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Chapter 28: Problem 8

If \(r=0.5\) and \(N=4\), would you conclude that a positive correlation exists between the two variables? Explain your answer. What if \(N=500\) ?

Short Answer

Expert verified
A given r value of 0.5 indicates a moderate positive correlation between the two variables. However, with a small sample size of 4, it might not be wise to draw firm conclusions about the correlation, as the data may not be representative. On the other hand, with a sample size of 500, the given r value of 0.5 stands for a moderate positive correlation with higher certainty.

Step by step solution

01

Analyze given information

First, look at the initial r and N values, which are 0.5 and 4, respectively. An r of 0.5 suggests a moderate positive correlation. However, with a sample size of only 4, it is risky to derive any definitive conclusions from this r value itself. This is because the smaller the sample size, the greater the chance of a spurious correlation because of a lack of sufficient data.
02

R Vs Sample size

Increase the sample size to N=500. The same r value of 0.5, but with such a large sample size, is more meaningful and can be said to represent a moderate positive correlation with a higher degree of certainty. This happens because with a larger sample size, outliers and random variance have a lesser impact on the r value, making it a more accurate representation of the true correlation between the two variables.

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