Relationship between ESL program variables and English proficiency test scores

¶ … groups or the relationship between variables?

The hypothesis involves a relationship between variables. ESL programs are intended to help students who have a deficiency in English skills. In many instances the program has many individuals who are from other countries and speak another language. The Stanford English Language Proficiency Test is designed to gauge to proficiency of students English skills. Therefore, we would like to determine the relationship between involvement in ESL programs and the overall improvement of English skills of students.

How many independent variables do you have? How many dependent variables? What are they?

In the case of ESL programs and the link to improved scores, there are many independent variables. For example prior education is an independent variable that impacts test scores. The education of parents and their impact on learning comprehension and assessment is an independent variable. The overall caliber of the both the teacher and the school itself are also variables that need consideration. In regards to dependent variables, the actual time spent studying English material is a dependent variable. Exam scores ultimately will depend on the amount a time a student spends studying the material.

Are there any covariates being controlled?

The school and teacher covariates are being controlled.

Is the independent variable categorical or continuous?

The independent variables are categorical. For example many of the variables mentioned above can be placed in their respective categories. Parental education can be placed in a category of high school, college, some college, graduate and doctoral. Schools are often ranked by their respective states. For example, in Florida, schools are ranked from "A" to "F." These categories can therefore be used in the regression. Much like schools, teachers are also ranked by their respective states. Online reviews, teacher assessments, and overall classroom grade are all categories that can be used to assess the overall strength of the teacher.

Is it possible to use a Chi-Square Test and why

The Chi-Square test would be ideal for this situation as it is designed to measure the relationship between two categorical variables. In addition, the sampling distribution can be made to approximate a chi-square distribution as closely as desired by making the sample size large enough. In this instance, students in ESL classes should constitute a large enough sample size. The only downside to using the chi-squared test is that the population may not be normally distributed in some instances. For example very few students will have failing grades in some instances. The distribution could potentially be positively skewed as more observations are around the "A" and "B" level. Some failing schools may have a large distribution of students who are failing resulting in a negatively skewed distribution. As a result, more observations will be needed with varying schools to make the distribution normal (Bagdonavicius, 2011).