Given the same underlying data, the post-hoc procedure most likely to yield a significant result is: Tukeys t-test Levenes Bonferonni

The choice of post-hoc procedure that is most likely to yield a significant result given the same underlying data depends on various factors such as the nature of the data, the specific research question, and the statistical power of the test. However, generally speaking:

1. Tukey's test: This is a single-step multiple comparison procedure and statistical test. It is used to find means that are significantly different from each other. It's generally considered to have more power than the Bonferroni correction, which can be overly conservative.

2. t-test: This is used to determine if there is a significant difference between the means of two groups. It's generally more powerful than Tukey's test when comparing just two groups, but less powerful when comparing multiple groups.

3. Levene's test: This is used to assess the equality of variances for a variable calculated for two or more groups. It's not a post-hoc test, but a test for homogeneity of variances.

4. Bonferroni correction: This is a method used to counteract the problem of multiple comparisons. It's generally considered to be the most conservative of these methods, and thus the least likely to yield a significant result.

So, if you're comparing multiple groups and want to control the Type I error rate, Tukey's test is likely to yield a significant result more often than the Bonferroni correction. However, if you're only comparing two groups, a t-test might be more powerful. Levene's test isn't really comparable to the others as it tests a different hypothesis.