14.4 Observing relationships

For the small kidney stone data, the odds of a success for Method A is different than the odds of a successes for Method B, in the sample. Broadly, two possible reasons exist to explain the differences in the sample:

• The odds in the population are the same for Method A and Method B, but a difference is observed in the sample odds simply because of who ended up in the sample. Every sample is likely to be different, and the sample we ended up with happened to show a difference. Sampling variation explains the difference in the sample odds.

• The odds in the population are different for Method A and Method B, and the difference in the sample odds simply reflects this difference between the population odds.

Similarly, the proportion (or percentage) of successes for Method A and B are quite different in the sample, and two possible reasons exist to explain the differences in the sample:

• No difference exists between the proportion (or percentage) in the population, but a difference is observed in the sample simply because of who ended up in the sample. Sampling variation explains the difference in the sample proportion (or percentage).

• A difference does exist between the proportion (or percentage) in the population, and this difference in the sample simply reflects this difference between the population proportion (or percentage).

The difficulty, of course, is knowing which of these two reasons (‘hypotheses’) is the most likely reason for the difference between the sample odds. This question is of prime importance (after all, it answers the RQ), and is addressed at length later in this book.