I'd like to perform an ANOVA or similar with data whose residuals are nonnormal. My dependent variable is 1-7, but about 30% of my respondents provided 1's and the plurality of the rest provided 2's. I've tried log and square root transformations with no luck. Any advice on how to proceed?

Basically, the distribution looks like this (with each 1 representing an interval of 10 cases):

1

1

1

1

1

1

11

11

11

11 1

11111

1111111

1111111

Gratefully,

Psychmajor