I want to point out that your analyses, while consistent with the way that statistics is commonly taught (badly) and with most introductory statistics books, is increasingly seen as bad practice. Evidence such as you have should not be viewed as answer the question: is there a relationship between x and y or is there not a relationship? All results are in terms of probabilities, i.e., shades of gray rather than yes/no questions. Dichotomizing the answer, in my opinion, is poor statistical practice. Decisions are often dichotomies, but the evidence never is. Determining causal relationships is even more nebulous. I'd recommend focusing on how good (or not) the data is, and how much variation there is in the data. Your data set is fairly small for such qualitative questions, so I don't think it is appropriate to conclude anything from this data. Rather, the best you can do is say whether your limited data is consistent with a particular hypothesis or not. And, if you reject the hypothesis that there is no relationship, don't interpret this as supporting whatever particular alternative hypothesis you have been considering. Rejection just means you are judging the evidence sufficient to say that something more than random variation is accounting for the patterns you are seeing (or as some others have said, the null hypothesis - no effect - is surely wrong; what is of more interest is what you can say about the effect size: it is definitely not zero, but the real question is how large is it?).
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