You take a sample of n = 70 from a population of adolescents, and conduct a correlation analysis to investigate the relationship between level of anxiety and time spent exercising. Both variables are measured continuously via self-report questionnaires. You find that r = -.45 and p

Question

You take a sample of n = 70 from a population of adolescents, and conduct a correlation analysis to investigate the relationship between level of anxiety and time spent exercising. Both variables are measured continuously via self-report questionnaires. You find that r = -.45 and p < .05. What can you conclude on the basis of your sample?

BlackTom AI · Accepted Answer

The question asks us to interpret a correlation result from a sample of n = 70, examining the relationship between anxiety (continuous) and time spent exercising (continuous).
Option analysis:
Option: 'There is sufficient evidence to doubt the null hypothesis.'
This statement aligns with standard inferential reasoning for a Pearson correlation test. Given r = -0.45 and p < .05, we have statistically significant evidence against the null hypothesis that the population correlation ρ equals zero. Because p is below the conventional alpha level (often 0.05), we reject H0 and conclude that there is evidence of a nonzero linear relationship between anxiety and time spent exercising in the population from which the sample was drawn.
To deepen the interpretation, note that the negative sign of r indicates an inverse relationship: as anxiety increases, time spent exercising tends to decrease, or conversely, more exercise is associated with lower anxiety, according to this sample.
Additionally, consider the magnitude: r = -0.45 is a moderate negative correlation. Squaring it gives r^2 ≈ 0.20, suggesting that about 20% of the variance in one variable is explained by the other in this sample. This informs about practical significance, not just statistical significance.
Important caveats:
- Statistical significance (p < .05) does not prove causation. We cannot conclude that changing anxiety causes changes in exercise time or vice versa based on this correlational analysis alone.
- The result is sample-dependent; replication in other samples would help assess generalizability.
- Self-report measures can introduce biases (e.g., social desirability, recall bias) that may affect the strength and direction of the observed association.
In sum, the result supports rejecting the null hypothesis of no linear association and indicates a moderate, negative relationship between anxiety and exercise time within this sample, with the usual cautions about causality and measurement.

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