I think I am looking at odds or likelihood ratios in this scenario, but I'm having trouble figuring out how to actually calculate my numbers to get an answer to my questions.

I have 309,508 total 3rd graders in the state. 179,107 are economically disadvantaged and 130,401 are not. Of the students economically disadvantaged, 101,464 did meet reading level standards and 77,643 did not meet standards. Of the students that are not economically disadvantaged, 108,269 did meet reading level standards and 22,132 did not meet standards.

My ultimate questions to answer is: Of 3rd grade students in the state, how LESS likely is it that economically disadvantaged students will be on or above reading level standards?

I calculated my odds ratio as (A x D)/(C x B) then AD/CB to get my percentage. This can be seen in the chart below;

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Could I then interpret this as: Economically disadvantaged students are 27 percent more likely to not be reading on or above grade level standards by 3rd grade than their peers who are not economically disadvantaged.

I'm stuck on where likelihood comes in, how it's different from odds, and how to calculate it for this scenario so I can get a less likely answer.

  • $\begingroup$ Quick clarification question: do you have data for the entire population of interest here? From the language, it sounds like you have data on every 3rd grader in your state, so if the goal of this is to say something about how economic disadvantage affects 3rd grade reading, then you don't need a statistic -- you don't need inference because you have the population's data. If you do want to generalize your sample to other populations (e.g., other grades in your state, 3rd graders in other states, etc), then identifying the correct statistic does become a concern $\endgroup$
    – Billy
    Jul 20 at 19:30
  • $\begingroup$ This is just for the 3rd grade students in the state and the numbers above comprise all of those 3rd graders only. I'm not trying to generalize to other populations. Does that answer your question? $\endgroup$
    – Annie
    Jul 20 at 22:25
  • $\begingroup$ Yeah: in that case, you don't need to worry about computing odds or anything like that. You can just state the data: 43% of those who are disadvantaged do not meet reading standards compared to 17% of those who are not disadvantaged. That's something like there being a 152% greater chance of a student who is economically disadvantaged not meeting reading expectations than a non-economically disadvantaged student $\endgroup$
    – Billy
    Jul 20 at 23:11

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