Report On Descriptive Statistics

REPORT ON DESCRIPTIVE STATISTICS AND ITEM ANALYSIS OF A DRAMA TEST

M E MOKOENA 2009

ACKNOWLEDGEMENTS My greatest gratitude goes to the following people and institution: •

The Gauteng Department of Education for their financial support in my studies,

•

My colleagues at the Tshwane South District for their advice and encouragement,

•

My family and friends for their support and interest.

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TABLE OF CONTENTS 1 2 3 4 5 6 7 8

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Introduction Procedure followed Descriptive statistics Item analysis Discrimination index Summary Reference list. Appendices

1 1 1 3 4 4 5 6

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TABLE OF TABLES Table 1: Table 2: Table 3: Table 4:

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Grouped frequency distribution of the drama test scores The mean, mode, median and standard deviation Difficulty indices of the questions Discrimination indices for the questions

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1 2 3 4

TABLE OF FIGURES Figure 1

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Frequency Polygon for drama test

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1

TERMINOLOGY LIST

Term Descriptive statistics

Difficulty index

Discrimination index

Definition and reference - Mathematical techniques for organizing, summarizing, and displaying a set of numerical data. Meredith, D.G. (1996). Educational Research: An Introduction. USA: Longman Publishers. p 757 - The percentage of a specified group, such as students of a given age or grade, who answer a test item correctly. Tuckman, B.W. (1975). Measuring Educational Outcomes, Fundamentals of Testing. New York: Harcourt - The ability of a test item to differentiate between persons possessing much or little of a certain trait, skill, or proficiency. Tuckman, B.W. (1975). Measuring Educational Outcomes, Fundamentals of Testing. New York: Harcourt Brace Jovanovich, Inc. p 477.

Item analysis

Mean

Median

- The process of identifying items that may not be suitable for use in the instrument. Maree, K. (2007).First Steps in Research. Pretoria. Van Schaik Publishers. p 218 - Is the most commonly used measure of location and is calculated as the arithmetic average of all the values. Maree, K. (2007).First Steps in Research. Pretoria. Van Schaik Publishers. p 187 - Is the middle value of a distribution – it splits the distribution into two halves. Maree, K. (2007).First Steps in Research. Pretoria. Van Schaik Publishers. p 187

Mode

- Is the score that occurs most frequently. Salkind, N.J. (2003). Exploring Research. New Jersey: Pearson Education Inc.p106 - Is the difference between the highest and the lowest scores in a distribution.

Range

Salkind, N.J. (2003). Exploring Research. New Jersey: Pearson Education Inc.p106

Standard deviation

- Is a value that approximates the average distance of a score from the mean. Shaughnesey, J.J. (1997). Research Methods in Psychology. New York: MacGraw Hill, p105.

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1. Introduction The purpose of this report is to disseminate information on a drama test consisting of twenty questions. A total of twenty five learners participated in the test. 2. Procedure followed Twenty five learners were given a drama test composed of twenty questions. The data of the scores was tabulated and the scores recoded. The scores for each learner were calculated in terms of the total number of questions answered, the number correct as well as the percentage obtained. The scores were then sorted in descending order according to percentage. The learners were then divided into two groups namely the upper and the lower group. The upper group was composed of thirteen learners whereas the lower group had only twelve. The difficulty as well as the discrimination indices of each question were calculated and recorded. Thereafter the data was summarized in terms of its central tendency i.e. the mean, median and the mode. The ranges as well as the standard deviation were also determined. An interval and frequency column was then constructed. A polygon to represent the test scores was drawn using Microsoft Excel 2003. 3. Descriptive statistics 3.1. Tabulation of data Data represented in table 1 one contains intervals and frequency values of the distribution. Table 1: Grouped frequency distribution of the drama test scores Interval 105-110 98-104 91-97 84-90 77-83 70-76 63-69 56-62 49-55 42-48 35-41 28-34 21-27 14-20 7-13

