In the hypothetical case, A school district has analyzed data on student performance and noticed there are is a significant proportion of the student population with potential learning disabilities. To remedy the situation, the school district applied a range of interventions, including 1) systematic and explicit instruction, 2) visual representation of relationships and functions, 3) peer-assisted instruction and 4) ongoing formative assessment. However, the school district needed to assess the efficacy of each intervention in addressing the challenge of poor performance by students.
Research Question
Two main research questions can be used within the context of the case.
1.    Do systematic and explicit instruction, visual representation of relationships and functions, peer-assisted instruction and ongoing formative assessment affect student performance?
2.    Are there differences in student performance by intervention type/level, i.e., 1) systematic and explicit instruction, 2) visual representation of relationships and functions, 3) peer-assisted instruction and 4) ongoing formative assessment?
Variables
Independent Variables
The independent variables will include the four interventions used to assist students with learning disabilities. As such, the analysis will entail four independent variables, i.e.,
1.    systematic and explicit instruction
2.    visual representation of relationships and functions
3.    peer-assisted instruction
4.    ongoing formative assessment.
Dependent Variable
The dependent variable, in this case, entails student performance because this is the main objective of the research. The application of the interventions is designed to improve the performance of students, which makes this the ideal dependent variable.
    Student performance
Level of Measurement
The variables employed in the research will use different levels of measurement. Each of the four independent variables, i.e., 1) systematic and explicit instruction, 2) visual representation of relationships and functions, 3) peer-assisted instruction and 4) ongoing formative assessment, will employ the nominal level of measurement. The four independent variables are nominal values as they represent levels of the same variable, i.e., intervention. However, the value on names or uniquely identifies each level instead of ordering them. However, for the dependent variable, i.e., student performance, the researcher will use ratio level of measurement. Student performance entails a count variable, which is also a ratio variable because it has a meaningful zero, where zero reflects no score (Huck, 2012).
Planned Analysis
      To answer the first research question, there is a need to conduct a regression analysis. Regression analysis is required for the first research question as it would allow the researcher to measure how each of the independent variables in the data set affects the dependent variables. Additionally, it would also indicate how each of the independent variables affects the other independent variables (Morgan, et al., 2002). Such an analysis would employ a data analysis tool such as excel. The second research question essentially seeks to determine the existence of any differences between the means of the four interventions, or four groups of students. As such, an ANOVA analysis will be conducted on the independent and dependent variables. An ANOVA analysis best describes any differences between the performance of students for each of the four types or levels of intervention. Ascertaining the existence of underlying differences is integral to determining the most effective method(s) to improve student performance within the district. This is useful in ascertaining the types of resources that are required and the expected outcomes using one or a combination of interventions.
References
Huck, S. W. (2012). Reading statistics and research (6th ed.). Boston: Pearson Education Inc. Companion Website -http://www.readingstats.com/Sixth/index.htm
Morgan, S. E., Reichert, T., & Harrison, T. R. (2002). From numbers to words: Reporting                statistical results for the social sciences. Boston, MA: Allyn & Bacon. ISBN: 9781138638082