I am trying to analyze responses from a survey. The outcome variable is named "reading_proficiency" and is dichotomous with two values 0 and 1. The data set has 3,539 observations so the column "reading_proficiency" has 3,539 observations of either 0 or 1.
I am trying to understand whether I can use the ideas of binomial distribution here. Can the variable "reading_proficiency" be a random variable?
The definition of a random variable I am using is as follows. A random variable is a variable that takes on different values determined by chance. In other words, it is a numerical quantity that varies at random.
Are the values of "reading_proficiency" truly determined by chance? Are two observations of "reading_proficiency" truly independent of one another?
If two observations are from the same survey cluster, they might have attended the same schools, been taught by the same teachers and thus have the same "reading_proficiency".
Is the fact that many observations are from the same cluster disqualify "reading_proficiency" from being a random variable?
I was reading that each observation of "reading_proficency" should be mutually independent but this is not the case for survey data, or...?
Does it mean survey data cannot be random variables?