There is only a significant difference in beta diversity between infected and non_infected groups, and no significant difference in alpha diversity and not clearly separable in PCoA plots. Whether can we think there is a significant difference between infected and non_infected groups?
Yes. I have the data from two groups (infected and non_infected groups). Firstly, I did alpha diversity analysis and the result showed that there is no significant difference between the two groups. Then, I did beta diversity analysis and the result showed that there is a significant difference between the two groups. And the two groups have not clearly separable in PCoA plots. The metrics used in PCoA plots are identical with the metrics in beta diversity.
Whether can we think there is a significant difference between the two groups?
@terren, are you asking whether there is a significant difference between your infected and non-infected groups?
Without knowing specifically what your results are, it's impossible to give you a definitive answer, but I'm confident you can figure it out.
First, though, a question for you to answer:
Do the results of your alpha diversity commands have anything to do with the between-group difference you're trying to quantify? What are alpha and beta diversity?
This post has already done a rather comprehensive job of answering your questions about interpreting beta-diversity, and seems to answer the question I think you're asking.
In case it helps, you can think about Emperor/PCoA plots (like most data visualization tools) as useful tools for visually identifying trends in your data. Quantitative analysis, on the other hand, is necessary for determining whether the differences you're seeing are statistically significant. Pictures make it easy to figure out what's going on, but the numbers allow you to turn those insights into concrete findings.