How to find out if a person likes some type of clothing? Imagine, I want to build a more or less intelligent agent, which finds out, which clothing a person likes.
Clothing has certain characteristics like type (shirt, T-shirt, pants, skirt etc.), color and style.
Let's assume that first I want to find out, what types of clothing a person likes. For that purpose, I show to him or her several items of different types (i. e. several shirts, several T-shirts etc.) and ask him to tell me, if he or she likes that piece.
At the end, I will have following information:


*

*Type of clothing

*Number of times a piece of clothing of that type was presented to a person

*Number of times the person liked a piece from that type


From that information, I need to find out, if that person likes that type of clothing or not.
How can I test the hypothesis like User X likes shirts apart from using cumulative binomial probabilities (see below) ? Are there other, better ways to do it?
Binomial probability method
At highschool I learned that such hypotheses can be tested using the Binomial probability.
In order to test, whether the user like a particular type of clothing, I do following:


*

*Calculate the cumulative binomial probability.

*If cumulative binomial probability is higher than 50 % for a particular data set (number of times the user saw the picture, number of times she liked it), then I regard the hypothesis "User likes type of clothing X" as confirmed. If the probability is less than or equal to 50 %, then this result may have occured by accident.


Example. Let's say I have shown 10 different shirts to a user. I assume that the success (user likes a particular shirt) is equal to 50 %. The table below shows different situations, which may occur - from when the user did not like any of the shirts to the one, where she liked all of them.
The column "Bin. prob. > 50 %" shows whether in that particular situation I regard the hypothesis that the user likes shirts as confirmed.

The cumulative binomial probabilities are calculated using Google Docs function =BINOMDIST(A2,10,0.5,TRUE).
 A: It sounds like you want a system that, given some training data about a person's likes and dislikes, is able to predict whether the person will like something.  That problem is known as classification.  The basic idea is to collect a data table where each row is an article of clothing, the columns describe the article via numerical or discrete attributes (such as 'color'), and one column gives the label ('like' or 'dislike').  Then you can apply an algorithm such as logistic regression to learn a classifier from this data.
A: I share other users' confusion as to what the heart of your question is. But you reference an 'intelligent agent' you'd like to build, so I gather that your ultimate goal is to suggest products a user is likely to prefer. Systems that perform this task are called recommender systems. 
Collaborative filtering is a common approach to this problem. Taking your example, say you wanted to predict whether or not I would like a certain shirt. As you get at in your comment, designing an experiment to measure my likes and dislikes could be rather impractical. Very simplified, a collaborative filter would attempt to find one of:


*

*users like myself, and suggest their items 

*items similar to ones I like, based on other users' histories


As for the approachable literature mentioned in your comment, an oft-cited and wonderful resource is Andrew Ng's open course on machine learning. This video begins the series on recommender systems and collaborative filtering.
