Question from 2016 papaer

Hi there!
I have a question from the 2016 paper Q 2 bii)

So the relative risk calculated in the marking schedule is the risk of Jazz being diseased over the risk of Beauty being diseased. We compare this to the RR of diseased depending on the growing method.

I don’t understand why we are calculating this RR because by doing it this, we are determining how many times more likely it is for Jazz to be diseased compared to Beauty, and we compare this to how many times more likely it is for conventionally grown to be disease compared to organically. When the question in asking how many times more likely it is for the type of apples to cause disease compared to the growing method.

The way I worked out the problem was by finding out the risk of Jazz variety + risk of Beauty variety being diseased.

52/890 + 128/310 = 0.4713 (4d.p)

I then worked out the risk of organically grown+ risk of conventionally grown.
122/640 +58/560 = 0.2941 (4d.p)

I then compared the risk of these.

0.4713/ 0.2941 = 1.602

Therefore apples are 1.602 times more like to be diseased because of variety compared to the growing method.

So my answer is incorrect, any kind of clarity or insight would be really useful for me!

The question is asking if “apples are more likely to be diseased depending on their variety than
whether they have been conventionally or organically grown”. It is not asking how many times it is more likely to be diseased depending on the type of apples compared to the method of growth.

When you made your calculations you got two different answers because the distribution of the apples between the groups is not equal (you have more Jazz apples than Beauty and more conventionally grown apples than organically). You can’t simply add the probabilities of apples becoming diseased for Jazz and Beauty apples to find a total probability for the apple from the given group to have a disease as these types of apples in the group are represented by samples of a different size. For example, Jazz apples have a 52/890=0.0584 probability to have a disease and Beauty apples 128/310 = 0.4129. But there is almost three times more Jazz apples in the group compared to Beauty apples so Jazz apples’ contribution to the total probability to pick up a diseased apple from the whole group would be more significant.

But you are asked to decide which factor affects disease more - type of apples or the method of growth. Comparing 0.4129 (probability of Beauty apple to have disease) to 0.0584 (probability of Jazz apple to have disease) we can see that the former is over 7 times more likely than the latter. When you compare the probabilities of conventionally grown apples to have disease (122/640 = 0.1906) and organically grown apples to have disease (58/560 = 0.1036) you can see that first is just 1.8 times more likely than second. So you may conclude that method of the growth has lesser effect on the disease than type of apple grown.