If you entered data onto a column table and requested a correlation matrix, Prism will report a P value for the correlation of each column with every other column. To make a strong conclusion, you’ll need data from a larger experiment. On the other hand, if the confidence interval contains correlation coefficients that you would consider biologically important, then you couldn't make any strong conclusion from this experiment. If the entire interval consists of values near zero that you would consider biologically trivial, then you have strong evidence that either there is no correlation in the population or that there is a weak (biologically trivial) association. It will extend from a negative correlation to a positive correlation. You just have no compelling evidence that the correlation is real and not due to chance. This is not the same as saying that there is no correlation at all. If the P value is large, the data do not give you any reason to conclude that the correlation is real. If the P value is small, you can reject the idea that the correlation is due to random sampling. If there really is no correlation between X and Y overall, what is the chance that random sampling would result in a correlation coefficient as far from zero (or further) as observed in this experiment? It is not appropriate to compute r2 from the nonparametric Spearman correlation coefficient. Prism only calculates an r 2 value from the Pearson correlation coefficient. More simply, 59% of the variance is shared between X and Y. Likewise, 59% of the variance in Y can be explained by variation in X. For example, if r 2 =0.59, then 59% of the variance in X can be explained by variation in Y. It is a value that ranges from zero to one, and is the fraction of the variance in the two variables that is “shared”. Statisticians call this quantity the coefficient of determination, but scientists call it "r squared". Perhaps the best way to interpret the value of r is to square it to calculate r 2.
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