Categorical data

Obviously, this is right. There can be no doubt about it. :smile:

But please don't round off this much. Without rounding off during calculation of the two odds, you would have got the value of the odds ratio as 5.

I don't think I've ever come across this phrasing in interpretation of odds. I can't this wrong, but I'm more familiar with any of the following forms:

When people are rich, following politics is 0.29 times more likely than not following politics

, or, equivalently,

When people are rich, not following politics is 3.5 times more likely than following politics

, as 3.5 = 280 / 80, and it is the odds of not following politics among the rich people.

I don't know which book you're following, but in our college, and in many of the colleges in India, An Introduction to Categorical Data Analysis by Alan Agresti is used. Let me quote from Section 2.3 from 2nd edition of that book:

For a probability of success π, the odds of success are defined to be odds = π/(1 − π).

For instance, if π = 0.75, then the odds of success equal 0.75/0.25 = 3.
The odds are nonnegative, with value greater than 1.0 when a success is more
likely than a failure. When odds = 4.0, a success is four times as likely as a failure.
The probability of success is 0.8, the probability of failure is 0.2, and the odds equal
0.8/0.2 = 4.0. We then expect to observe four successes for every one failure. When
odds = 1/4, a failure is four times as likely as a success. We then expect to observe
one success for every four failures.

Hope this helps.

PS

From your previous two or three questions, it seems to me that these are all homework related. Though I completely understand that you're not posting any verbatim assignment, I think you should at least be familiar with the following post:

Also, since you're more interested in the interpretations of the results, which have nothing to do with R or RStudio, so probably (I'm not sure, and certainly I've no authority at all to say this) this forum is not an appropriate place to ask these questions.

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