# Statistics: Item and Test Analysis

I. Frequency Distributions

The following are 50 scores on a History examination.

37 39 42 30 38 20 17 16 15 6

25 22 15 25 31 18 21 13 5 11

27 26 26 22 31 15 16 22 17 6

22 27 27 32 17 32 14 12 23 18

28 29 33 28 19 19 34 20 21 29

From these scores, construct a frequency distribution table.

Use nine classes, with the first class 0-4, and the last 40-44

Class Interval tally frequency

40-44 1 1. (_____)_

35-39 3 2. (_____)_

30-34 7 3. (_____)_

25-29 11 4. (_____)_

20-24 9 5. (_____)_

15-19 12 6. (_____)_

10-14 4 7. (_____)_

5-9 3 8. (_____)_

0-4 ___ N/A 9. (_____)_

II. From the following scores on two tests, calculate the following values:

Test 1 (X): 29, 28, 25, 25, 22, 22, 21, 20, 19, 19

Test 2 (Y): 34, 31, 35, 30, 31, 28, 28, 25, 24, 24

Mean of Test 1 (X)

10. Mx= 23

Mean of Test 2 (Y)

11. My= 29

12. Summation of squared deviations scores for Test 1

Σx2= (______)

Summation of squared deviations scores for Test 2

13. Σy2 = (______)

Summation of the product of deviation scores for Test 1 and Test 2

14. Σxy = (______)

Correlation Coefficient:

15. r = (_____)

III. Twenty students received the following scores on a short quiz:

23, 20, 20, 19, 19, 19, 18, 18, 18, 18,

17, 17, 17, 15, 14, 13, 13, 12, 12, 18.

Calculate the following:

16. Mean= 17

17. Median= 18

18. Mode= 18

19. SD = 2.96

20. If this small sample is normally distributed, 68% of the scores should fall between what two values? ______________and___________________.

IV. A student takes examinations in a History course and an English course.

The following information is taken from the two tests:

History English

Student Score 64 80

Mean 54 70

SD 4 10

21. What is the z-score for History? -1.27

22. What is the z-score for English? -1.41

23. What is the T-score for History? 37.3

24. What is the T-score for English? 35.9

V. Use the following data to answer questions 25 - 30. (*indicates the correct answer).

ITEM 1 A B C D* ITEM 2 A B C* D

UPPER 2 4 2 4 UPPER 0 5 5 5

LOWER 6 1 3 2 LOWER 0 3 11 1

Circle the letter of the correct answer.

25. What is the difficulty level of item 1? 26. What is the difficulty level of item 2?

a. 4/12 a. 5/15

b. 6/12 b. 6/15

c. 2/24 c. 5/30

d. 4/24 d. 6/30

e. 6/24 e. 16/30

27. What is the discrimination index of item 1? 28. What is item 2's discrimination index?

a. 2/12 a. 6/15

b. 6/12 b. 4/15

c. 2/24 c. -6/15

d. 6/24 d. -6/30

29. Which distractor on Item 1 needs revision or elimination?

a. 1-A

b. 1-B

c. 1-C

d. None of these

30. Which of the following is indicated by Item 2?

a. Ambiguous

b. Guessing

c. Miskeyed

d. Too difficult

31. The majority of Mr. Smith's students made very high scores on this test. The curve of the distribution of scores on this test would most likely be

a. normal

b. symmetrical

c. positively skewed

d. negatively skewed

32. Which of the following r's have the least predictive value?

a. 0.91

b. 0.50

c. 0.17

d. 0.23

e. -1.00

33. The reliability procedure that involves correlation of partial scores from one administration of one test is

a. test-retest

b. parallel forms

c. split half

d. none of the above

Total: _____ x 3+1 =_______/100

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#### Solution Preview

Dear Student,

Please find the answer document attached. Also I have attached the Excel Sheet used to calculate the answers.

Determination of Difficulty Index and the Discrimination Index.

1. After the students are arranged with the highest overall scores at the top,

get the number of students in the upper and lower group who got each

item correct.

2. Determine the Difficulty Index by ...

#### Solution Summary

Solution explores the Correlation Analysis, Item and Test Analysis where test cases are used.