Assignment 2: Test And Item Analysis Report

TEST AND ITEM ANALYSIS REPORT

by FJ Meintjes

TEST AND ITEM ANALYSIS REPORT by Frans Johannes Meintjes

Submitted in partial fulfillment for the degree Baccalaureus Educationis Honores in Computer-Integrated Education

Department of Curriculum Studies

Faculty of Education University of Pretoria

Supervisor: Professor J G Knoetze

September 2007

2

Descriptive abstract This report disseminates descriptive statistics (measure of tendency and variability) on the raw data given. Raw data was tabulated to summarize the data. Descriptive statistics and item analysis are included.

Acknowledgements

Thanks to Professors J. G. Knoetze for his enthusiastic guidance and support.

ii

Table of Contents Descriptive abstract Acknowledgements List of Tables List of Figures List of Terminology 1. Introduction 2. Purpose of report 3. Test analyses 3.1 Descriptive statistics 3.2 Frequency histogram 3.3 Test reliability 4. Item analyses 4.1 Difficulty indices 4.2 Discrimination indices 5 Conclusion References Test data

i ii iv v vi 1 1 1 1 3 4 5 5 5 6 7 8

iii

List of tables Table 1 Table 2 Table 3 Table 4 Table 5 Table 6

Descriptive statistics Steps in constructing a grouped frequency distribution Frequency distribution Standard deviation and KR20 Difficulty index Discrimination index

iv

1 2 2 5 5 6

List of Figures Figure 1 Figure 2 Figure 3

The histogram based on a group frequency distribution A frequency distribution polygon Cumulative value

v

3 4 4

List of Terminology Cumulative frequency

“The cumulative frequency is the number of data less than (or equal to) a reference value (X) divided by the total number of data” (Kubiszyn & Borich 2006). Numbers used to describe or summerise a larger body of numbers (Kubiszyn & Borich 2006). “Frequency is the measurement of the number of occurrences of a repeated event” (Kubiszyn & Borich 2006). “Frequency analysis is done to obtain insight into how often a certain feature occurs” (Kubiszyn & Borich 2006). “Straight lines to connect the midpoint of each interval, witch vary in height depending on the frequency of scores in the interval” (Kubiszyn & Borich 2006). “Reliability is the consistency of a set of measurements or measuring instrument” (Kubiszyn & Borich 2006).

Descriptive statistics Frequency Frequency analysis Frequency polygons

Reliability

vi

1. Introduction In this report data was tabulated to make it more interpretable. Raw data was used and were listed into a descending order. 2

Purpose of report

The purpose of this report is to disseminate descriptive statistics on raw data given. The test data was tabulated and a graph was created to summarize the data.

3. Test analyses 3.1 Descriptive statistics Table 1 shows the mean, mode, median and standard deviation of the test. The average score was 65.5%. Mean Mode Median Stdv

65.8 65.0 65.5 21.9

Table 1: Descriptive statistics Table 1 indicates that this test had a slightly positive skewed distribution and indicates that the test was good. The mean presents the impression that the averaged students scored 65.8% and passed the test. The median shows that 50% of the students scored 65.5% or below. The average learner passed the test. In Table 2 the steps to construct a group frequency distribution are shown where the highest number is shown as 100. The range is determined by subtracting the lowest number from the highest number. After deciding that my number of intervals would be 10, the size of the interval was rounded to the nearest odd number.

1

Highest score Lowest score Range of scores Number of Intervals Size of interval

100 15 85 10 9

Table 2: Steps in constructing a grouped frequency distribution Table 3 shows the interpretation of a frequency distribution. This table shows that the highest score of 100% was scored by two learners. The lowest score of 15% was scored by one of the twenty five learners. Since 65% of the class scored 65% and higher one interpretation is that the test has been acceptable. Table 3 also shows the grouped frequency distribution of the twenty five learners. The size of interval was added to the lower value to determine the upper value. The frequency shows how many learners scored inside the interval. Since 15 of the 25 learners in the class scored 65% and higher one interpretation is that the test may have been acceptable. Intervals Lower Upper Middle Value Value Value 15 24 19.5 25 34 29.5 35 44 39.5 45 54 49.5 55 64 59.5 65 74 69.5 75 84 79.5 85 94 89.5 95 100 97.5

