Test evaluation

Assessment Criteria for Option 2

STANDARD DEVIATION

Standard deviation (s) is a statistical measure of how precise your data is. It is calculated using the following equation, where is the data average, xi is the individual data point, and N is the number of data points:

To calculate the standard deviation, you would begin with calculating the quantity (xi - ), which is the deviation of each data point from the average. You would square square each one, then add them up and divide by one less than the number of data points. Finally, you would find the square root of this value. The standard deviation is a measure of how precise the average is, that is, how well the individual numbers agree with each other. It is a measure of a type of error called random error - the kind of error people can't control very well.

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently the squares of the differences are added. The sum of the squares is then divided by the number of observations minus oneto give the mean of the squares, and the square root is taken to bring the measurements back to the units we started with. (The division by the number of observations minus oneinstead of the number of observations itself to obtain the mean square is because "degrees of freedom" must be used. In these circumstances they are one less than the total. The theoretical justification for this need not trouble the user in practice.)

To gain an intuitive feel for degrees of freedom, consider choosing a chocolate from a box of n chocolates. Every time we come to choose a chocolate we have a choice, until we come to the last one (normally one with a nut in it!), and then we have no choice. Thus we have n-1 choices, or "degrees of freedom".

Table 1. The Whole Original Test Items Analysis

QUESTIONS (ITEMS)

TOTAL SCORE (30)

TOTAL SCORE (%)

STUDENT NAME

STUDENT NO.

(6)

(5)

4))

(3)

(2)

(1)

1

1

1

1

1

1

30

100

A

1

1

1

1

0.92

1

1

29.5

98.33

B

2

1

1

1

1

0.91

0.83

29

96.66

C

3

0.50

1

0.92

0.85

1

1

28

93.33

D

4

1

0.91

0.85

0.71

1

0.83

26

86.66

E

5

0.50

0.83

1

0.71

0.83

0.83

25

83.33

F

6

1

0.75

0.78

0.85

0.83

0.83

24.5

81.66

G

7

0.50

0.91

0.78

0.78

0.58

1

23.5

78.33

H

8

1

0.83

0.78

0.50

0.83

0.83

22.5

75

I

9

1

0.75

0.71

0.57

0.66

1

21.5

71.66

J

10

0.50

0.58

0.78

0.71

0.58

0.33

19

63.33

K

11

0.50

0.58

0.64

0.28

0.50

1

16.5

55

L

12

0.50

0.25

0.57

0.42

0.66

1

16

53.5

M

13

1

0.41

0.50

0.21

0.66

1

15.5

51.66

N

14

1

0.33

0.50

0.21

0.33

0.66

12

40

O

15

0

0.41

0.42

0.21

0.25

0.83

11

36.66

P

16

0.75

0.72

0.76

0.62

0.72

0.87

IF

0.34

0.62

0.53

0.76

0.56

0.11

ID

Answer the following questions:

1. Which question was the easiest? Question 1

2. Which question was the most difficult? Question 3

3. Which item has the poorest discrimination? Question 6

4. Which question(s) would you eliminate first and why? Question 1, because it is very basic.

Table 2. Actual Scoring of The Original Test Items

QUESTIONS (ITEMS)

TOTAL SCORE (30)

TOTAL SCORE (%)

STUDENT NAME

STUDENT NO.

(6) out of 1

(5) out of 6

(4) out of 7

(3) out of 7

(2) out of 6

(1) out of 3

1

6

7

7

6

3

30

100

A

1

1

6

7

6.50

6

3

29.5

98.33

B

2

1

6

7

7

5.50

2.50

29

96.66

C

3

0.50

6

6.50

6

6

3

28

93.33

D

4

1

5.50

6

5

6

2.50

26

86.66

E

5

0.50

5

7

5

5

2.50

25

83.33

F

6

1

4.50

5.50

6

5

2.50

24.5

81.66

G

7

0.50

5.50

5.50

5.50

3.50

3

23.5

78.33

H

8

1

5

5.50

3.50

5

2.50

22.5

75

I

9

1

4.50

5

4

4

3

21.5

71.66

J

10

0.50

3.50

5.50

5

3.50

1

19

63.33

K

11

0.50

3.50

4.50

2

3

3

16.5

55

L

12

0.50

1.50

4

3

4

3

16

53.5

M

13

1

2.50

3.50

1.50

4

3

15.5

51.66

N

14

1

2

3.50

1.50

2

2

12

40

O

15

0

2.50

3

1.50

1.50

2.50

11

36.66

P

16

0.75

4.34

5.37

4.37

4.37

2.62

21.84

Mean (M)

Table 3. Frequency Table

FREQUENCY

TOTAL SCORE

STUDENT NAME

STUDENT NO.

1

30

A

1

1

29.5

B

2

1

29

C

3

1

28

D

4

1

26

E

5

1

25

F

6

1

24.5

G

7

1

23.5

H

8

1

22.5

I

9

1

21.5

J

10

1

19

K

11

1

16.5

L

12

1

16

M

13

1

15.5

N

14

1

12

O

15

1

11

P

16

Overall original test mean (M): =

= 21.84

Mode: the most common score, hence zero. ( no frequent scores ).

Median: the middle two scores divided by 2. The scores in an order.

=

= 23

Range: ( highest score - lowest score ) + 1 = ( 30 - 11 ) + 1 = 20

Standard Deviation (S):

S =

x = one student score out of 30 M = mean ...