RESEARCH STUDY 8.1: Dr. Guidry conducts a study examining the relationship between the number of friends one has and the experience of daily stress and life satisfaction. She randomly samples 1,500 elderly men and women in Nashville, Tennessee (the state capital), located in the southern United States. Below are her findings:

• Life satisfaction and experience of daily stress: r = –.57, 95% CI [–.77, –.37]

• Number of friends one has and experience of daily stress: r = .09, 95% CI [–.27, .45]

• Number of friends one has and life satisfaction: r = .36, 95% CI [.12, .60]

In determining whether the relationship between two of Dr. Guidry’s variables was statistically significant, which of the following must be considered?

Question

RESEARCH STUDY 8.1: Dr. Guidry conducts a study examining the relationship between the number of friends one has and the experience of daily stress and life satisfaction. She randomly samples 1,500 elderly men and women in Nashville, Tennessee (the state capital), located in the southern United States. Below are her findings:

• Life satisfaction and experience of daily stress: r = –.57, 95% CI [–.77, –.37]

• Number of friends one has and experience of daily stress: r = .09, 95% CI [–.27, .45]

• Number of friends one has and life satisfaction: r = .36, 95% CI [.12, .60]

In determining whether the relationship between two of Dr. Guidry’s variables was statistically significant, which of the following must be considered?

BlackTom AI · Accepted Answer

To determine statistical significance between two variables, we should examine factors that influence our ability to detect an effect beyond just the observed relationship.
Option 1: 'direction of the association and strength of the association' describes qualitative and quantitative aspects of the relationship, but significance specifically depends on whether the observed effect would likely occur if there were no true effect, which is governed by sample size and effect size, not merely direction or whether the association is strong.
Option 2: 'sample size and effect size' directly correspond to the core determinants of statistical significance. Larger samples increase the precision of the estimate (smaller standard errors), and the effect size measures how large the relationship is. Both together influence whether the observed association would be unlikely under the null hypothesis.
Option 3: 'sample size and number of variables analyzed' is not the standard pair for assessing significance. The number of variables analyzed affects model complexity and multiple comparisons concerns, but significance for a specific relationship is driven by its own sample size and effect size, not merely how many variables are included.
Option 4: 'the number of outliers and the direction of the association' can affect results and may distort significance, but they are not the primary determinants used to declare statistical significance in standard analyses. Outliers can influence estimates, yet the formal assessment hinges on sample size and effect size through test statistics and confidence intervals.
In this context, the most appropriate consideration for whether the relationship between two variables is statistically significant is the interplay of how large the sample is (n) and how big the observed effect is (effect size), which informs the test statistic, p-value, and confidence intervals.

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