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I did a repeated measure correlation (package: rmcorr) inculding two data points. But if I look also at the correlation separately for each point, I´m a little bit confused because the repeated measure correlation gave me a positive correlation and the separate correlations gave me at each point a negative correlation (see results below). Is this result only explainable through the violation of independence? Thank you for answering my question.

Kind regards,

Daniel Groß

Repeated measures correlation

r 0.2760491 degrees of freedom 43 p-value 0.06642702 95% confidence interval -0.0264911 0.5322632

T1 (cor.test) Pearson's product-moment correlation

t = -1.1941, df = 42, p-value = 0.2391 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: -0.4536775 0.1222541 sample estimates: cor -0.181203

T2 (cor.test) Pearson's product-moment correlation

t = -4.1108, df = 42, p-value = 0.0001791 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: -0.7182965 -0.2839074 sample estimates: cor -0.5356405

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    $\begingroup$ Note that for both the rm and t1 correlations that the confidence interval includes 0, so the evidence that these correlations are either positive or negative is weak. $\endgroup$ Jul 19 '17 at 9:31
  • $\begingroup$ It is perfectly possible but I am not sure what you mean by lack of independence. $\endgroup$
    – mdewey
    Jul 19 '17 at 10:49
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It's true that the confidence intervals include 0 for both the repeated measures correlation and for the T1 correlation, so in this case I probably wouldn't read too much into the change of directions.

In general, it is certainly possible to see very different results for the repeated measures correlation vs. separate, cross-sectional correlations. In one case, you're looking at a correlation within individuals; in the other, you're looking at correlations across individuals.

For example, consider the relationship between reaction time and accuracy for a given task. It may be the case that within individuals, performance on both dimensions improves with practice, which would lead to a negative repeated measures correlation (RT decreases as accuracy increases). Looking across individuals, however, perhaps some people sacrifice speed for very high accuracy, while others sacrifice accuracy for very fast speeds. If this is the case, you might see a positive cross-sectional correlation (RTs get longer as accuracy improves).

For more information, see http://journal.frontiersin.org/article/10.3389/fpsyg.2017.00456/full

and http://journal.frontiersin.org/article/10.3389/fpsyg.2013.00513/full

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i had a similar question and i found that the answer to this question helped X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it mean? Also try this: Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?

there are multiple links within that question that will lead you to similar but slightly different questions.

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