With the current flourishing use of technology in education, a school district wants to conduct a study to determine which high-tech, the student-centered instructional method would be more successful in preparing students to take standardized tests in the district. You are hired as a statistician for the district to help them elucidated this issue.

As the statistician, you are investigating the longitudinal effects (one academic year) of different high-tech, student-centered instructional methods on the results of standardized mathematical tests. You have four groups; each one will be using a different high-tech, student-centered instructional method approach (inquiry-based learning, expeditionary learning, personalized learning, and game-based learning).

Describe the data analysis plan for this project, and be sure to address the following in your response:

1. Define your independent and dependent variables and your design
2. What is your research hypothesis (hypotheses) and the corresponding null hypothesis (hypotheses)?
3. Which statistical methods or tests do you plan to use to describe your data and test your hypothesis? Briefly explain the purpose for including each of the methods or tests in your analysis.
4. What are the assumptions for the statistical test of your hypotheses? How will you determine if those assumptions are reasonable for your data?
5. What descriptive or follow-up (post hoc) tests do you anticipate may be needed?
6. Assume that your data analysis supports your primary research hypothesis. Write one or two paragraphs that describe the results of the statistical tests of the hypotheses (i.e., just the results related to the anticipated main finding).

Part 3:

Assume you are an educational researcher who wants to investigate the effects of socioeconomic status (SES), home environment, and school and neighborhood environment on the academic achievement of middle school students. You designed a survey to collect the necessary demographic (SES, home environment, neighborhood environment) data to match it with their standardized test results.

Your survey is divided into three sections. Section 1 includes SES information: parent's education, employment status (currently employed: yes or no), income level, and receiving free or reduced lunch at school. In Section 2, the questions are regarding the environment at home, time spent watching (playing video games) TV at home, having a TV in their rooms, computer available at home, Internet access at home, etc. Finally, Section 3 includes questions related to the safety of the neighborhood environment; some examples include if the students walk to school, how safe they feel while walking to and from school, do they feel safe at school, are there a lot of fights at school, etc.

The purpose of collecting these data was to develop a model that can help to predict academic achievement in middle school children using some of these variables.

1. There are many variables collected in these data. Your first task is to discuss some of the considerations that you must make to determine which variables could or should be included in the model. Be sure to discuss the concept of multicollinearity.
2. How could you measure for multicollinearity? How could you address multicollinearity?
3. If you decide to eliminate several of the independent variables, in order to reduce the number, how should you determine which variables are more important than others to include in the model?
4. Assume that the end result included five variables that were significant predictors of academic achievement. Write the estimated regression equation for the model with all five variables.