By testing i found my data is non-normal so i can't apply t-test moving toward non-parametric test(mann whitney -U) the assumption that both distribution have same shape is violated although it is non normal,ordinal scale so which test I should chose to apply on data
If the hypothesis you want to test is ‡
Ho: The probability that an observation in Group1 is greater than an observation in Group2 is 0.50 (Stochastic equality)
then there is no assumption that the distributions are similar in shape.
The assumptions listed by Conover † are:
1) Both samples are random samples from their respective populations.
2) In addition to independence within each sample, there is mutual independence between the two samples.
3) The measurement scale is at least ordinal.
The assumption about the shape of the distributions comes in to play only if you would like to test a hypothesis about the location difference (difference in median, say) between the two Groups.
‡ My phrasing for the hypothesis
† Conover, W.J. 1999. Practical Nonparametric Statistics, 3rd ed. Section 5.1.