A TEST AND ITEM ANALYSIS REPORT

BY

JOSEPH A AZAGSIBA

TABLE OF CONTENTS

Section Page

1 Introduction 6

1.1 Purpose of report 6

1.2 Approach 6

1.3 Report structure 7

2 Test Analysis 7

2.1 Frequency histogram 7

2.2 Descriptive statistics 9

3 Item Analysis 10

3.1 Difficulty index 10

3.2 Discrimination index 12

3.3 Item reliability 13

4 Conclusion 13

APPENDIX A: CODED DATA 15

2

APPENDIX B: DISCRIMINATION INDEX 17

APPENDIX C: DIFFICULTY INDEX 18

REFERENCES 19

List of Tables

3

Table Table name Page

1 Report structure 7

2 Measurements of values of central

tendency, standard deviation and KR20

9

3 Difficulty index 10

4 Discrimination index 12

5 Reliability co-efficient 13

List of Figures

Figure Figure name Page

4

1 Histogram of grouped frequency

distribution

8

2 Normal distribution curve 9

1. INTRODUCTION

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This is a test and item analysis report on the variability and reliability of twenty multiple-choice

questions answered by twenty-five learners. It comprises the Introduction, the Test Analysis, the

Item Analysis and a Conclusion.

1.1 Purpose of Report

The purpose of this report is to disseminate information on the measure of tendency and variability

on a set of data of twenty multiple choice questions that have been answered by twenty-five

learners.

1.2 Approach

The methodology employed to arrive at the purpose of this report consisted of the following steps:

The relevant data was collected.

The collected data was recorded and tabulated using Microsoft Excel.

The mean, mode, median and standard deviation of the scores obtained by learners were

calculated.

The difficulty index and the discrimination index were then calculated.

The reliability coefficient was also calculated using the Kuder-Richardson procedure (KR20).

The scores of learners were grouped into upper and lower levels.

A histogram of the data was drawn.

Conclusions were then made based on the analysed data.

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1.3 Report structure

The structure of this report comprises an introduction, a test analysis, an item analysis and a

conclusion. These sections are subdivided into subsections as shown in Table 1.

Table1: Report structure

Section Heading Subheading

1 Introduction Purpose

Approach

Report structure

2 Test Analysis Frequency graph

Descriptive statistics

3 Item analysis Difficulty index

Discrimination index

4 Conclusion Conclusion

2 TEST ANALYSIS

2.1 Frequency histogram

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The histogram or bar graph in Figure 1 displays statistical data about the number of learners who

answered the multiple-choice questions correctly. From the histogram, one learner each fell within

each of the score intervals of 20-28, 38- 46, 56-64, and 74-81; whilst two learners each were

represented within the score intervals of 29-37 and 100-108. Five learners fell within the score

interval of 47 and 55. No learner fell within the 91-99 score interval, whilst six learners were placed

within the score intervals of 65-73 and 82-90.

Figure 1: Frequency histogram

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2.2 Descriptive statistics

Table 2: Measurements of values of central tendency, standard deviation and KR20.

Mean 65.99Mode 65Median 65STDEV 21.90#Upper 13#Lower 12STDEV2 479.39#Question 20k-1 19KR20 1.04

The mean (M), which is a measure of central tendency, is 65.99. The mode is 65 and the median

(MDN) is 65. The mean, median and mode of this data are almost the same. This means that about

half of the learners fell on either side of these values. The data distribution is therefore normal.

Figure 2 illustrates a normal distribution curve. The standard deviation (SD) is 21.90.

Figure 2: Normal distribution curve

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3. ITEM ANALYSIS

3.1 Difficulty index

The difficulty index for each item computed using the formula,

p= Number of students selecting correct answer Total number of students attempting the item

is given in Table 3.

