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Theoretically if one variable (Black and White Imagery) does not significantly correlate with another variable (Perceived Usability), in practice (real world situation) does this mean that there is no relationship between the two variables; in other words, can I say that the Black and White Imagery is considered to be non-usable in this context?

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    $\begingroup$ No, variables can be dependent even if they're uncorrelated. For example, see here and here. $\endgroup$ – user20160 Feb 28 '18 at 5:35
  • $\begingroup$ Can someone explain how two variables can be dependent on each other even if there is no correlation between the two variables, in a psychology context. I cannot understand the mathematical formulae in the link above. Thanks $\endgroup$ – Vyas Mar 2 '18 at 3:38
  • $\begingroup$ Look at the pictures in those links. Correlation only measures linear relationships. Variables can be uncorrelated but dependent if they have a nonlinear relationship. You can think of dependence as measuring how well you can predict the value of one variable by knowing the value of the other variable. $\endgroup$ – user20160 Mar 2 '18 at 5:09
  • $\begingroup$ Is dependence of variable referring to causal relationship in correlation/ or regression? I have never come across a situation for example, if the correlation between two variables small or none, and non-signifiant (p<0.05), then there is still a dependency between the two variables. $\endgroup$ – Vyas Mar 3 '18 at 16:59
  • $\begingroup$ No, that's not the case. Dependence/independence are fundamental concepts in statistics and probability. I'd like to strongly encourage you to read more about this in a stats textbook, as I think it will be a richer and more productive experience than trying to glean information from this comment thread. If you have specific questions based on what you've read, please ask, and we'd be happy to help! $\endgroup$ – user20160 Mar 4 '18 at 0:08