Martin has found a correlation of r =.18 between the two variables of using prescription stimulants (e.g., Adderall) and frontal lobe activity. This correlation is more likely to be statistically significant if

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In evaluating why a correlation of r = .18 between two variables might become statistically significant, several factors come into play beyond the observed effect size.
Option: 'Martin used a larger number of subjects.' This suggestion aligns with statistical principles: increasing the sample size reduces the standard error of the correlation coefficient, which can make a small but true effect reach conventional significance thresholds even when the correlation remains modest. A larger N improves the study’s power to detect a real relationship, assuming the effect is present and not due to sampling error.
If we consider the role of sample size more generally, significance depends on the test statistic for correlation, which is influenced by both r and N. Specifically, for a given r, a larger N yields a larger t statistic (or a smaller p-value) when testing whether the population correlation is different from zero. Therefore, increasing the number of subjects can turn an r of .18 into a statistically significant result, provided the data meet assumptions (e.g., bivariate normality) and there is no major violations.
Other common factors that could affect significance are not listed here, since no alternative options are provided. In typical analyses, effect size (the magnitude of r), sample size (N), and variability in the data collectively determine significance. With a small sample, an r of .18 might fail to reach significance due to low power; with a larger sample, the same r could become significant, illustrating the power–sample size relationship.
In summary, among the standard routes to achieving statistical significance for a modest correlation, increasing the sample size is the most direct and reliable method, because it reduces uncertainty and increases the test’s ability to detect a real association, assuming all other conditions are appropriate.

PSC 041 001 SQ 2025 Week 6 Quiz

Martin has found a correlation of r =.18 between the two variables of using prescription stimulants (e.g., Adderall) and frontal lobe activity. This correlation is more likely to be statistically significant if

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