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# Analyzing and Improving Test Using Statistics

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Analyzing and Improving a Test Using Statistics
Maurice Isaiah McCall

Introduction:
Hypothetical Psychology Test
This hypothetical psychology test consisted of five test questions. These test items and questions were not unambiguous and there were no evidence of instructions or explanations given for either test question. In our text it was mentioned there were several steps the admitter need to take before administering, analyzing and improving a test or assessment. There was no evidence these test questions were constructed and that it matched any objective. However the guidelines for packaging the test states [items need to be in a similar format, grouped together, test items need to be arranged from easy to hardest, have items properly spaced as well as checking for directions, clarity and proofreading the test before it is reproduced and distributed]. (Kubiszyn & Borich, p. 223 & 224). It is very obvious these test questions lack validity and were poorly written, these test questions were more in line with the intended audience partaking in a survey. A survey question refers to the quantitative research or a statistical survey, for the sole purpose of collecting quantitative information about the general population or a product. Each of these test questions contained its own set of problems and uniqueness about them. For example every given answer had an asterisk mark beside of it and for any test taker this is a distraction, and the test itself was not formatted or lined up. A well-constructed test question is generally administered as a descriptive question, informal question or relational question, which is used to describe the subsistence of something. The informal question requires more than one outcome variables. The relational looks at the relationship essentially between genders.
In my report I will discuss item response theory for analyzing test data, scoring test, based on mathematical testing data to improve on high stakes testing and conditions on both quantitative and qualitative item analysis. I will discuss the functions and effectiveness of the hypothetical psychology test to understand the analyzation and the order for the test. In this paper I will calculate the mean score for each question, mean score for the entire test and a graph that represents the scores for each question in the form of mathematics and measurements that represent the outcomes on a visible scale.
The report is broken down by the number of students and how each student scores on their test.
The students test scores were broken down my each question one at a time. Each test item yielded two points each based on the student answers being right or wrong. According to the text book when creating test it was suggested that you allow yourself plenty of time to write, review and correct any miskeyed items.
The Mean Score for Each Question:
Kubiszyn & Borich, states the means has three characteristic that is measured for the central tendency most frequently used are means, median and mode (p 280). In this report the letter (M) will represent the means for this report. For this report I am using the arithmetic mean by adding the numbers and dividing the sum by the number in the data listed below in the charts. The first question provided had five questions each of the questions had a total based upon ten students.
Question one had a total of 18
Question two had a total of 14
Question three had a total of 2
Question four had a total of 20
Question five had a total of 2 the grand total 56. The total was divided by the 5 questions for each item then the mean score is 11.2.
The Mean Score for the Entire Test:
The mean score is the average of what each student could possibly have scored on each test question. The entire test was calculated to find the average for each test question and the sum then was divided by the number of students and the number of questions. This test contained five questions worth a possible two points each for a total of ten students, which was calculated for a total of 20 points per question. I multiplied 20 (twenty) by the number of students 10 (ten) so the total possible points earned would be a score of 100(one hundred) for all answers correct so for answering all parts of the question for 1 question you could earn 20 points. After analyzing data, below are the report results for the mean score total and the sum of all the correct answers divided by 100. After carefully keying in the scores for an average of each question per student I used my Microsoft excel spread sheet to help calculate the total numbers, to find the average and grand total for me. To get the calculated mean score all of the scores were added then divided by the number of scores to get the mean data.
To get the average of all students’ scores; the scores were added up and divided by the number of scores that were listed in each column.
The advantage of the mean will reflect the value of all the scores in distribution and many statistical properties. However the disadvantage of the mean usually is not an actual score in the distribution, it can be misleading and skewed. The advantage of the range is easy to calculate, the use of the entire distribution or data. The disadvantage of the range will depend on two scores and there for is not reliable.

Two types of Graphs that Represents Students Scores:

| Question1 | Question 2 | Question 3 | Question 4 | Question 5 | | Student 1 | 2 | 2 | 0 | 2 | 0 | 1.2 | Student 2 | 2 | 2 | 0 | 2 | 0 | 1.2 | Student 3 | 2 | 0 | 0 | 2 | 0 | 0.8 | Student 4 | 2 | 2 | 0 | 2 | 0 | 1.6 | Student 5 | 2 | 2 | 2 | 2 | 2 | 2 | Student 6 | 2 | 0 | 0 | 2 | 0 | 0.8 | Student 7 | 2 | 2 | 0 | 2 | 0 | 1.2 | Student 8 | 0 | 0 | 0 | 2 | 0 | 0.4 | Student 9 | 2 | 2 | 0 | 2 | 0 | 1.2 | Student 10 | 2 | 2 | 0 | 2 | 0 | 1.2 | Total Score | 90 | 70 | 10 | 100 | 10 | | Average of all scores | | | | | 1.16 | |
Means Score {for each test question}

B | C | D | E | F |

1.8 | 1.4 | 0.2 | 2 | 0.2 |

Qualitative and Quantitative Analysis:
Kubiszyn & Borich, mentioned, quantitative item analysis is a technique that will enable us to assess the quality of utility of an item (p.228). This refers to the arithmetic method for analyzing test items. Conditions for students identifying distractors provide a response or option. Qualitative item analysis is being able to format your items, at this stage the instructors are looking for questions to match the objectives, content validity and if the test item were of quality high stakes test items, well written or poorly written and if to see if there were any editing being done (p.234). In this report the charts were used to best describe quantitative analysis, given account that 10 students selected and answered the questions correctly then divided by the total number of students that even made an attempt to answer any of the questions. Because the test consisted of 5 questions and answers from the number of students, student number 5 answered all test questions correctly, while the other nine students made an attempt to answer the questions.
Over View of Hypothetical Psychology Test

1. Who came up with the psychosexual stages?
*Sigmund Freud
Skinner
Gardner
2.Which psychologist tested classical conditioning with dogs?
B. F. Skinner
*Ivan Pavlov
Igor Pavlov
Sigmund Freud
3. Explain the difference between operant conditioning and classical conditioning, and provide an example of each
4. The act of removing a stimulus to reinforce a certain behavior *...is called negative reinforcement positive reinforcement punishment all of the above
5. Psychology is
*the study of the psyche

These test questions were poorly written and allowed to many distractors.

Results:
When analyzing the results for a hypothetical psychology test, I calculated to find the mean score for all the questions. The scores were totaled by using electronic Microsoft excel for each question per student to calculate the average. The data then was collected by adding the M-mean and dividing by each score. The average was added, and then divided by the number of scores in each column. These test questions provided a lot of distracters all test answers had asterisks and questions that were provided lack instructions and validity, the questions needed more details or the test questions could have been rewritten also the multiply choice questions need more or better choices. In order to ensure that students are not constantly second guessing themselves and that they successful during testing the admitter could have allowed time for proofreading his or her material before administering the test. In our text it states a well written item should consist of both quantitative and qualitative item analysis. To improve on test we should assemble test well in advance and review our material, look for grammatical errors, distracters, double negatives and most importantly making sure the material matches what has been taught as well as test items matching their objectives.
Conclusion:
As a final result we need to do an overall assessment to analyze for the qualitative items to pin point any possible problem before administering test items to students; by looking for content validity and technical item errors, so validity and reliability measurements can be valid. In closing according to Kubiszyn & Borich, as we keep in mind the following steps to assembling test write clear measurable instructional objectives, prepare a blueprint of your test by specifying the number of items for each content process area, as a balance by using the test assembly these steps will help evaluate specified items from our reference to determine accuracy of test questions and answers (p. 232).

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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