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Question 710:



No answer provided yet.It is often the case that we want to know if one variable is associated with another variable. Another way to put it is, is one variable have a dependence on another variable?   When two variables are continuous, we can use the Pearson correlation to test for the relationship in the form of a correlation. The correlation ranges from -1 (perfect inverse relationship) to 1 (perfect positive relationship), with 0 meaning no relationship at all.

When we conduct a correlation, say between height and weight from a sample we can test the significance of the correlation using the t-distribution. The Null Hypothesis with a correlation is the correlation is not significantly different than 0: ρ = 0. The alternative hypothesis is that the correlation is significantly different than ρ 0 ( The Greek symbol Rho, ρ is used to denote the population correlation, whereas the English letter r denotes the sample correlation).

The Pearson correlation formula should be applied, as stated above when the data are continuous (can be subdivided into smaller meaningful units). When the data being correlated are naturally ranked (the rankings of cities for example) it is appropriate to use the Spearman Correlation. If the data are not ranked, they can be converted to ranks then used in the Spearman. In fact, the best way to apply the Spearman Correlation is to use the Pearson correlation formula on the ranked data.

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