# #StackBounty: #r #hypothesis-testing #classification #experiment-design #double-blind Design a double-blind expert test when there is i…

### Bounty: 50

I would like to submit to an expert group a set of images from two genetically different types of plants to see if they can find a difference. I have 20 images for each of the two types. Images are images of cells that are so specific that only a small group of 10 experts are able to see the potential differences (without knowing which type it is).

To have a powerful test, I choose to work with a two-out-of-five test, which means that I show experts five images in which 3 are from type1 and 2 are from type2. The have to define two groups of images. I chose this test because of its power. The probability to group the images correctly by chance is only 1/10. Because the number of experts is really small, using this test instead of a triangular test or a simple two images test, is in my point of view more powerful.

The variability of intra-type images is quite high. If there is a difference between the two types, it will be small, within this set of 2*20 images. Hence, if there is a difference, I would like to know which images are the most different. I cannot show more than ~50 sets of 5 images to my experts as they do not have a lot of time to perform the analysis. The problem is that there is about 400000 possibilities if sets of 5 images (3 type1 – 2 type2).

I think that choosing randomly my 50 sets among 400000 for each expert is not really representative. It would be more interesting to choose the sets so that each image has been compared to each other, so that I can define if there are similar or different (which can be infered from the 2-out-of-5 grouping). Randomly, I will not be sure that I tested all images against all (at least indirectly) with my only 10 experts. Thus, I decided to create a sample of 50 sets, different for each expert, that maximises the number of couples compared either directly or indirectly. However, with this sampling, some couples of images are more compared than others, which is why I forced my selection so that each couple is compared at least 3 times directly or indirectly.

This seems to be a quite complicated sampling procedure. For me, this is the only one that makes me sure I will be able to correctly compare all my images, in a few shot for each expert, knowing that once I have shown it to my experts, I will not have any other chance to find another expert group. And they won’t be able to take more time to do it again.

To summarize, I want to know :

1. Are my two types different ?
2. Which cell images are more different than the others ?

Do you think I am going in a too complicated way ? Is random a better solution even if I will be able to only test 50 sets * 10 experts among 400000 possible sets ? How can I be sure not to bias my sets selection procedure ?

By the way, I work with R, but I don’t think this is really important for this question

Get this bounty!!!