I think you are asking if there is a difference in the utility scores (the preference) among three levels within your fourth attribute.

There are multiple ways to do this:

1. From Aggregate Logit report. For each attribute level, you obtain a raw utility score and a standard error. The t-test is to divide the difference in the utilities between two levels of interest within that fourth attribute by the pooled standard error, where the pooled standard error is equal to Sqrt (SE1^2 + SE2^2), where SE1 is the standard error for the first level and SE2 is the standard error of the second level. A t with absolute magnitude of 1.96 or greater indicates 95% confidence that there is a difference between those levels (in aggregate across the sample).

2. From individual-level HB utilities (paired sample t-test). Open the individual-level utility file (as produced by CBC/HB software...and I'd prefer the zero-centered diffs normalized output rather than the raw utilities) within Excel. Create a new column in the spreadsheet which is one of the attribute levels within the fourth attribute minus the other one you are comparing within the fourth attribute. Copy that down across all records. Take the mean and the standard error of that new column. The standard error is equal to the standard deviation of that new column divided by the SQRT(N), where N is the sample size. The t-test is the mean divided by the standard error. Again, look for t > |1.96|.

3. From the draws of population alpha .csv file (after convergence is assumed...so ignore the first 5000 or 10000 draws) as produced by CBC/HB software, count how many times one level within that fourth attribute is preferred to another level within that fourth attribute. The % of draws where one level is favored over the other is a direct statement of the probability that one level is preferred to the other for the sample.

I've given these tests in rank order (worst to best) of their effectiveness. The 3rd Bayesian test is probably the strongest of the tests. And, the paired samples t-test is preferred over the aggregate logit test.