I’ve created this spreadsheet in Excel: http://sdrv.ms/14JrMBx (Opens in SkyDrive, then hit “download” to open it locally on your computer with Excel.)
I’m using it to explain to folks the significance of “odds ratios.” For example, if there is an outbreak of measles in a group of children, and a lot of the children in the outbreak are vaccinated, the odds ratios (OR, for short) will explain to you why children in that outbreak are far more likely to be unvaccinated. Intuitively, people look at a group of kids with measles and think, “Hey, most of the kids were vaccinated, so, obviously, the vaccine doesn’t work!” This would only be the case if the population in question was mostly unvaccinated.
When the population where the outbreak is happening is highly vaccinated, you would expect to see a lot of vaccinated children as part of the outbreak. This is not because the vaccine doesn’t work as expected. It’s because the vaccine is not 100% effective. No vaccine is. Yet they are better than nothing.
So look at the spreadsheet and play with it a little bit, plug in some numbers. See how many children in an outbreak would have to be vaccinated before you can say that the vaccine is worthless. Let me know if you have any questions.