Suppose a researcher reports a correlation of .83 based on a study, which has on

Question

Suppose a researcher reports a correlation of .83 based on a study, which has only two observations. What would you conclude?

a. t is not possible to observe such a correlation in such a small sample.

b. The correlation which is reported is most likely a Spearman rank correlation (estimate the degree of association between two quantitative variables– non-parametirc), given the small sample size implies a lack of certainty about the normality assumptions of the data.

c. It is possible to observe such a correlation, but it is unlikely that even such a high correlation is statistically significant.

d. Correlations of this magnitude could be observed for continuous, but not categorical data

Explanation / Answer

a) In this case observed value of t is 0 as in the numerator of the test statistic we have (n-2) and here n = 2. So it's possible to observe t. Also here it is not mentioned whether data is categorical or not and for categorical data also we can have this magnitude. So the correct choice is Option (c) It is possible to observe such a high correlation, but it is unlikely that even such a high correlation is statistically significant. (Ans).

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