Final answer:
When a researcher establishes a true relationship through the correct statistical test, they are determining its b. significance, not causation. Significance indicates that the relationship in the sample is meaningful for the entire population, but it is important to note that correlation, measured by the correlation coefficient, does not prove causation.
Step-by-step explanation:
When a researcher determines a true relationship exists in the population by means of the correct statistical test, they establish its significance. This significance indicates that the evidence found in the sample is strong enough to suggest a meaningful relationship exists within the larger population. A common misconception, however, is that significance equals causation which is not the case. To demonstrate causation, experiments must be specifically designed to show that one variable directly affects another.
Testing the significance of the correlation coefficient involves assuming that there is a linear relationship in the population that models the sample data. The correlation coefficient, often denoted as r, describes the strength and direction of this relationship but does not provide evidence of causation. A common critical point within research is ensuring that the p-value is low enough (typically less than 0.05) to deem the findings significant and not just due to chance, with some experts raising concerns about rigid adherence to specific p-value thresholds.