Interpreting contradicting results T-Test vs. Mann-Whitney test (2 independent samples) I want to test if two indepent experimental groups are sign. different in terms of one outcome variable, but face the following questions:
Basic setup


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*2 groups with 200 observations each

*Outcome variable: 


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*continuous

*ranging between 0 and 600

*very peaked: more than 60% of values are equal to 300

*Group 1: mean = 221.9807, median = 300

*Group 2: mean = 239.6396, median = 300



Result of statistical tests
Although the outcome varible violates the normality assumption, I orginally used a two-sample independent t-test based on my large group sizes and the central-limit theorem:
Result of T-test: no signifcant difference (p=0.166).
However, to be on the safe side I also used a nonparmetric test, i.e. the Mann-Whitney U test:
Result: of Mann-Whitney U test significant difference (p=0.023).
Questions


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*My interpretation: Mean outcome not sig. different, but distribution of outcome varible differs between groups. Is that correct?

*Could it be a problem that the vast majority of my values are equal to 300? Does the MW test ignore values that are equal to the median?

 A: The original Mann-Whitney test assumes continuous distributions.
If there are many observations and few ties, a normal approximation with a correctly-calculated variance is sufficient.
To deal with heavy ties, the Mann-Whitney test needs to properly deal with the effect those ties have on the distribution of ranks under the null; in some cases the effect can be substantial.
What happens in that situation varies from package to package - some packages don't handle heavy ties well. 
The p-value from the t-test may well be suspect.
I'd be inclined to perform a permutation test on the actual set of ranks, or if primary interest focuses on testing for a difference in means, perhaps a permutation test based on the means; this way I don't have to rely on either the t-statistic having a distribution close to the t-distribution under the null, nor on the Mann-Whitney correctly dealing with heavy ties.
A: The Mann Whitney test and the t-test ask different questions, so they give different answers. The t-test is a test of difference in means, the MW is a test of difference in distributions.  In addition (as you noted), the t-test makes assumptions about the distributions that the MW does not. 
However, if the vast majority of your values are equal to exactly 300, then I think you might want some other method, but I am not sure what. Clearly, your data is not continuous (or values would not be exactly 300) and the t-test definitely assumes continuous variables.  In addition, all those values will have the same rank in the MW test (which may be what you mean by "ignoring medians").  
I think you need to think about what exactly you want to test between these two distributions. 
