.00 0.08 0.07
0.33
8 16 24 0.33 8.0 0.00 0.67 0.22
Test & Item Analysis Report A.M.C. Nolan 96006758
0.53
13 12 25 0.52 10.0 3.00 0.48 0.25
0.47
12 11 23 0.52 10.0 2.00 0.48 0.25
0.53
11
17 8
14 25
25 0.68
0.44 9.0
12.0
0.56
2.00
0.32
5.00
C Q 2 0 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0
0.25
0.47
0 1 1 0
0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0
B Q 1 9 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0
0.22
0.47
21 4 25 0.84 15.0
0 1 1 0
D Q 1 8 1 1 1 0 1
0.16
6.00
C Q 1 7 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0
0.13
0.60
12 13 25 0.48 8.0 4.00
A Q 1 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0.52
0.27
17
1
0 0 0 0
A Q 1 5 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 1 0
0.25
PQ
Q
D
#L
#U
P
#A
#I
#C
19
22
24
8
1
3
15
25
17
25
22
0.68
7
0.88
21
14.0
6
Q 9 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0
15.0
10
Q 8 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1
3.00
23
Q 7 1 1 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0
7.00
18
Q 6 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0
0.73
9
Q 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1
D Q 1 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0
0.53
8
Q 4 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1
B Q 1 3 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 0
0.32
12
Q 3 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0
C Q 1 2 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0
0.12
4
Q 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0
A Q 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
0.11
5
Q 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0
B Q 1 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0
0.22
20
C
21
13
A
4
14
D
25
25
C
0.84
3
B
15.0
2
D
6.00
16
D
0.60
11
B
0.16
St N o
C
0.13
K ey
12
G U U U U U U U U U U U U U U U L L L L L L L L L L