Frequency 1 2 0 4 3 6 1 6 2

Table 3: Frequency distribution

3.2

Frequency histogram 2

Cumulative frequency 1 3 3 7 10 16 17 23 25

A histogram of the frequency distribution is shown in Figure 1. It shows that 6 learners scored between 65% and 74% and 6 learners scored between 85 and 94%. The frequency polygon is shown in Figure 2. The frequency polygon indicates that a smooth curve increases from left to right. This indicates that more learners scored above 65%. Therefore it also indicates that the test may have been acceptable. Figure 2 shows that the majority of scores fall above the middle of the score distribution. There are many high scores and few low scores. The interpretation we can make is that the learners did well on the test. There could be a number of reasons for this. The test could be too easy, too much time may have been given to complete the test or the class may be exceptionally bright. Histogram based on frequency distribution 7

Frequency

6 5 4

Series1

3 2 1 0 15-24 25-34 35-44 45-54 55-64 65-74 75-84 85-94 95-100 Intervals

Figure 1: The histogram based on a group frequency distribution

3

Frequency distribution polygon 7

Frequency

6 5 4

Series1

3 2 1 0 19.5 29.5 39.5 49.5 59.5 69.5 79.5 89.5 97.5 Middle value

Figure 2: A frequency distribution polygon The cumulative frequency graph is shown in Figure 3 Cumulative frequency

Cumulative frequency

30 25 20 15

Series1

10 5 0 24

34

44

54

64

74

84

94

100

Upper value

Figure 3: Cumulative value

3.3

Test reliability

The standard deviation is shown in Table 4. The standard deviation refers to the spread of the values around the mean. Where the standard deviation is big as shown in Table 4 the scores tend to be further away from the mean. Such a distribution is said to be heterogenic. The KR20 is the extend to witch items in one form of the test 4

have as much in common with one another as do the items in that one form with corresponding items in an equivalents form. K k-1 Total pq Stdev Stdev2 KR20

25 24 3.7 21.9 479.6 1.03

Table 4: Standard deviation and KR20

4 Item analyses 4.1

Difficulty indices

The difficulty indices are shown in Table 5. Questions 1, 2, 5, 11, 12, 14, 15 and 16 were too easy. All the other questions were acceptable. Thirty two percent of the questions were too easy. Sixty eight percent of the questions were acceptable. Question Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20

p-value 0.84 0.9 0.7 0.5 0.8 0.7 0.4 0.5 0.5 0.3 0.9 0.8 0.6 0.8 0.8 0.9 0.6 0.3 0.5 0.6

Unacceptable Unacceptable Acceptable Acceptable Unacceptable Acceptable Acceptable Acceptable Acceptable Acceptable Unacceptable Unacceptable Acceptable Unacceptable Unacceptable Unacceptable Acceptable Acceptable Acceptable Acceptable

Table 5: Difficulty index 5

Too easy Too easy

Too easy

Too easy Too easy Too easy Too easy Too easy

4.2

Discrimination indices

Table 6 shows the discrimination indices. It shows that all the questions asked were acceptable. Question number Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20

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

Table 6: Discrimination index

5 Conclusion Thirty two percent of the questions asked in this test were too easy. Some of the questions showed to be too easy can be changed. The discrimination indices were all acceptable.

References 6

Kubiszyn, T. & Borich, G. 2006. Educational Testing and Measurement: Classroom Application and Practice (2nd ed.)

