Directions:  The purpose of this final is to test your ability to appropriately apply and interpret the statistical techniques learned in class.  As discussed this semester, the application of the techniques depends on the research question and the structure of the data.  To this end, your job is to 1) fully comprehend the research question presented in the scenario 2) appropriately identify the level of measurement for each variable 3) use the correct methodological technique and 4) properly and adequately interpret the results.  When interpreting the results you should discuss your findings as if you were communicating with someone who does not have a statistical background in addition.

The Farfromperfect School District is looking for ways to improve student test scores due to recent changes in the state funding scheme.  The state has long tied funding to student performance on standardized testing.  Over the years, research has shown that while teacher quality does impact test scores, the greatest predictor of success on the state’s standardized test is socio-economic background.  The bottom line is schools with more low-income students have lower overall test scores than schools with fewer low-income students.  As a way to provide low-income students with adequate academic support, the state as devised a new scheme to reward schools for advancing low-income student achievement on the test.  Specifically, the state has calculated average scores for low-income students in the state and has developed a funding formula that awards more money to schools when their low-income studentsexceed these averages.

The Farfromperfect School District is experimenting with a new program in hopes of increasing low-income student test scores.  This program seeks to provide students with a holistic support system.  The Farfromperfect School District provides a stipend to teachers to work with a group of 5-7 students to ensure they are staying up on their school work, assist students in resolving school and home issues, and tutoring for students who are struggling with specific subject matter.

The Farfromperfect School District would like to know if their efforts will pay off at test time.  Recently the students participating in this program took a practice test designed to mimic the material on the State standardized test.  There are three components to the State test; reading, math, and science.  The following variables contain data for the practice test ASReading2 (reading score) , ASMath2 (math score ), and ASScience2 (science score).  The State average for low-income students in these areas are as follows: Reading 16.5, Math 14.6, Science 19.

Question 1: Is there a significant difference between the practice test scores of low income students participating in the afterschool program and the state averages in each test area?

The practice test noted above is actually the second time students have taken the test.  The Farfromperfect School District wanted to measure student progress through the program.  Each student took the practice test at the beginning of the year and was given the test again at the end of the year.  The test scores taken at the beginning of the year could then be compared to test scores taken later in the year to see if students improved their test scores.  The variables ASReading1, ASMath1 and ASScience1 contain data for the test taken by students at the beginning of the year. ASReading2, ASMath2, and ASScience2 contain data on scores taken later in the school year.

Question 2: Have students improved their test scores in reading, math, and science?

Because the Farfromperfect School District is really concerned with improving tests scores of their low-income students, the school district would like to consider potential cultural and gender differences that may influence testing and test preparation.  For example, research shows that female students sometimes do not put forth full effort because they fear "being made fun of" by other students.  There is also a cultural bias that steers females away from math and science because these are male dominated subjects.  Additionally, the Farfromperfect School District has a high Hispanic population and language barriers may inhibit performance on the test.  In sum the FarfromperfectSchool District wants to identify patterns related to race and gender so that they may alter their efforts to accommodate the needs of their students. (Use the test scores from the second test e.g. ASReading2 etc.)

Question 3: Do gender differences exist in math, science, and reading scores?

Question 4: Do differences exist between races in math, science, and reading scores?

Question 5: Do our conclusions change or are there any additional insights if we consider the interactive effect of race and gender?

Question 6: Considering Question 5, do our conclusions change if we control for high likely the student is to pursue college?

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The Farfromperfect School District was able to gather limited data from the parents of the kids enrolled in the program.  Given the abundance of literature that notes how important parents are in influencing the academic success of their children, the school wants to know if their students were influenced in the same way as noted in the literature.  Three questions are of particular concern to school officials.  The first question asks parents how many hours they spend with their child per week.  The motivation behind this question is that the more time a parent spends with their child the better the child will do academically.  The second question asked identifies the highest education achievement of the parents.  Numerous studies have found a link between the parent’s education level and the academic success of their children.  The final question asks parents about their attitudes toward their children earning good grades in school.  Specifically, the question asked parents if they believed that getting high grades (A’s and B’s) in school is important for the future success of their children.  The idea behind this question is that students may not do as well in school because academic success is not reinforced at home.

Question 7: Test the assumptions proposed in the above paragraph.  The variable Achievement contains data on how well the student is doing academically (Note: this measure is an altered measured of GPA.  Legal council advised against making actual GPA of each student available). ParEd contains data on the highest education level of the student’s parents. HoursKids contains data on the number of hours parents spend with their kids per week. GradesImport contains data on if parents think getting high grades is important for future success .

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Given that the State is now tying school funding directly to test scores, there is heighten attention to increasing test scores.  At the last school board meeting, board members had a lively discussion centered around the factors that influence test scores.  The board asked the superintendent to do a study of the local school system so the board and community could start brainstorming ways to improve tests scores in the district.  The board suggested several theories of what might influence test scores.

To answer the questions below first create a variable called Success by combining the three test scores from the second round of testing.  For the below question you will need to identify the correct variable(s) to test the hypothesis put forth by the board member.  Take your time and think through each concept in the hypothesis and consider which variables in the data set most accurately measures the concept.

The Board Member’s statements will direct you toward the variables to include. Run a test for each question below.

Question 8: Board Member A believes academic success all comes down to personal responsibility and motivation.  He states, "Quite simply, personal motivation will predict how well students do on the state test.  Students with direction will have higher test scores because they have the motivation to succeed." He believes that students that know they want to go to college will have higher test scores than students that do no plan to go or are unsure if they plan to go to college. Is Board Member A’s theory correct?

Question 9: Several other Board Members pose their own theories of what influences student test scores.  Read the statements below and test the assumptions.  Be sure to include Board Member A’s theory in your model.

Board Member B agrees with Board Member A , expect he thinks that students that have athletic abilities may not focus on test achievement because they have another path to enter college.  He said, "because athletes may be more focused on honing their athletic talent rather than their test score, we need to control for those involved in athletics."

Board Member C is willing to entertain the ideas presented above, but she puts forth the argument that these students are young, and in most cases are still considered children, so we must not forget the influence of their parents.  She notes that parents who value education will likely instill the same values in their children, regardless of the student’s desire to attend college.

Board Member D throws her hands up in disgust and says the only reasonable idea put forth so far is from Board Member C , but even this theory is flawed.  She argues that this is a classic example of nature versus nurture, and the success of a student is  driven by how much they are nurtured.  The amount of attention the student receives in school and the amount of attention the student receives from their parents are what clearly matters.

Board Member E adds, "we cannot forget about an earlier report that was presented to us that noted our Hispanic students scored significantly lower than our other students.  We need to make sure we take this into account so we can understand the real effect of these other factors on success.

Board Member F jumps into the conversation and challenges Board Member D .  He says that while he disagrees with Board Member A’s conceptual definition of personal motivation, his theory is sound.  Students that take it upon themselves to succeed are more likely to do so.  He even goes as far as to say that, while nurturing will probably influence success, the most important factor of success will the amount of extra effort the student puts into being successful.  He says, "it’s like running a business or being a professional athlete.  Those who are willing to put in the hard work will be successful."  In light of this, he thinks the biggest predictor of success will be the amount of time a student spends studying outside of school hours.

Question 10: Board Member G chimes in….  " Board Member F, you have a point. But don’t forget that we also have data on attendance."  It would probably be prudent to consider this variable in addition to your theory.  After all, a student may attend several of the afterschool sessions and get most of their homework done. Even though they have less hours spent outside of school studying, they are still putting in the time in hitting the books.  Additionally, it is likely that someone that attends the afterschool sessions and studies at home will have very high test scores.

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