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Item Analysis looks at how student responses to individual tests items or questions. This is used in effort to assess or determine the quality the test items and the test as a whole. Item Analysis can be used to improve test items as well as to determine which test items can be used to eliminate ambiguous or misleading test items. Additionally, item analysis can be a valuable tool for increasing or improving instructor’s skills in the development or construction and identifying specific areas of the course content the may need more clarity.
You will be provided with the responses to a set of items to perform an item analysis and interpret the results. Use the handout provided in Modules to-conduct this item analysis. Please read and follow the provided instructions.
Please make no adjustments to the Item Analysis
ITEM ANALYSIS
After you create your objective assessment items and give your test, how can you
be sure that the items are appropriate — not too difficult and not too easy? How
will you know if the test effectively differentiates between students who do well
on the overall test and those who do not? An item analysis is a valuable, yet
relatively easy, procedure that teachers can use to answer the following questions.
In order to determine the difficulty level of test items, a measure called the Difficulty Index is
used. This measure asks teachers to calculate the proportion of students who answered the test
item accurately.
By looking at each alternative (for multiple choice), we can also find out if there are answer
choices that should be replaced. For example, let’s say you gave a multiple-choice quiz and there
were four answer choices (A, B, C, and D). The following table illustrates how many students
selected each answer choice for Question #1 and #2.
Question
A B C D
#
1
0 3 24*
3
#2 12* 13 3
2
* Denotes correct answer.
For Question #1, we can see that A was not a very good distractor — no one selected that answer.
We can also compute the difficulty of the item by dividing the number of students who choose
the correct answer (24) by the number of total students (30). Using this formula, the difficulty of
Question #1 (referred to as p) is equal to 24/30 or .80. A rough “rule-of-thumb” is that if the item
difficulty is more than .75, it is an easy item; if the difficulty is below .25, it is a difficult item.
Given these parameters, this item could be regarded moderately easy — lots (80%) of students
got it correct. In contrast, Question #2 is much more difficult (12/30 = .40). In fact, on Question
#2, more students selected an incorrect answer (B) than selected the correct answer (A). This
item should be carefully analyzed to ensure that B is an appropriate distractor.
Another measure, the Discrimination Index, refers to how well an assessment differentiates
between high and low scorers. In other words, you should be able to expect that the high-
performing students would select the correct answer for each question more often than the low
performing students. If this is true, then the assessment is said to have a positive discrimination
index (between 0 and 1) – indicating that students who received a high total score chose the
correct answer for a specific item more often than the students who had a lower overall
score. If, however, you find that more of the low-performing students got a specific item correct,
then the item has a negative discrimination index (between-1 and 0). Let’s look at an example.
Table 2: Displays the results of ten questions on a quiz. Note that the students are arranged with
the top overall scorers at the top of the table.
STUDENT
TOTAL SCORE %
QUESTIONS
1 2 3
Asif
90 1 0 11
Anthony
90 1 0 1
Mike
80 0 0 1
Sharon
80 1 0 1
Charles
70 1 0 1
Bruce
60 1 0 0
Catherine
60 1 0 1
Patricia
50 1 1 0
Kelly
50 1 1 0
Tonya
40 0 1 0
“1” indicates the answer was correct; “0” indicates it was incorrect.
Follow these steps to determine the Difficulty Index and the Discrimination
Index.
1. After the students are arranged with the highest overall scores at the top,
count the number of students in the upper and lower group who got each
item correct. For Question #1, there were 4 students in the top half who got
it correct, and 4 students in the bottom half.
2. Determine the Difficulty Index by dividing the number who got it correct
by the total number of students. For Question #1, this would be 8/10 or
p=.80.
3. Determine the Discrimination Index by subtracting the number of students
in the lower group who got the item correct from the number of students in
the upper group who got the item correct. Then, divide by the number of
students in each group (in this case, there are five in each group). For
Question #1, that means you would subtract 4 from 4, and divide by 5,
which results in a Discrimination Index of 0.
4. The answers for Questions 1-3 are provided in Table 2.
Item
# Correct
(Upper Group)
# Correct
(Lower group)
Difficulty (p) Discrimination
(D)
Question
1
4 4 .80 0
Question
2
0 3 .30 -0.6
Question
3
5 1 .60 0.8
Now that we have the table filled in, what does it mean? We can see that Question #2 had a
difficulty index of .30 (meaning it was quite difficult), and it also had a negative discrimination
index of -0.6 (meaning that the low performing
students were more likely to get this item correct). This question should be carefully analyzed,
and probably deleted or changed. Our “best” overall question is Question 3, which had a
moderate difficulty level (.60), and
discriminated extremely well (0.8).
Another consideration for an item analysis is the cognitive level that is being
assessed. For example, you might categorize the questions based on Bloom’s
taxonomy (perhaps grouping questions that address Level I and those that
address Level II). In this manner, you would be able to determine if the difficulty
index and discrimination index of those groups of questions are appropriate. For
example, you might note that the majority of the questions that demand higher
levels of thinking skills are too difficult or do not discriminate well. You could
then concentrate on improving those questions and focus your instructional
strategies on higher-level skills.
ITEM ANALYSIS WORKSHEET
Ten students have taken an objective assessment. The quiz contained 10 questions. In the table
below, the students’ scores have been listed from high to low (David, Tommy, Dennis, Sara, and
Johnny are in the upper half). There are five (5) students in the upper half and five students (5)
in the lower half. The number “1” indicates a correct answer on the question, a “0” indicate an
incorrect answer.
Student Name
Total
Score
(%)
Questions
1 2 3 4 5 6 7 8 9 10
David 100 1 1 1 1 1 1 1 1 1 1
Tommy 90 1 1 1 1 1 1 1 1 0 1
Dennis 80 1 1 0 1 1 1 1 1 0 0
Sara 70 0 1 1 1 1 1 0 1 0 1
Johnny 70 1 1 1 0 1 1 0 1 0 0
Tammy 60 1 1 1 0 1 1 0 1 0 0
Grace 60 0 1 1 0 1 1 0 1 0 1
Mary 50 0 1 1 1 0 0 1 0 1 0
Darrell 40 1 1 1 0 1 0 0 0 0 1
Jeanette 30 0 1 0 0 0 1 0 0 1 0
Calculate the Difficulty Index (p) and the Discrimination Index (D) for each question.
Item #Correct (Upper
Group)
# Correct (Lower
Group)
Difficulty (p) Discrimination
(D)
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Answer the following questions:
1. Which question was the easiest?
2. Which question was the most difficulty?
3. Which item has the poorest discrimination?
4. Which questions would you eliminate first (if any) – Why?