I am wanting to compare two independent groups on a likert-like item. To explain, the dependent variable is structured so that a 1 = <1 units, 2 = 1-<2, 3 = 2-<3, all the way up to option 7 = >6. Initially, I was planning to use a t-test to compare the two groups as I have read that with seven items, even a likert scale item can be used as interval data. I have a single outlier on this dependent variable. While I have gone through the data and have not found anything that would suggest the response is inaccurate, it is very influential to my distribution. It brings the Skew from .792 to 1.2, above the rule of thumb for skew < |1| and above the CI cutoff. I would look to a Mann-Whitney U, but have found that this one outlier also significantly impacts the distribution of one group, creating unequal distributions. From what I have read, this eliminates the Mann-Whitney U as an option. Since it is a single data point that is creating this problem, I would love to be able to simply remove it (I have a large enough sample size that losing one participant won't make much of an impact), but I do not want to bias my results by doing so. I am seriously stuck on where to go with this analysis!
After running the t-test with and without the outlier it results in a p-value of .047 with, and .014 without. While both are significant at a level of .05, I am also running t-tests with two other dependent variables (not correlated so multivariate methods were not warranted). So after a Bonferroni correction, only values < .016 can be accepted as significant. This makes the t-test with the outlier non-significant and without the outlier significant.
Out of 179 responses, only one had a value of 7 and the next lowest option was 5. Most responses were between 1-4 so the 7 has pulled the distribution to the right.