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I'm studying a dataset and observed a positive correlation between two variables, but when I plot them, it seems that they are heteroscedastics, what conclusions can I get from it ? (Can I really assume that the positive correlation is real ?)

Thanks, L.L.

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Your description is very vague. In the simplest case, suppose you have 10 observations $X_1, \dots, X_{10}$ and 10 observations $Y_1, \dots, Y_{10}$ and you want to find the correlation between them.

If the sample variances $S_x^2$ and $X_y^2$ are very different, that does not interfere with computing or interpreting a correlation. For example if the $X$-values are $X = (1,2,3,4,5,6,7,8,9,10)$ and the $Y$-values are $Y = (100,200,300,400,500,600,700,800,900,1000),$ then the variances are quite different, but the correlation is $r = 1,$ reflecting the obvious linear relationship between the $X$'s and the $Y$'s.

If you had something more complicated in mind, please explain it in more detail.

Addendum: The correlation $r$ has no units, and so is not influenced by the scale of either of the two variables. Changing units of $X$ from meters to cm would increase the numerical SD by 100, but would not change the correlation $r$ with another variable $Y$ (perhaps measured in kg).

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