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This relatively short question raises numerous different issues. Here are some: In statistics, independence is an absolute condition, not something that exists in degrees. Correlation measures cor …

Assuming a two-way table of species $\times$ environments, then so-called Pearson residuals can be defined for the frequencies in the table as $(\text{observed} - \text{expected}) / \sqrt{\text{expect …

If your sample size is 9, then multiple regression is a real strain. Think that even with two predictors $X_1, X_2$ and a response variable $Y$, you are estimating three parameters (constants to be …

You are correct. A fuller quotation is If the p-value is less than the significance level (in this case 0.05, a 95% confidence interval), the null hypothesis that the data is normally distrib …

I don't think this is anything to do with P-values. In any case you nowhere specify what test you have in mind. The usual definition of a fair coin I take to be that heads and tails are equally prob …

If you consider the form of the classical Pearson chi-squared statistic, as the sum of (observed frequency $-$ expected frequency)$^2$ / expected frequency, you can see that the sign of the discrepanc …

If two sets of observed counts (two rows say of a $2 \times k$ contingency table) are exactly equal, then the corresponding expected counts are also equal to them and a chi-square test should yield a …

I agree with the general tenor of other comments (including an aversion to stepwise). Like others I have reservations about polynomials here, and would tend to prefer splines, but you can do one simpl …

This is another example of a widespread phenomenon, whereby significance tests from larger sample sizes give lower P-values for otherwise equivalent results. Consider a simpler example from tossing …

Averaging Pearson and Spearman is an original idea, but in practice it just avoids the key issue of what you should be estimating in an arbitrary way. Why not use weights other than equal weights, s …

As pointed out in comments, the more complicated model has too many predictors to be taken seriously. I focus here on models with 6 predictors. I have used MATLAB very occasionally in the past but n …

This broadens the discussion to ask whether you're focusing on one question -- the comparison of overall levels -- when other questions arise that seem as or possibly even more important. The boxplots …

The $P$-value reported for a correlation depends on the sample correlation, the sample size, and a bundle of assumptions not always checked (independence being, in my experience, least checked of all) …

Here are your data shown more plainly: response HIST1H3F_rna NCF1_rna WDR66_rna PTH2R_rna HAVCR2_rna CD200R1_rna 1 0 1.0986123 2.772589 5.068904 0.6931472 4.488636 2.4849066 2 …

This is intended to complement the nice answer from Paul, not contradict it. The simplest theory for estimating correlation (indeed anything) is to postulate that there is one unknown constant value …