Question

Describe the range of values for the correlation coefficient. Discuss the difference between "r" and "p". In your own words, what does it mean to say "correlation does not imply causation?" write a full paragraph (5) sentences, min of 75 words, in APA format

Answer 1

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1.

The correlation coefficient takes a range between -1 and 1. A -1 means perfect negative correlation indicating a perfect relation between variables but in opposite direction. As correation tends to 0 , strenght of relation wean off. As it tends to 1, again, a perfect relation , this time positive, is indicated.

2.

r is essentially a sample correaltion, wheras p is the population correation. For further explanation in difference please read below to understand difference:

Population correlation coefficient (p) is a parameter that needs estimation. The Pearson’s correlation coefficient )r) is an estimator that is used to estimate the population correlation coefficient. Actually, it is the method of moment estimator of the population coefficient so it is consistent, i.e., as the sample size grows (n→∞), the sample correlation coefficient converges in probability to the population coefficient (r→ρ)

3.

By correlation doesn't mean causation it means that you cannot interpret which variable was driving the other variable. For example, if cities with higher expenditure have higher salaries is a perfect example. We don't know whether high expenditure is what triggers people to earn more, or its the other way around: Cities with higher salaries have higher purchasing power and hence high expenditure capacity. Hence, direction of relation can't be discerned in correlation.