By the way, your data seem to be ipsative, i.e. the sum of the rankings, for each participant, is constant. If there are, e.g. 5 foods to be ranked, the sum is 1+2+3+4+5.
Greer & Dunlap have argued one can run ANOVAs on such measures. Just run a repeated measures ANOVA with the Food rankings as repeated measures factor.
Citation:
Greer, T., & Dunlap, W. P. (1997). Analysis of variance with ipsative measures. Psychological Methods, 2(2), 200-207 .
Jos Feys Thank for your sharing the syntax files! I prefer to analysis my data in SPSS. Can you explain more on repeated measures ANOVA? Do you meant the ONE-WAY REPEATED MEASURES ANOVA?