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I have two variables. Sense of belonging and anxiety. I found a Pearson's correlation that was weak but significant. The significance was probably due to sample size (n=400). Then I conducted a t-test of high and low sense of belonging and anxiety. The t-test found a significant difference between the group of 0.6, had a medium effect size. I'm having trouble now though because I don't understand how one can say there is weak/no relationship and then the t test indicates there are significant differences between the groups. Can anyone help me 'get' why this happens/what it means?

I don't think there is a contradiction I just don't understand how to interpret the results.

Jess
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  • I'd plot your data to understand what is going on; that is essential. Essentially the $t$ test and the correlation answer quite different questions. Consider that $x$ has mean $0$. Then any $Y = bX, b > 0$ also has mean $0$ and has correlation $1$ with $X$. So "no difference in means" is compatible with "perfect correlation". Similarly it is possible that $X, Y$ are not correlated but have quite different means. – Nick Cox May 07 '15 at 11:16
  • plot as in look at a scatter plot/histogram? – Jess May 07 '15 at 12:53
  • Plot, in the first instance, as in scatter plot. A histogram won't tell you about correlation, but you can plot the means of the two variables on the scatter plot. – Nick Cox May 07 '15 at 13:30

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