Table 3: Difficulty index

DIFFICULTY INDEX Quest #Ans #Cor p Remarks1 25 21 0.84 Too Easy2 25 22 0.88 Too Easy3 25 17 0.68 Moderate4 25 12 0.48 Moderate5 25 21 0.84 Too Easy6 25 17 0.68 Moderate7 25 11 0.44 Moderate8 23 12 0.52 Moderate9 25 13 0.52 Moderate10 24 8 0.33 Moderate11 25 23 0.92 Too Easy12 25 19 0.76 Moderate

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Table 3: Difficulty index

DIFFICULTY INDEXQuest #Ans #Cor p Remarks13 25 15 0.6 Moderate14 25 21 0.84 Too Easy15 25 20 0.8 Moderate16 24 22 0.92 Too Easy17 24 15 0.63 Moderate18 24 8 0.33 Moderate19 25 13 0.52 Moderate20 25 16 0.64 Moderate

From this information the level of difficulty or easiness of each item was determined. Items that have

p values less than 0.20 are relatively difficult and those that have p values above 0.80, relatively

easy. Thus six items or 30% of the items were relatively easy and 14 or 70% were moderately

difficult.

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3.2 Discrimination index

The discrimination index for each item is provided in Table 4.

Table 4: Discrimination index

DISCRIMINATION INDEX

Quest U L D Remarks1 15 6 0.69 Desirable2 15 7 0.54 Desirable3 14 3 0.85 Desirable4 8 4 0.31 Desirable5 15 6 0.69 Desirable6 12 5 0.54 Desirable7 9 2 0.54 Desirable8 10 2 0.62 Desirable9 10 3 0.54 Desirable10 8 0 0.62 Desirable11 14 9 0.38 Desirable12 14 5 0.69 Desirable13 12 3 0.69 Desirable14 15 6 0.69 Desirable15 14 6 0.62 Desirable16 17 7 0.62 Desirable17 12 3 0.69 Desirable18 5 3 0.15 Desirable19 12 1 0.85 Desirable20 11 5 0.46 Desirable

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A positive discrimination index (D) indicates that the item’s discrimination is adequate. All these

items show positive discrimination index values implying that all items have adequate

discrimination.

3.3 Item reliability

The item reliability coefficient was calculated using the Kuder-Richardson procedure. The resulting

coefficient ( KR20), 1.04, is provided in Table 5.

Table 5: Reliability coefficient

KR20 1.04

The reliability coefficient of 1.04 reflects the SD value of 21.9 as being a large variability score. With

30% of the test items being too easy, the test reliability is affected to some extent as when some

items become very easy or very difficult, the test’s reliability goes down.

4. CONCLUSION

From the data analysis all the test items are desirable as they all show positive discrimination

abilities. However,of the twenty test items, six of them, items 1, 2, 5, 11, 14 and 16, have p values in

excess of 0.80 thus rendering them relatively easy items. This enabled the students who did not

even know their stuff to easily pick out the correct answers.

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To prevent students who do not know their stuff from scoring undeserved marks therefore, it is

recommended that items 1, 2, 5, 11, 14 and 16 be reconsidered and reconstructed to improve their

difficulty levels.

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Data coding

Appendix A

Key C B D D B C D A C B A C B D A A C D B C          

St No Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 #Cor #Incor #Ans % Group

11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 20 0 20 100.00 U

16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 20 0 20 100.00 U

2 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 18 2 20 90.00 U

3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 18 2 20 90.00 U

25 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 18 2 20 90.00 U

14 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0   1 1 17 2 19 89.47 U

13 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 17 3 20 85.00 U

20 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 17 3 20 85.00 U

5 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 15 5 20 75.00 U

4 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 1 14 6 20 70.00 U

12 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 1 0 14 6 20 70.00 U

8 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 0 13 7 20 65.00 U

9 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 13 7 20 65.00 U

18 1 1 0 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1 13 7 20 65.00 L

23 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 0 13 7 20 65.00 L

10 1 1 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1 1 1 1 12 8 20 60.00 L

6 1 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 0 1 11 9 20 55.00 L

21 1 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 0 1 11 9 20 55.00 L

7 0 1 0 0 1 1 0 0 0 0 1 1 1 1 0 1 0 1 0 1 10 10 20 50.00 L

22 0 1 0 0 1 1 0 0 0 0 1 1 1 1 0 1 0 1 0 1 10 10 20 50.00 L

17 0 1 0 0 1 0 1 0 1   1 0 1 1 1     0 0 0 8 9 17 47.06 L

15 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 9 11 20 45.00 L

1 1 1 0 0 0 0 0   0 0 1 0 0 0 1 1 1 0 0 0 6 13 19 31.58 L

24 1 1 0 0 0 0 0   0 0 1 0 0 0 1 1 1 0 0 0 6 13 19 31.58 L

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19 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 4 16 20 20.00 L

                                                   

