Samuel, a teacher in middle school, created two forms of the final exam for his students. He distributed them equally to the class. You task is to help Samuel solve the following questions using the following formula
EDF 6432 Foundations of Measurement
Project2 Part 2
NOTE: Each person is expected to work on their own, using resources and information from class, the library etc.
Question 1: Correlation and Validity Discussion (6 points)
The principal is upset. The results of the four-year follow-up study are in. The correlation between the grades assigned by you to your gifted students and their college GPA is lower than the correlation between grades and college GPA for non-gifted students. The principal wants to abandon the gifted program. Explain how you would defend yourself and your program.
Make sure to refer to appropriate materials and to consider the principles discussed in your textbook regarding validity. Your answer should be at least 2 paragraphs in length and will be evaluated based on accuracy and quality of explanation.
Question 2: Reliability, Accuracy, and Error (10 points)
Samuel, a teacher in middle school, created two forms of the final exam for his students. He distributed them equally to the class.
You task is to help Samuel solve the following questions using the following formula related to standard error of measurement (SEM), standard deviation (SD), and reliability (r) of the test. (Show all your computational work)
Standard Error of Measurement = Standard Deviation * Squared Root of (1-reliability)
OR
1. Form A of the final exam has a standard deviation of 20 and a reliability of .75. What is the standard error of measurement for Form A?
2. A student, Susan, had a score of 83 on Form A. What does her true score fall at a 95% confidence level?
3. Form B has a standard error of measurement of 6 with a reliability of 0.84. What is the standard deviation for Form B?
4. Form B has a mean of 150 and Josh performed 1 standard deviation above the mean. What score did Josh have on Form B?
5. Again, Form B has a mean of 150 and David performed 2.5 standard deviation below the mean. What score did David have?
Question 3: Band Interpretation (subtotal: 16 points)
You have a student, Sallie, who just took the FCAT test. Her parents received her FCAT standardized score reports and requested a meeting with you to help them interpret how she performed among these four subjects, that is, they wanted to know which subject Sallie performed better than others.
The following represents Sallie’s obtained score on each subject. For the following subjects, each test has the same mean of 150 and the same standard deviation of 10. Each subject test also has the same reliability of .84. Based on the information mentioned above, please construct 68% and 95% confidence bands for each subject and use them to solve her parents’ question.
Subject
Obtained Score
Math
146
Writing
158
Social Studies
152
Reading
165
Note: M=150,
SD=10, and reliability=.84 for each subject test.
1. Construct 68% confidence bands (CBs) for each subtest (4 points)
Subject
Obtained Score
68% CB: Lower limit
68%: Upper Limit
Math
146
Writing
158
Social Studies
152
Reading
165
2. Discuss how you would interpret Sallie’s performance on these four subjects to parents using these 68% bands above? (i.e., different performance among four subjects is due to chance or true difference?) (2 points)
3. Construct 95% confidence bands (CBs) for each exam. (4 points)
Subject
Obtained Score
95% CB: Lower limit
95%: Upper Limit
Math
146
Writing
158
Social Studies
152
Reading
165
4. Discuss how you would interpret Sallie’s performance on these four subjects to parents using these 95% bands above? (i.e., different performance among four subjects due to chance or true differences?) (2 points)
5. What do you find when comparing your conclusions on Items 2 and 4 in Question 3 based on 68% and 95% confidence bands? That is, which approach (68% or 95%) yields more conservative conclusions? Why? What situation is appropriate for using 68% confidence bands and what situation is appropriate for using 95% confidence bands? (4 points
Question 4: Aptitude-Achievement Discrepancies (subtotal: 18 points)
Your principal asks you to evaluate three students’ performance on mathematics computations and concepts, compared to their aptitude. They will be classified into three categories: “Overachieving”, “At Expectance”, and “Underachieving”. Your principal will make important decisions about these three students based on your classifications.
Three students’ scores on three standard tests, including math aptitude, math computations, and math concepts, are presented below. The standard error of measurement for each test is shown below as well. These three standard tests have the same mean of 52 and the same standard deviation of 8.
Student
Math Aptitude
Math Computations
Math Concepts
Jose
50
60
66
Maryann
62
40
50
Thao
65
85
48
SEM=4
SEM=5
SEM=3
Use the information presented above to answer the following questions
1. Calculate the reliabilities of each subtest: including math aptitude, math computations, and math concepts. (Show all your computational processes.) (3 points)
2. Which test is the most reliable for the set of students tested? Why? (i.e., explain what reliability represents and what high value of reliability represents.) (3 points)
Math aptitude is often referred to as math potential. Compared to the math aptitude score, students’ performance on math computations and math concepts can be classified into three categories: Overachievers, underachievers, and achiever at expectance.
3. Based on Jose’s performance on math computations and math concepts, which category should he be classified into? (i.e., Aptitude vs. Computations and Aptitude vs. Concepts?) Provide your statistical evidence and explain why? Do NOT forget that this is an important decision. (4 points)
4. Based on Maryann’s performance on math computations and math concepts, which category should she be classified into? (i.e., Aptitude vs. Computations and Aptitude vs. Concepts?) Provide your statistical evidence and explain why? Do NOT forget that this is an important decision. (4 points)
5. Based on Thao’s performance on math computations and math concepts, which category should she be classified into? (i.e., Aptitude vs. Computations and Aptitude vs. Concepts?) Provide your statistical evidence and explain why? Do NOT forget that this is an important decision. (4 points)
