Analyzing and Improving
a Test Using Statistics
Dawn Stevane
EDU645: Learning &
Assessment for the 21st Century (MRB1231B)
Richard Newman
August 27, 2012
What is the definition of mean? Mean
is the average of the numbers. A good question is how we find the mean score
for each question? I had to research it because it has been a long time since I
had a math course. You find the mean by adding up all the numbers, then
dividing by how many numbers there are.
The questions provided had five questions each of the questions had a
total based upon ten students. The first question had a total of 18, the second
question had a total of 14, the third question had a total of 2, the fourth
question had a total of 20, and the fifth question had a total of 2. There were a total of 56; if you divided the
total by 5 questions then you will get 11.2. The mean score for each question
is 11.2. These scores reflect what the students may have scored on each
question.
The Mean Score for the Entire
Test
The mean score for the entire test can be calculated
by also finding the average for each question and then divided the sum by the
number of students and questions. The sum for the scores of each question is
56. There are ten students that may have
been administered the test so we can add the tenth student to the sum of the
score for the test of 56 and also add the number of questions and then divide
the three (students, questions, and sum of score). The mean score for the
entire test is 23.6. I came up with this score by adding the sum of 56 to the
amount of students which was 10, and also adding the number of question, which
is 5, and then divide the total by three entities of the questions, students,
and sum of scores.
A Graph that Represents the Scores
Qualitative and Quantitative
analysis are used to find the bad items on a test. Quantitative item analysis
is a numerical method for analyzing a test items utility, with data that can be
measured (Kubiszyn and Borich, 2010). Away to remember Quantitative is
quantitative equal’s quantity. Qualitative item analysis is non-numerical
method for analyzing a test items utility, with data that can be observed not
measured (Kubiszyn and Borich, 2010). A way to remember Qualitative is
qualitative equals quality. In this chart it shows the scoring that each
student received for the questions. The quantitative items in such chart show
the analysis of the questions whereas the qualitative analysis reflects the
amount of students that test was administered to. The qualitative analysis of
the test shows the more subjective part of the chart, and the quantitative
analysis was more objective. The quantitative analysis of the chart would be
taking the ten students who have selected correct answers and divide by the
total number of students who made an attempt. Student 5 answered all five
questions correctly, whereas there were nine other students who did make an
attempt to answer all of the answers correctly.
The test questions that were given
to each student were to short and did not give the test taker enough evidence
to use qualitative and quantitative research. There was enough evidence to be
able to evaluate the qualitative research. But, the quantitative item analysis
assesses the quality of the chart and it was able to identify the distracters
that are not doing what they should be doing. The Quantitative part of the test
was the questions were multiple-choice questions. In using the mean score of
the questions, I found that quantitative was also utilized as quantitative is
taking the total number of students who select the correct answer and then
divide that by the number of students who attempted the item.
By observing the answers from
students in this graph, we can determine if miskeying has taken place, did the
student guess or was there ambiguity. This is where qualitative item analysis
plays a part in determining if the problem is a lack of mastery or a poorly
written item. Qualitative item analysis checks the validity of the item and any
technical faults that may exist. You want to match items and objectives and
edit any items that are poorly written. The benefits of these two types of
analysis are that they must be used together to get the best results. They
allow you to find out where the problem areas are and make sure your test
questions past the validity test.
In my opinion there is no test or
score that is completely valid or reliable “the tests come with varying degrees
of goodness” Kubiszn & Borich (Chapt. 18). If they are used together than
the teachers can grade the tests effectively. Their benefits to learning and
assessment are “they help us decide whether to retain or eliminate an item,
which distracters should be modified or eliminated, whether an item is miss
keyed, whether guessing occurred, and whether ambiguity is present—quantitative
analysis” (Kubiszyn and Borich, 2010). The risks to learning and assessment if
these types of analyses are not administered are as follows: Qualitative
analysis is limited because it shows the items that have errors but it doesn’t
help you to find them. Quantitative analysis is timely and the teachers can get
very frustrated using type of analysis.
References:
Kubiszyn, T. & Borich, G.
(2010). Educational testing & measurement: Classroom application and
practice (9th ed.). John Wiley & Sons, Inc., Hoboken, NJ.
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