Group 2: 1. Miss. Duong Sochivy 2. Miss. Im Samphy 3. Miss. Lay Sreyleap 4. Miss. Seng Puthy 1 ROYAL UNIVERSITY OF PHNOM PENH INSTITUTE OF FOREIGN LANGUAGES DEPARTMENT OF ENGLISH Mrs. San Sotheary Lecturer: Mrs. San Sotheary Subject: TM402 ACADEMIC YEAR: Topic: Interpreting Test Score

C ONTENTS I. Frequency Distribution(Puthy) II. Measures of central tendency 1. Mode 2. Median 3. Mean III. Measures of dispersion (Chivy) 1. Range 2. Standard Deviation IV. Item and Test analysis (Samphy) 1. Item difficulty 2. Item Discrimination V. Guessing (Leap) VI. Example of Test Score Interpretation 2

I.F REQUENCY DISTRIBUTION

II. M EASURES OF CENTRAL TENDENCY 1. Mode Mode refers to the score which most candidates obtained. 19,20,22,23,23,24,25,25,25, 26, 26, 26, 26, 26,27,27,27,29, 29,30,30,32,33,33,34,35 Mode =26

2. M EDIAN Odd number Median refers to the score gained by the middle candidate. Even number Median = the lowest score in the top half____ the highest score in the bottom half

2. M EDIAN (C ONT.) the bottom half 19,20,22,23,23,24,25,25,25,26,26,26, 26, 26,27,27,27,29,29,30,30,32,33,33,34,35 the top half = 26 6

3. M EAN m= mean f = frequency x = score N =number of testees = the sum of

E XAMPLE 1 m = m =56.2

E XAMPLE 2 m = m =67.4

D ISTRIBUTION OF SCORES

III. M EASURES OF DISPERSION 1. Range  measure the difference between highest and lowest score 12 Range = Highest Score – Lowest Score

2. Standard Deviation Standard Deviation (s.d) measures the degree to which the group of score deviates from the mean. s.d: standard deviation N: number of the scores d: deviation of each score from mean 13 s.d. =  d ²/N

S TEPS TO CALCULATE S.D S TEPS TO CALCULATE S.D 14

15 IV. Item and test analysis Item is the smallest unit that produces distinctive and meaningful information on a test or rating scale. Test analysis examine how the test items perform as a set. There are three tools for test analysis: item difficulty, item discrimination and item distractors.

1. Item Difficulty Item difficulty (p) is simply the percentage of students taking the test who answered the item correctly P value directly restrict the variability of the test scores P value of o. (p=0) and p value of 1.0 (p=1.0), there is no individual difference P = the number of people answering the item correctly / total number of the people answering the item

No Individual Difference Table 1 (Minimum Item Difficulty) Note. * denotes correct response GroupItem Response * ABCD Upper group 4506 Lower group 2607 P: (0+0)/30 =.00p D: (0-0)/15 =.00

No Individual Difference Table 2 (Maximum Item Difficulty) Note. * denotes correct response GroupItem Response * ABCD Upper group Lower group P : (15+15)/30 = 1.00p D : (15-15)/15 =.00

Individual Difference Table 3 (Maximum Item Difficulty) Note. * denotes correct response GroupItem Response * ABCD Upper group Lower group 2556 P: (13+5)/30 =.60p D : (13-5)/15 =.53

2.Item Discrimination One would expect people who do well on the test to answer that item correctly, and those who do poorly to answer the item incorrectly Two way can be determined the item discrimination are the item discrimination index, D and discrimination coefficients

A.Item discrimination Index, D The discrimination index, D, is the number of people in the upper group who answered the item correctly minus the number of people in the lower group who answered the item correctly, divide by the number of people in the largest of two group A good job of discrimination, when more people in the top- scoring group will have answered the item correctly. (see in table 3) A negative discrimination index, when number of lower group answered the correct item are more than upper group, thus that such a test doesn’t valid. (see in table 7)

A rule of thumb, in the terms of discrimination index -.40 and greater are very good items -.30 t0.39 are reasonably good but possibly subject to improvement -.20 t0.29 are marginal item and need some revision - below.19 are considered poor items

Table 7 (Negative Item Discrimination Index D) Note. *denotes correct response GroupItem Response * ABCD Upper group 0000 Lower group P : (0+15)/30 =.50p D : (0-15)/15 = -1.0

B.Distractors Distractors are the incorrect alternative choices in each item Items should be modified if students consistently fail to select certain multiple choice alternatives Distractors should be implausible

V. G UESSING Individual candidates approach guessing in different ways  the reliability of the subsequent scores may seriously affected. N: the correct score R: the number of correct answers w: the number of incorrect answers A: the number of options in each items 25 N= R-w/(A-1)

Simpler formula of Correct Score (N) Option per items Corrected Scores 5 R-1/4w 4 R-1/3w 3 R-1/2w 2 R-w 26

Eg: A student who has scored 61% in a test comprising multiple choice items with 4 options will have 61 correct answers and 39 incorrect. => N = 61 – 39/4-1 = 61 – 39/3 = 61 – 13 = 48 This means that the actual ability of that Ss should be 48 without guessing. 27

Compare class A and B taught by the same teacher and explain their implications for further teaching and learning. It was a progress test conducted to check Ss’ monthly progress in three month of a five month intermediate general English course. 28

I NTERPRETATION N A = N B = 25 Mean B > Mean A => Class B outperform Class A S.d B > S.d A => Class B is Heterogeneous Bottom 4 A < Bottom 4 B => Use cooperative learning in Class B Mean is respectively low in both class A and B => Find out what the main causes of the low performances are and take solution especially Class A. 30

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