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What i observe from the picture below that the data is bivariate normal distributed not exact and it has a negative association but i notice that there is a outlier which i marked with black circle. if i remove this i can get a better ellipse but on the other hand i don't want to remove it only for normality and i want to execute the correlation test with data. Any suggestion that this data is normal enough to execute correlation test?

enter image description here

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  1. Correlation does not assume normality.
  2. Even if it did, we rarely assume exact normality; such assumptions usually are concerned with approximate normality.
  3. Nevertheless, the primary concern is that your data is small. From your plots it does not follow that it is either normal, or nor normal.
  4. I cannot see why would you assume the marked point as an outlier. It is not more outlying then at least few other points. How do you define outlier? In most cases you should not remove outliers.
  5. Finally, does it really matter? Your data is small, removing the point or nor, in either of the cases your correlation coefficient would be small and insignificant. With such a small data it is hard to tell if there is any correlation at all.
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  • $\begingroup$ thanks for explaination :-) , i checked again my book and it says if we want to run a hypothese test for correlation , our data should be normal(bivariate). second, it says if i can sketch an ellipse it means my data is bivariate normal , so if i want to sketch an ellipse i see that point which is marked as black , creates problem. and yes i got co-efficient = -0.07.(Pearson) $\endgroup$ – Khan Saab Dec 20 '16 at 12:20

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