Test Data 7

Key St No 11 16 2 3

C Q1 1 1 1 1

B Q2 1 1 1 1

D Q3 1 1 1 1

D Q4 1 1 1 1

B Q5 1 1 1 1

C Q6 1 1 0 1

D Q7 1 1 0 1

A Q8 1 1 1 1

25

1

1

1

1

1

0

0

1

14

1

1

1

0

1

1

1

1

13 20 5 4 12 8 9 18 23 10 6

1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 0

1 1 1 1 1 1 1 0 1 0 1

0 1 0 0 1 0 0 1 0 0 1

1 1 1 1 1 1 1 1 1 1 0

1 1 1 1 1 1 1 0 1 1 1

1 1 0 0 1 0 1 1 0 1 0

1 1 1 1 0 0 0 0 0 0 0

21

1

0

1

1

0

1

0

0

7 22 17 15 1 24 19 #CORRECT

0 0 0 1 1 1 0 21

1 1 1 1 1 1 0 22

0 0 0 1 0 0 0 17

0 0 0 1 0 0 1 12

1 1 1 1 0 0 1 21

1 1 0 0 0 0 0 17

0 0 1 0 0 0 0 11

0 0 0 1

1 12

#INCORRECT

4

3

8

13

4

8

14

11

8

Key St No 11 16 2 3

C Q9 1 1 1 1

B Q10 1 1 1 1

A Q11 1 1 1 1

B Q12 1 1 1 1

B Q13 1 1 1 1

D Q14 1 1 1 1

A Q15 1 1 1 1

A Q16 1 1 1 1

25

1

1

1

1

1

1

1

1

14

1

1

1

1

1

1

1

1

13 20 5 4 12 8 9 18 23 10 6

1 1 1 1 0 0 0 0 0 0 1

1 0 0 1 0 0 0 0 0 0 0

1 0 1 1 1 1 1 1 1 1 1

1 0 1 1 1 1 1 1 1 0 1

1 1 1 0 0 1 1 0 1 0 0

1 1 1 1 1 1 1 1 1 1 1

1 1 1 0 1 1 1 1 1 0 1

1 1 1 1 1 1 1 1 1 1 1

21

1

0

1

1

0

1

1

1

7 22 17 15 1 24 19 #CORRECT

0 0 1 0 0 0 0 13

0 0

1 1 0 1 0 0 0 19

1 1 1 0 0 0 0 15

1 1 1 0 0 0 0 21

0 0 1 1 1 1 0 20

1 1

0 0 0 0 8

1 1 1 1 1 1 0 23

0 1 1 0 22

#INCORRECT

12

16

2

6

10

4

5

2

9

Key St No 11 16 2 3

C Q17 1 1 1 1

D Q18 1 1 1 0

B Q19 1 1 1 0

C Q20 1 1 1 1

#CORRECT

#ANSWERED

%

%MEAN

MEAN*MEAN

GROUP

20 20 18 18

20 20 20 20

100.0 100.0 90.0 90.0

34.2 34.2 24.2 24.2

1169.6 1169.6 585.6 585.6

U U U U

25

1

1

1

1

18

20

90.0

24.2

585.6

U

14

0

1

1

17

19

89.5

23.7

560.4

U

13 20 5 4 12 8 9 18 23 10 6

0 1 0 1 1 1 1 1 1 1 0

0 1 0 0 0 0 0 0 0 1 0

1 1 1 0 1 1 0 1 1 1 0

1 1 1 1 0 0 0 1 0 1 1

17 17 15 14 14 13 13 13 13 12 11

20 20 20 20 20 20 20 20 20 20 20

85.0 85.0 75.0 70.0 70.0 65.0 65.0 65.0 65.0 60.0 55.0

19.2 19.2 9.2 4.2 4.2 -0.8 -0.8 -0.8 -0.8 -5.8 -10.8

368.6 368.6 84.6 17.6 17.6 0.6 0.6 0.6 0.6 33.6 116.6

U U U U U U U U U L L

21

0

0

0

1

11

20

55.0

-10.8

116.6

L

7 22 17 15 1 24 19 #CORRECT

0 0 0 1 1 0 15

1 1 0 0 0 0 0 8

0 0 0 0 0 0 0 13

1 1 0 0 0 0 0 16

10 10 8 9 6 6 3

20 20 17 20 19 19 20

50.0 50.0 47.1 45.0 31.6 31.6 15.0

-15.8 -15.8 -18.7 -20.8 -34.2 -34.2 -50.8

249.6 249.6 351.2 432.6 1171.1 1171.1 2580.6 11989.3

L L L L L L L

#INCORRECT

9

16

12

9

STDEV2

479.6