# Preference Index: Observed v Expected?

I am in the process of forming an index for frugivore preference/avoidance of certain fruit types of differing colours. It is hypothesised that for a given fruit type of a certain colour, the frugivore will either prefer or avoid it. For simplicity purposes, let's assume the fruit types are A, B, and C. And the colours are 1, 2, and 3.

I know that for a preference index, I need to know the observed and the expected values. Observed should be the proportion of food type x in the 'gut' whereas expected should be the proportion of food type x in the environment of all available food.

I am fairly certain that Observed should then be written off as, for example:

number of Fruit Type A of Colour 1 eaten / Sum (Fruit of colour 1 eaten)

I am having a bit of trouble grasping the expected value. I am imagining it as being either:

number of Fruit Type A of Colour 1 total / Sum (Fruit of colour 1 total)


or

number of Fruit Type A total / Sum (all fruit total)


My data will be set-up in a spreadsheet in the following way:

Fruit Type

Capsule   Drupe   Fig


and

Fruit Colour

Yellow

Orange

Red

Brown

Green


Any comments or thoughts on this would be greatly appreciated!

• So the way you've defined expected value here "proportion of food type x in the environment of all available food", leads to the 2nd interpretation. – VCG Aug 19 '16 at 15:05
• Perhaps I actually meant to define it as "proportion of food type x of colour type y in the gut" and "proportion of food type x of colour type y in the environment." in this case, I suppose it would be interpretation 1? – Ryan Rothman Aug 19 '16 at 15:09
• Okay then in that case I would do fruit type+color as that in itself is a complete 'type' of fruit, given your specification? So every combination of type x color would be the `goods' that the animals have preferences over. It would be interesting to see if their preferences are transitive. – VCG Aug 19 '16 at 15:12
• Yes, this is actually what I think it should be. Interpretation 1 where fruit type and fruit colour are together as a single 'type' or 'food item' if you will. This will lead to every possible combination being tested as you mentioned. – Ryan Rothman Aug 19 '16 at 15:16