#Cor 21 23 17 12 21 17 11 12 13 8 23 19 15 21 20 22 15 8 13 16   Upper 13    

#Incor 4 2 8 13 4 8 14 11 12 16 2 6 10 4 5 2 9 16 12 9   Lower 12    

#Ans 25 25 25 25 25 25 25 23 25 24 25 25 25 25 25 24 24 24 25 25          

p 0.84 0.92 0.68 0.48 0.84 0.68 0.44 0.52 0.52 0.33 0.92 0.76 0.60 0.84 0.8 0.92 0.63 0.33 0.52 0.64          

#U 15 15 14 8 15 12 9 10 10 8 14 14 12 15 14 15 12 5 12 11          

#L 6 8 3 4 6 5 2 2 3 0 9 5 3 6 6 7 3 3 1 5          

D 0.69 0.54 0.85 0.31 0.69 0.54 0.54 0.62 0.54 0.62 0.38 0.69 0.69 0.69 0.62 0.62 0.69 0.15 0.85 0.46          

P 0.84 0.92 0.68 0.48 0.84 0.68 0.44 0.52 0.52 0.33 0.92 0.76 0.60 0.84 0.80 0.92 0.63 0.33 0.52 0.64          

Q 0.16 0.08 0.32 0.52 0.16 0.32 0.56 0.48 0.48 0.67 0.08 0.24 0.40 0.16 0.20 0.08 0.38 0.67 0.48 0.36          

PQ 0.13 0.07 0.22 0.25 0.13 0.22 0.25 0.25 0.25 0.22 0.07 0.18 0.24 0.13 0.16 0.08 0.23 0.22 0.25 0.23 3.80        

Discrimination index Appendix B

DIFFICULTY INDEX Quest #Ans #Cor p Remarks

1 25 21 0.84Too Easy2 25 22 0.92Too Easy3 25 17 0.68Moderate4 25 12 0.48Moderate5 25 21 0.84Too Easy6 25 17 0.68Moderate7 25 11 0.44Moderate8 23 12 0.52Moderate9 25 13 0.52Moderate

10 24 8 0.33Moderate11 25 23 0.92Too Easy12 25 19 0.76Moderate13 25 15 0.6Moderate14 25 21 0.84Too Easy15 25 20 0.8Moderate16 24 22 0.92Moderate17 24 15 0.63Moderate18 24 8 0.33Moderate19 25 13 0.52Moderate20 25 16 0.64Moderate

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DISCRIMINATION INDEX Quest U L D Remarks

1 15 6 0.69Acceptable2 15 7 0.54Acceptable3 14 3 0.85Acceptable4 8 4 0.31Acceptable5 15 6 0.69Acceptable6 12 5 0.54Acceptable7 9 2 0.54Acceptable8 10 2 0.62Acceptable9 10 3 0.54Acceptable

10 8 0 0.62Acceptable11 14 9 0.38Acceptable12 14 5 0.69Acceptable13 12 3 0.69Acceptable14 15 6 0.69Acceptable15 14 6 0.62Acceptable16 17 7 0.62Acceptable17 12 3 0.69Acceptable18 5 3 0.15Acceptable19 12 1 0.85Acceptable20 11 5 0.46Acceptable

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Difficulty index Appendix C

DIFFICULTY INDEX Quest #Ans #Cor p Remarks1 25 21 0.84 Too Easy2 25 22 0.92 Too Easy3 25 17 0.68 Moderate4 25 12 0.48 Moderate5 25 21 0.84 Too Easy6 25 17 0.68 Moderate7 25 11 0.44 Moderate8 23 12 0.52 Moderate9 25 13 0.52 Moderate10 24 8 0.33 Moderate11 25 23 0.92 Too Easy12 25 19 0.76 Moderate13 25 15 0.6 Moderate14 25 21 0.84 Too Easy15 25 20 0.8 Moderate16 24 22 0.92 Moderate17 24 15 0.63 Moderate18 24 8 0.33 Moderate19 25 13 0.52 Moderate20 25 16 0.64 Moderate

References:

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1. Knoetze, J. (2007) Test data. Retrieved August 16, 2007, from Web site

www.eSnips.com/web/CIA7222007.

2. Kubiszyn, T., & Borich, G. (2007). Educational Testing and Measurement: Classroom Application

and Practice 8th ed. John Wiley & Sons Inc. United States of America

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