Frequency 0 2 0 3 1 3 3 2 4 1 3 2 0 1 0 1

From table 1, it is clear that 56% of the learners obtained a score greater than 56%.Only 44% of them got a score less than 56%. 3.2 Frequency polygon The frequency polygon in figure 1 shows the shape of the distribution of drama test scores. Figure 1: Frequency polygon Frequency polygon for drama test results

Frequency

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0

20

40

60

80

100

120

Midpoint

The polygon indicates that the highest point in the frequency distribution is 4 where as the lowest is 0. 3.3 The mean, mode, median, range and standard deviation The data in table 2 indicates the descriptive statistics based on the score of twenty five learners. Table 2: The mean, mode, median, range and standard deviation Descriptive statistic Mean Mode Median Range STDEV

Value 65 65 65 85 22.7

From the table it is clear that the mode, the mean and the median share the same value. Due to the fact that the mode, the median and the mode are equal, the test results will therefore represent a normal distribution. 2

4. Item analysis The data in table 3 is a summary of the difficulty indices of the questions. Table 3: Difficulty indices of the questions P VALUE p≥0 and p<20 p≥20 and p< 30 p≥ 30 and p<70 p≥70 and p<80 p≥80

MEANING Unacceptable Too difficult Acceptable Too easy Unacceptable

QUESTIONS Q13,15 Q3,4,6,7,8,9,10,17,18,19,20 Q12, Q1,2,5,11,14,16

The table clearly indicates that 55% of the questions were unacceptable, 40% were unacceptable and only 5% were too easy.

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5. Discrimination index The data in table 4 describes the discrimination of the distracters of each question. Table 4: Discrimination indices for the questions Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Discrimination index 0.38 0.31 0.54 0.31 0.38 0.23 0.38 0.62 0.54 0.62 0.77 0.38 0.38 0.38 0.31 0.31 0.38 0.15 0.69 0.46

Meaning Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable Acceptable

The table indicates that 100% of the questions were acceptable, meaning that they all had a positive discrimination. 6. Summary This small exercise in my opinion constituted and attempt to prove that computer integrated assessment has come as a major breakthrough in the world of education. Through the use of the computer it has now become relatively easy to organize and interpret large volumes of data. Through graphical representations of data, e.g on the histogram or frequency polygon, educationists are able to process data with ease. This also shows how imperative it has become that all educator training programmes should include computer literacy.

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7. Reference list. 1. Maree, K. (2007).First Steps in Research. Pretoria. Van Schaik Publishers. 2. Meredith, D.G. (1996). Educational Research: An Introduction. USA: Longman Publishers. 3. Salkind, N.J. (2003). Exploring Research. New Jersey: Pearson Education Inc. 4. Tuckman, B.W. (1975). Measuring Educational Outcomes, Fundamentals of Testing. New York: Harcourt

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Appendix A : Tabulation of test scores Key St No

C

B

D

D

B

C

D

A

C

B

A

C

B

D

A

A

C

D

B

C

Q1

Q2

Q3

Q4

Q5

Q6

Q7

Q8

Q9

Q10

Q11

Q12

Q13

Q14

Q15

Q16

Q17

Q18

Q19

Q20

11 16 2 25 3 14 13 20 5 4 12 18 8 23 9 10 6 21 7 22 15 17 24 1 19

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1 0

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

1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 0 1 0 0 0 0

1 1 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0 1

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

1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0

1 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0

1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0

1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0

1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0

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

1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0

1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0

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

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 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0

1 1 1 1 0

1 1 0

1 1 0

1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0

1

0 0 0

6

0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0

#Correct

#Answered

%

Groups

20 20 18 18 18 17 17 17 15 14 14 13 13 13 13 12 11 11 10 10 9 8 6 6 3

20 20 20 20 20 19 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 17 19 19 20

100 100 90 90 90 85 85 85 75 70 70 65 65 65 65 60 55 55 50 50 45 40 30 30 15

UG UG UG UG UG UG UG UG UG UG UG UG UG LG LG LG LG LG LG LG LG LG LG LG LG