If I now have a dataset like this:

Person; Fruit; Rank

1 ; Apple; 1

1 ; Banana; 2

1 ; Pear; 3

2 ; Apple; 2

2 ; Banana; 3

2 ; Pear; 1

[...]

50 ; Apple; 1

50 ; Banana; 3

50 ; Pear; 2

What is the best way to analyse this data?

I could do a Chi-squared test on a contingency table built up from the data where rank==1, thus showing that preference is non-random. But then I lose data on the other rankings. What I'd really like to do is have an outcome that is more informative.

For example, I would like to be able to say that bananas were given a mean rank of 1.3+/-0.2 and this was significantly different from the ranking of apples (2.5+/-0.1). But to simply do t-tests to compare ranking scores for bananas vs. ranking scores for apples would violate the assumptions of the t-test (independence of data points.)

Sorry for rambling a bit, but I hope you get my point.

Any ideas? Or maybe you can point me to some references.

Thanks,

jo